The late morning in Lindau was a non-stop marathon of medical researchers – first Harald zur Hausen talked about the links between infections and cancer, then Luc Montagnier gave an insight into his research that analyzes DNA under physical as well as biological aspects – venomous tongues may have linked that talk to homeopathy. At last Francoise Barré-Sinoussi talked about the discovery of HIV and how it was faciliated by global translational research.
Concerning the history of the relationship between infections and cancer, Martin has already written a great article a few weeks ago. Professor zur Hausens lecture let the audience awestruck by the Laureate's quick and clever demonstration of how much cancer can possibly be caused by infections. As such he mentioned of course the papilloma virus (HPV), for whichs role in cervical cancer he was awarded with half the Nobel Prize in 2008 (the other half went to Montagnier/Barré-Sinoussi). But there are several further viruses and bacterias that can be indirect causes to human cancers, as for example helicobacter pylori is linked to gastric cancer, HIV 1 and 2 increase several cancer risks due to weakening the entire immune system, tuberculosis increases the risk of developing a later lung cancer and borrelia burgdorferi is known to increase the risk of b-cell lymphomas. Zur Hausen explained how many of those viruses even introduct oncogenes into their host cells. In some cases even parasites can lead to cancers, as for example schistosoma is associated with bladder cancer – in Egypt the parasite is one of the main causes of this type cancer. Alltoghether zur Hausen estimated that 21 percent of all global cancer incidents are linked to infections – and many of them are preventable.
And zur Hausen also showed another interesting aspect that might lead to new ways to reduce cancer prevalences. In comparing risk factors for early-childhood leukemia, he pointed out that infections during our childhood in general lower the risk of developing such a cancer. However, if a high number of infections occur in the first year of life, the risk of leukemia is increased – supposedly the immune system can't mature efficiently. This example also explained how children with a higher socioeconomic status are under this aspect disadvantage.
To prevent such infection-induced cancers he suggested to develop further vaccines so that infections can be prevented. Toghether with Prof. Ethel-Michele de Villiers he currently does research on the TT-Virus – a virus that for itself "just" harms the liver but is linked to causing brain tumours as well as promoting autoimmune diseases such as asthmatic conditions and multiple sclerosis.
The past decades have been filled with discoveries of links between cancer and infections. Not only did zur Hausens lecture encourage young medical researchers to focus on vaccines – but it also showed that there are a lot more viruses, bacterias and parasites to explore.


text:
The Hogfish Epoch Begins
By Steve | April 9, 1995
This was the beginning of "Phase 3" of the Microship project. This was kind of insane, but an amazing opportunity presented itself and I couldn't resist. We luck into a great deal on a piece of multihull history, a folding 30-footer that predates the Corsair F-31 (though it's a bare hull). We zoom to Seattle to swap the Libra kayaks for a pair of rotomolded Storms, and the turret and manpack are becoming successful student projects. Digital Ocean, Digital Vision, and Yakima join the sponsor roster.
Microship Status Report #85
* News Flash! * We Have A Boat! *
The physical shape of the project has just been defined, and we no longer have to consider the grim prospect of boatbuilding! I just wrote a modest check as payment in full for a rather unusual trimaran…
The boat, affectionately and informally known as Hogfish by its former owner, was built about a decade ago by John Walton (son of Sam Walton and long-time president of Corsair Marine). It was essentially the prototype of the F/31 trimaran, and incorporates an approximate clone of Ian Farrier's four-bar folding system. The length is about 30 feet, deployed beam is 22 feet, and empty weight is 3,000 pounds. Construction is S-Glass epoxy over foam core, and the crossbeams are carbon-fiber box sections. She comes equipped with kick-up rudder, tiller, centerboard, bow and stern pulpits, rusty trailer, mainsheet traveler, and a 40-foot aluminum mast… but no deck rigging and virtually no interior. We have our work cut out for us, but this is a HUGE step forward!
The nice thing about this is that it eliminates the massive time commitment of trying to build, yet is vastly cheaper than buying a ready-to-sail trimaran. In other words, we scored — the critical substrate is already done, and we don't have to hack finished work to support the custom additions that will turn this into the Microship… or LEVIATHAN, which is again a tempting name now that we've reached yacht-scale.
A netfriend from Canada, Paul Picot, just arrived today for a visit, and we're taking off for Marina del Rey tomorrow to trailer the ship to San Diego — initially to be stored in a local storage yard until we establish a new lab. You'll be hearing a lot more about this in the months ahead.
For now, since we're in catch-up mode, a quick overview description will have to suffice. The boat has an aft cabin — a huge plus, since it provides a dedicated space for the lab/office/computer/comm center. Under the spacious center cockpit is a small engine room, and forward is the main cabin. It's a bit odd as cabins go — a huge centerboard trunk eats space, and all the tankage is glassed in around its base. Forward of the mast-support arch is a forepeak where we'll probably put the head, and the bed will mode-change to form a dinette that coexists with the galley. Bear in mind that this is a folding tri, and there is considerable hull flare that yields both a fine waterline shape and a cramped interior.
Outside, of course, she's huge. There's about 15 feet between the crossbeams, so much that I'm worried about the stiffness of the folding solar array unless we find a new way to do it (I'm even considering tiling the deck and crossbeams, but I worry about the loss of non-skid surface). The amas have access hatches, and will probably host the kayaks (delightful new Current Designs "Storms" — more on those in a moment). Originally, the boat was built with an innovative freestanding wing mast, but that's an invitation to structural disaster on a boat with many tons of positive righting moment… so we're using a conventional stayed rig that can be stepped on-water using one of the winches. There's a convenient anchor locker in the deck, as well as under-seat stowage in the cockpit.
I've discussed this boat with Ian Farrier and John Marples, both well-known multihull designers, and the only cautionary note has concerned the excessive dihedral — yielding a tendency to rock between the amas when at anchor. We don't know the PPI (pounds per inch immersion) spec yet, but I suspect that the problem will be considerably eased with our full electronics and touring load — it's only been tested empty.
Anyway, more as this develops, but the good news is that the quest for a substrate is at last over. Here she parked next to the Fulmar:
Seattle Tour Report
Since my last update, Faun and I have done another one of those 3,000-mile marathon drives (bringing our total in this 9-month relationship to roughly 14,000… over 50 miles a day). This time, it began with a 4-day filming with the French TF-1 television network — a half-hour documentary will air in Europe around the end of this month. We did get in a good Microship interview and some lab footage, but the star, as usual, was the bike — including a brutal 30-degree rain/snow ride in Joshua Tree National Monument and some amusing human encounters in Palm Springs and Lake Elsinore.
Once that was over, Faun and I zoomed north in the Mothership with the Libra double kayaks nestled in their lovely new Yakima racks, dropped the bike trailer (the 20-foot Wells Cargo) at Alan Selfridge's house in the Santa Cruz mountains, and continued north to Ferndale, Washington — just south of Canada. Here, we swapped the big boats for the new rotomolded Storm singles… absolutely the sweetest plastic kayaks I've ever tried. We spent a few hours kayaking around the north side of Bainbridge Island, picked up the Fulmar trimaran from its storage spot in Port Orchard, and couch-circuited our way south… stopping to spend a day kayaking and sailing with Greg Jacobs on Black Butte Lake. From there we dropped in on Faun's mom to make a household-goods raid, recovered the bike from the mountains, did a speaking gig at IBM Santa Theresa Labs, hung out with Dave Berkstresser for an evening, then borrowed his Volvo to convoy back to San Diego with both trailers… stopping enroute in Marina del Rey to buy a 30-foot trimaran.
And it's good to be back to the land of powerful espresso and eager students!
Student Projects, Old & New
Yes, the student projects continue to be a big part of all this. First, you might enjoy the following brief vignette, saved from an email exchange with the turret team a few weeks ago:
Steve Roberts: "What's the startup procedure for the video turret? We managed to load the board and run INIT from HyperTalk, which reset the turret position, but all other commands crashed… Some trick phrase I need to type to launch the multitasker? XYZZY?"
Nathan Parker: "But if we told you then we'd have no job security! Ok, here's the trick to get it to work: You have to wrap the power cord around your thumb three times so that it will pick up the RF transmissions from the secret dongle Alex has imbedded in his skull, and then put a drop of my blood between pins 24 and 25 of the HC11 where it will slowly vaporize while the A/D converter reads its conductivity and matches it against my daily blood-ion-count cycles. Or you could just download the correct file. I forget which one…"
Last quarter yielded astonishing results. The ECE-190B program was a smashing success, with a finished turret control system complete with HyperTalk front end, a full set of well-documented tools and interface hooks for the manpacks, extensive progress on enclosure pressure monitoring, and new communication tools for the Hub. Thanks to all who participated! Some were so good that I wish I could flunk them… just to have them around again next quarter…
I'm just beginning to meet the new crew, and so far it looks like we have two mechanical engineering teams of two people each, as well as about 6-8 electrical engineers. The mechanical projects are the folding solar array and ultralight sealed manpack packaging; the electricals will probably involve reverse engineering and control of Sony DAT and 8mm video systems, solar performance monitoring, and further refinement of the data collection and communication tools. Pieces are coming together… it's actually conceivable that within a few months some of this FORTH code will be ROMable and we can turn our attention more to the front-end HyperTalk and equipment packaging.
Sponsor and News Updates
Finally, I'd like to thank our new sponsors!
Digital Ocean has shipped three of their Groupers — elegant wireless AppleTalk nodes that will allow the two manpack Macs to coexist transparently on the same network with the two shipboard Macs. This is a critical component in our overall control and file-management scheme, and will go a long way toward achieving a seamless work environment that migrates from ship to kayak to land with minimal disruption.
Digital Vision is providing a SCSI frame grabber that will live in the main Mac and appear as a node on the video crossbar — allowing any video source to be inhaled and converted to a publishable image. Our first demo of the wireless manpack, in fact, will use both this and a pair of Groupers to allow an ambulatory PowerBook user to control the video turret from a tool within Netscape, aim the camera at some part of the lab, and see an interlaced GIF appear on the LCD.
Yakima quite amazed me a couple of weeks ago by swiftly solving our kayak-portaging needs — with only two days elapsing between initial phone contact and Fed-Ex shipment of a full system for carrying two boats on the diesel truck. The racks went together easily and logically, and passed the brutal test of 3,000 miles and lots of on-off cycles.
Finally, my father, Ed Roberts, has just made a donation to help support the rigging and outfitting of the new boat. While we are by no means fully "bankrolled," this significantly reduces the impact of the myriad hardware needs for which we are unlikely to obtain sponsorship. You know what BOAT stands for… "Break Out Another Thousand"…
In a future issue, I'll recap the full sponsor list with a brief summary of each — the foregoing are just the latest. Our deep thanks go to everyone who helps make this possible!
With that, we bring this issue to a close — tomorrow I meet with all the new student teams, then take off for Los Angeles with Paul (who has just finished assembling a light bar while I've been writing this, allowing us to legally haul that rustbucket unlit trailer down the freeway!).
Posted in Microship Status Reports
← Cat vs TriMicroship Status – Issue 86 →

redpajama_set_name: RedPajamaCommonCrawl


This year the focus for World Mental Health Day is 'Young People and Mental Health in a Changing World'. We often forget that young people are at a stage of their lives when significant change is a common occurrence to them.
Can this app help autistic people with anxiety?
Available on the Apple App Store today, Molehill Mountain is the first evidence-led smartphone app aiming to help autistic adults understand and self-manage their own anxiety. The app has been developed by UK research charity Autistica and researchers at King's College London with input from autistic people.
Arriving early to an ACAMH Conference set Dr Mark Lovell off on an ever expanding journey with the Association.


text:
Nominations open for 2016 WA Youth Awards
Nominations open for 2016 WA…
West Australians will again be honoured for their inspirational and positive contributions at the 2016 WA Youth Awards.
Nationals WA MP and candidate for the seat of Geraldton, Paul Brown said nominations for the prestigious awards were now open and encouraged all members of the community to nominate an outstanding young person.
"The WA Youth Awards recognises the achievements of young people aged 12 to 25 from across WA for their contributions to the community, as well as outstanding youth groups and organisations that server and support the State's young people," Mr Brown said.
"In Geraldton there are many young people who work tirelessly to facilitate change, assist others and make a positive difference in their communities.
"It is important that they are recognised for their contribution to their communities, particularly in regional WA."
Nominations are open for the following categories:
Minister for Youth's Outstanding Youth Worker Award
Commissioner for Children and Young People Participate Award
ECU Community Leadership Award
Organisational Achievement Award – Small Organisation
Organisational Achievement Award – Large Organisation
Positive Achievement Award
Cultural Endeavours Award
Active Participation Award
The WA Young Person of the Year will be selected from the pool of category winners and will have the opportunity to travel throughout WA to participate in youth-related events and activities.
The awards are presented by the Youth Affairs Council of WA in partnership with the State Government and supported by Lotterywest.
The 2016 winners will be announced at the WA Youth Awards ceremony on November 25.
For more information, visit http://www.yacwa.org.au/wayouthawards
Category: News Archive 6 September 2016
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Regional voices from Moore silenced by new laws
Mid West health in crisis: Love


text:
Moving at a Slower Pace
March 6, 2013 by Jessica Gottlieb
Volumes have been written on the need to rest and still more will be written because we don't listen well the first time. I'm sitting on this little patio with the sound of magpies and cicadas as my only distractions. In the three days I've been in Byron Bay I've logged six hours of surfing, a half hour of hang gliding, two hours of Pilates, three solid meals a day, and more beer than I'd consumed in all of 2012.
I have slowed down and relaxed.
The residents of Byron Bay are unflappable. Half the downtown shops are closed with "back in 20 minutes" signs on their doors. They are seldom back in 20 minutes and if they are it's only to leave again. That this disrupts no one's bottom line is remarkable.
At yesterday's surf expedition a Canadian got fake hurt. Yes, a Canadian was a boorish lout and all us Americans were both startled and a bit giddy. I wanted to make an announcement to the international group that the US didn't have a monopoly on too-loud-asshats, Toronto had sent one of their very own.
You see he fell off his surfboard close to shore and legitimately bonked his knee. After that he he started howling for help and only after two surf instructors helped him hobble to shore did he tell anyone that moved that its an old knee injury and that his kneecap was "dislocated" but he'd popped it back into place. He also wanted a refund for day two of surfing because of his injury, oh he also couldn't understand why he hadn't been made to sign a waiver.
I need to reiterate. NOT AN AMERICAN.
Oh, and the release forms weren't available because the xerox machine was broken. Clearly Australia operates differently than Los Angeles. Were we in my hometown the beach would've stayed closed until someone had a guarantee that they wouldn't be sued. Had it been LA the fake injured Canadian weasel would've retained an attorney on his way home from the beach.
I don't love the litigiousness of the states but I do love the fact that our businesses stay open during all of their business hours. I'm definitely feeling wistful for a city where everyone over the age of four wears their shoes.
There are no signs here that read: No Shoes, No Shirt, No Service. I think I'm ready for those signs. Even in Sydney there's a relaxed vibe that allows for shoelessness and a general lack of grooming.
I look like a homeless woman. I'm weak and susceptible and should not spend too much time in a relaxed environment like this.
I have two cars that need to be reviewed and I can't bring myself to make sentences from the bulletpoints. I've got a stack of books that I traveled with and I'm finding myself reading a children's book, a book written for 10-12 year old boys actually. I'm sitting in restaurants laughing at fart jokes, which isn't necessarily out of character for me.
I've been to Woolworth's to buy Vegemite for friends and after I pack I'll have my last dinner in Australia. The service will be spectacularly slow, because here in Byron Bay no one is in a rush. The food will be good because I'm breaking my only rule which is to eat at each restaurant only once. I've found one that's so delicious I must return.
Tonight instead of reading Chicken Stu and giggling over a beer I'll dig into The Cider House Rules and sip a local Sangiovese ever so slowly because tomorrow the pace quickens and the day after that it returns to the frenzy I've come to enjoy.
Categories Australia, Daily Blogging, Travel Tags Australia, Bryon Bay, Travel
Possibly Mistaken for a Prostitute in Australia
Unprepared for Disappointment (updated)
2 thoughts on "Moving at a Slower Pace"
Kristi Davis
I'm glad to hear you are enjoying yourself :)
The Rebel Chick Jenn
Damn, that sounds marvelous. My inner hippie is screaming, "take me there right now!" Though I could do without the Canadian. ;)


I had to make a few changes to /etc/default/grub to get Ubuntu 14.04 to boot with a working console. Initially, my monitor just went dark.
GRUB_HIDDEN_TIMEOUT: if you want to see the Grub menu, this must be commented out.
GRUB_CMDLINE_LINUX: allows passing parameters to the linux startup command. Newer kernels (>3.5? or so) reinitialize the graphics card. My AMD Radeon something-or-other didn't like this at all. nomodeset forces linux to use/keep BIOS graphics settings.
GRUB_GFXMODE: select resolution for Grub graphical starup. 1280×1024 works on my aging ViewSonic. This setting is for the Grub menu.
GRUB_GFXPAYLOAD_LINUX: specifying keep, causes Grub to keep using the previous resolution (from GRUB_GFXMODE) for the rest of the boot.
NB: after making any changes, remember to update-grub (or nothing will happen).
My ISP (ding, dong) is stupid, so I need to disable IPv6.
Raspberry Pi (and Cubieboard) SD disk images typically have two (or three) partitions: the first is Fat32 (50-100MB) and includes the boot files, while the second (>1GB) contains the main Linux image. With compression, the combined image can be reduced from several GB (of mostly empty space) to a couple hundred MB.
You can save a lot of space by compressing dd image files.
These examples use gzip but many other compression apps will work just as well.
MiniDLNA – Ports ssdp (1900/udp) and trivnet1 (8200/tcp) are proper of this service.
The other port (37167/udp) varies in every execution.
If you haven't already done it, you have to set up the EPEL repository.
Next install Nginx and spawn-fcgi, I assume you have already installed PHP and all the modules you need.
Now it's time for the spawn-fcgi configuration. The config should be at /etc/sysconfig/spawn-fcgi.
# You must set some working options before the "spawn-fcgi" service will work.
# If SOCKET points to a file, then this file is cleaned up by the init script.
# See spawn-fcgi(1) for all possible options.
It's very important that you remember the port, you'll have to set the same in the nginx configuration. You should also use the same username and group as nginx.
Now let's make sure that spawn-fcgi and nginx automatically start after a reboot.
Next up we have to fix a folder permission. The group of the session cookies folder, the address can be found in the php.ini (session.save_path = "/var/lib/php/session"). The folder group has to be changed from apache to whatever you use, e. g. nginx. You should check this after every php update.
As a last step, just add the following line to the /etc/nginx.conf and/or your custom domain configuration in /etc/nginx/conf.d/yourdomain.conf.
You should also make some additional changes in your configuration.
Or perhaps it should be: how to retrieve an lvm partition from an xvda partition within an lvm partition.
Quite some time ago, I built a CentOS Xen DomU using lvm within an xvda partition. And the whole VM was hosted in yet another lvm partition. While lvm is easy to manage and physical backup and restore is straightforward, accessing the contents of the embedded partition without the VM running is tricky. Luckily, device mapping in Linux is very powerful and can be used recursively (not quite like Haskell or OCaml, but impressive none the less).
This recipe can be applied multiple times to dig deeper into your embedded file systems.
Kpartx is amazing as it will scan all your lvm volumes and create device mapper entries, which are required for the lvm tools to do their thing.
If you have additional embedded LVM, run vgscan to discover these, and vgchange -ay as required. You may need to repeat the kpartx and pvscan too.
The folks at Citrix have more detail here, especially if you're running Xen.
After rebooting, IPv6 will be disabled.


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UPDATE: It remains unclear exactly how sick Natasha Richardson is after yesterday's skiing accident, but it is believed that she has now been moved out of Canada.
E! News quotes a spokesperson from the hospital where she was being treated as saying, "I was informed by the family's rep…she has left Canada and the family should give [out] more information by tomorrow."
A family friend also told E! that the star is being flown back "home," which is believed to be New York City.
Details are starting to emerge about the ski accident that left Natasha Richardson with "critical" brain injuries.
Apparently her fall was pretty minor — and it was only an hour or so later in the day that she realized something was badly wrong.
Liam Neeson's wife was taking a private ski lesson at about 3 p.m. on March 16 on a beginners' slope at Quebec's Mont Tremblant resort.
Bloomberg is reporting that she stumbled and fell into soft, wet snow near the bottom of the slope.
The British actress's instructor called ski patrol, according to Entertainment Tonight, but at that point she had no apparent injuries.
In fact, TMZ reports that Natasha was smiling and joking with the patrol guys.
Apparently she refused to see a doctor and said she felt fine.
A source at the hotel has confirmed to ET that the instructor accompanied Natasha to her hotel room, and later on (TMZ says about one hour after the fall) she said she "wasn't feeling well and began complaining of headaches."
It was only then that she agreed to call an ambulance and the hotel dialed 911.
She had been conscious the whole time between the fall and leaving the hotel.
First she was taken to a clinic near the resort, but later transferred to Hopital du Sacré-Coeur in Montreal, according to Bloomberg.
CBC Newsworld television reports that her husband — who had been shooting a movie in Toronto — is now by her side.
Reports say she was with their sons Micheal Richard Antonio, 13, and Daniel Jack, 12, are also with her.
For more on the drama, tune in to ET on Tuesday, March 17.
Want to stay on top of Natasha Richardson news? Sign up for OK INSIDER!


text:
Q: How to unlock protected vbaproject in a excel file from C#? Could somebody tel me how to unlock the vba project of my protected excel file?
I tried with below C# code:
Exc.wbook = (Excel._Workbook)Exc.Workbooks.Open(FilePath, 0, false, 5, "", "", false, Excel.XlPlatform.xlWindows, "", true, false, 0, true);
Exc.VBE.ActiveVBProject = Exc.wbook.VBProject;
Exc.Visible = true;
SendKeys.SendWait("%{F11}^r{TAB}~" + sPrd + "~~%{F11}");

This didn't unlock the vbaproject.
I tried with this C# code too....didn't work.
Exc.wbook = (Excel._Workbook)Exc.Workbooks.Open(FilePath, 0, false, 5, "", "", false, Excel.XlPlatform.xlWindows, "", true, false, 0, true);
Exc.VBE.ActiveVBProject = Exc.wbook.VBProject;
Exc.Visible = true;
Exc.Unprotect(sPrd );

I have put fake code to follow my comp rules.
Please look into it and tel me what`s wrong with my code.

A: Unfortunately, VBA does not expose the VBProject passwords in its object model. Consequently, the only way to achieve what you want is via a workaround.
The usual approach is to use SendKeys to simulate the keystrokes that would be used to enter the password for the project. You should be aware, however, that this approach is NOT particularly reliable and I certainly wouldn't want to risk its use in a product that I was distributing or selling, or putting into production anywhere that money or reputation could be affected!
Here is an example of code that I found on Ozgrid Forums (originally written by Bill Manville):
VB:
'need reference To VBA Extensibility
'need To make sure that the target project Is the active project
Sub test()
    UnprotectVBProject Workbooks("ABook.xls"), "password"
End Sub

Sub UnprotectVBProject(WB As Workbook, ByVal Password As String)
'
' Bill Manville, 29-Jan-2000
'
Dim VBP As VBProject, oWin As VBIDE.Window
Dim wbActive As Workbook
Dim i As Integer

Set VBP = WB.VBProject
Set wbActive = ActiveWorkbook

If VBP.Protection <> vbext_pp_locked Then Exit Sub

Application.ScreenUpdating = False

' Close any code windows To ensure we hit the right project
For Each oWin In VBP.VBE.Windows
    If InStr(oWin.Caption, "(") > 0 Then oWin.Close
Next oWin

WB.Activate
' now use lovely SendKeys To unprotect
Application.OnKey "%{F11}"
SendKeys "%{F11}%TE" & Password & "~~%{F11}", True

If VBP.Protection = vbext_pp_locked Then
    ' failed - maybe wrong password
    SendKeys "%{F11}%TE", True
End If

' leave no evidence of the password
Password = ""
' go back To the previously active workbook
wbActive.Activate

End Sub

''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
Sub ProtectVBProject(WB As Workbook, ByVal Password As String)

Dim VBP As VBProject, oWin As VBIDE.Window
Dim wbActive As Workbook
Dim i As Integer

Set VBP = WB.VBProject
Set wbActive = ActiveWorkbook

' Close any code windows To ensure we hit the right project
For Each oWin In VBP.VBE.Windows
    If InStr(oWin.Caption, "(") > 0 Then oWin.Close
Next oWin

WB.Activate
' now use lovely SendKeys To unprotect
    Application.OnKey "%{F11}"
    SendKeys "+{TAB}{RIGHT}%V{+}{TAB}" & Password & "{TAB}" & Password & "~"
    Application.VBE.CommandBars(1).FindControl(Id:=2578, recursive:=True).Execute
    WB.Save
End Sub

Use it at your own risk!
HTH

redpajama_set_name: RedPajamaStackExchange


text:
\section{Introduction}
\label{sec:intro}
While it is rare to find a martingale model for which the transition density is available in closed form
(the Black-Scholes model being a notable exception),
there is a veritable zoo of models for which the characteristic function is available explicitly
(exponential L\'evy models  and affine models~\cite{duffiepansingleton} for instance).
The existence of an analytically tractable characteristic function allows for (vanilla) option prices to be computed
quickly using (generalised) Fourier transforms~\cite{lewis2001simple,lipton2002}.
Every model contains unobservable parameters, which are usually calibrated to market data.
This calibration procedure is typically performed using implied volatilities rather than option prices,
the former being dimensionless.
For a given model, one therefore has to compute (by finite difference, Monte Carlo or numerical integration)
option prices first and then the corresponding implied volatilities by some root-finding algorithm.
Both steps require sophisticated numerical tools and occasionally somewhat of an artistic touch.
These are computationally expensive and render calibration a long and intensive task.

Over the past decade, many authors have focused on obtaining closed-form approximations
for both option prices and implied volatilities, partly in order to speed up this calibration process.
Perturbation methods have been used by Lorig and co-authors~\cite{lpp-2}
(see also~\cite{fouque2003proof,fpss,Fuka2011,sabr})
to obtain such approximations for diffusion-type models.
In extreme regions---where numerical schemes become less efficient---asymptotic expansions
of densities and of implied volatilities have been obtained in~\cite{BBF2004,DFJV2013,HGLOW2012,LabordereBook,Tankov2010}
in the small-maturity case (both for diffusions and jump models) and in~\cite{JKRM2013} for the large-time behaviour
of affine stochastic volatility models.
Roger Lee~\cite{Lee2004} pioneered the study of the tails of implied volatility,
and more recent (model-dependent and model-free) results have appeared
in~\cite{BF2009,DFJV2013,FGGS2011,GuliStein2010}.

The goal of this paper is to derive an approximation for the implied volatility in any model whose characteristic function is available in closed form.
This approximation contains no special function and does not require any numerical integration.
It can therefore be used efficiently to accelerate the aforementioned calibration issue.
The methodology follows and extends the previous works~\cite{lorig-jacquier-1,lorigCEV} and is related to some extent
to the works by Takahashi and Toda~\cite{Toda2013}.
Indeed, by writing the characteristic function as a perturbation around the Black-Scholes characteristic function,
our expansion has the form of a Black-Scholes price perturbed by some additional quantity (which we shall make precise later), which can then be turned into an expansion for the corresponding implied volatility.

The rest of the paper proceeds as follows:
in Section~\ref{sec:pricing}, we provide a brief review of the characteristic function approach to option pricing
and introduce some notations needed later in the paper.
Section~\ref{sec:iv} contains the main results, namely a series expansion for the implied volatility.
More precisely, we show (Section~\ref{sec:u.expand}) that, whenever the characteristic function is available in closed-form, the European call price can be written as a regular perturbation around the Black-Scholes price.
A similar result then holds for the implied volatility,
as detailed in Sections~\ref{sec:sig.expand} and~\ref{sec:simple}.
In Section~\ref{sec:examples} we numerically test our results and provide practical details about this implementation.

\section{Notations and preliminary results}
\label{sec:pricing}
We consider here a given probability space $\left(\Omega,(\mathcal{F}_t)_{t\geq 0},\mathbb{P}\right)$;
all the processes studied will be $\mathcal{F}$-adapted.
In particular $S=\E^X$ will denote the stock price process, namely a $\mathcal{F}$-adapted martingale under the risk-neutral probability measure $\mathbb{P}$.
The dynamics of $X$ may depend on some auxiliary process $Y\in\Rb^m$ ($m\geq 1$),
say some stochastic volatility.
The starting point $(X_0,Y_0)=(x,y)$ is assumed to be non-random.
For simplicity and notational convenience, we will assume that $m=1$ and that the risk-free interest rate is zero.

\subsection{Pricing via Fourier transforms}
Let $h$ be the payoff function of a European call option on $S=\E^{X}$ with strike $\E^{\zeta}$:
$h(z) \equiv (\E^z - \E^\zeta)^+$, and denote $\hh$ its (generalised) Fourier transform
$$
\hh(\lam) := \int_\Rb \E^{- \ii \lam z} h(z) \dd z
 = \frac{-\E^{\zeta-\ii \zeta \lam}}{ \ii \lam + \lam^2 } ,
\qquad\text{for }
\Im(\lam) < - 1.
$$
The results obtained below for option prices remain valid for Put options with payoff $h(z) \equiv (\E^\zeta - \E^z)^+$,
but we shall chiefly consider European call option prices unless otherwise stated.
For any $t\geq 0$, define the moment explosions
$p^*(t) := \sup\{ p\geq 0 : \Eb_{x} \left(\E^{p X_t}\right) < \infty \}$
and
$q^*(t) := \sup\{ q\geq 0 : \Eb_{x} \left(\E^{-q X_t}\right) < \infty \}$.
Since~$S$ is a martingale, we have $p^*(t)\geq 1$ and $q^*(t)\geq 0$.
We shall further make the stronger assumption:
\begin{assumption}\label{ass:Explosions}
For any $t\geq 0$, $p^*(t)>1$ and $q^*(t)>0$.
\end{assumption}
This assumption holds for most models in practice,
and allows us to write  the value of a call option as
\begin{align}\label{eq:InvFourierPrice}
u(t,x) := \Eb_{x} \, h(X_t)
 = \frac{1}{2\pi} \int_\Rb \hh(\lam) \Eb_{x} \left(\E^{\ii \lam X_t}\right)\dd \lam_r,
\qquad \text{with }\Im(\lambda)\in (-p^*(t), -1), \text{ for all }t\geq 0,
\end{align}
where we write $\lam = \lam_r + \ii \lam_i $ ($\lambda_r, \lambda_i \in\mathbb{R}$) for a complex number.
Of course the function~$u$ also depends on~$y$, the starting point of~$Y$, but we shall omit it in the notations for clarity.
In this paper, we consider models for which the characteristic function
$\Cb\ni\lambda\mapsto \Eb_{x} \left(\E^{\ii \lam X_t}\right)$  admits the representation
\begin{align}\label{eq:char.form}
\log \Eb_{x}\left(\E^{\ii \lam X_t}\right) = \ii \lam x + \phi(t,\lam),
\end{align}
for some analytic function $\phi:\Rb_+\times \Cb \to \Cb$, satisfying
$\phi(t,-\ii)=0$ for all $t\geq 0$ (martingale property).
From~\eqref{eq:InvFourierPrice}, this implies that the price of a call option may be written as (see also~\cite{lewis2001simple} or~\cite{lipton2002})
\begin{align}
u(t,x) &= \frac{1}{2\pi} \int_\Rb \hh(\lam) \E^{ \ii \lam x + \phi(t,\lam)}\dd \lam_r.
\end{align}
Several well-known models fit within this class
\begin{align}
\text{L\'evy models}:&&
\phi(t,\lam)
	&=	t \( \ii \mu\lam - \tfrac{1}{2}a^2 \lam^2 + \int_\Rb \nu(dz) ( \E^{\ii \lam z} - 1 - \ii \lam z ) \) , \\
\text{Additive models}:&&
\phi(t,\lam)
	&=	\ii \mu(t)\lam - \tfrac{1}{2}a^2(t) \lam^2 + \int_\Rb \nu(t,dz) ( \E^{\ii \lam z} - 1 - \ii \lam z )  , \\
\text{Affine models}:&&
\phi(t,\lam)
	&=	C(t,\lam) + y D(t,\lam), \label{eq:affine}
\end{align}
where $(\mu,a^2,\nu)$ is a L\'evy triplet, $(\mu(t),a^2(t),\nu(t))$ are the spot characteristics of an additive process, the function $C$ is fully characterised by $\tfrac{\dd}{\dd t} C = D$ and the function $D$ satisfies a Riccati equation.
For precise details on L\'evy and affine processes,
we refer the interested reader to the monograph by Sato~\cite{sato1999levy} and the groundbreaking paper by Duffie, Filipovi\'c and Schachermayer~\cite{DuffFilipScha}.

\subsection{Black-Scholes and implied volatility}
\label{subsec:imp.vol}
Option prices are commonly quoted in units of implied volatility (rather than in units of currency)
first because the latter is dimensionless, and second, because the shape and behaviour of the implied volatility
provide more information than option prices.
However, the implied volatility is scarcely available in closed form and has to be computed numerically via inversion of the Black-Scholes formula.
We derive here a closed-form expansion for the implied volatility for models whose characteristic function is of the form~\eqref{eq:char.form}.
We begin our analysis by defining the Black-Scholes price and the implied volatility.
\begin{definition}\label{def:BS}
The \emph{Black-Scholes price} $u^{\BS}:\Rb^+\times\Rb\times\Rb^+ \to \Rb^+$ is given by
\begin{align}
u^{\BS}(t,x,\sig_0) := \frac{1}{2\pi} \int_\Rb \E^{t \phi_0(\lam;\sig_0)} \hh(\lam) \E^{\ii \lam x}\dd \lam_r,
\qquad\text{where}\qquad
\phi_0(\lam;\sig_0) := -\frac{1}{2}\sig_0^2\left(\lam^2 + \ii \lam\right).
\label{eq:uBS}
\end{align}
\end{definition}
\begin{remark}
Note that $\phi_0(\cdot;\sig_0)$ is the L\'evy exponent of a Brownian motion with volatility $\sig_0$ and drift $-\frac{1}{2}\sig_0^2$,
so that~\eqref{eq:uBS} is the Fourier representation of the usual Black-Scholes price, more typically written as
\begin{align}
u^{\BS}(t,x,\sig_0)
	&= \E^x \Nc(d_+(x)) - \E^k \Nc(d_-(x)), &
d_\pm(x)
	&:=	\frac{1}{\sig_0 \sqrt{t}} \( x - \zeta \pm \frac{1}{2}\sig_0^2 t \), \label{eq:uBS.2}
\end{align}
where $\Nc$ is the cumulative distribution function of a standard normal random variable.
\end{remark}
\begin{definition}\label{def:imp.vol.def}
For any maturity $t$, starting point $x$ and (log) strike $\zeta$,
the implied volatility is defined as the unique non negative real solution $\sig$ to the equation
$u^{\BS}(t,x,\sig) = u$,
where $u$ is the (observed or computed) call option price with the same maturity and log strike.
\end{definition}
\begin{remark}
For any $t>0$, the existence and uniqueness of the implied volatility can be deduced using the general arbitrage bounds for call prices
and the monotonicity of $u^{\BS}$ (see~\cite[Section 2.1, Remark (i)]{fpss}).
\end{remark}
For any $t\geq 0$, $x\in\Rb$, the function $u^{\BS}(t,x,\cdot)$ is analytic on $(0,\infty)$, and hence
for any~$\sig_0>0$ and~$\delta\in\Rb$ such that~$\sig_0 + \del>0$,
the function $u^{\BS}(t, x, \cdot)$ at the point~$\sig_0 + \del$ is given by its Taylor series:
\begin{align}\label{rmk:analytic}
u^{\BS}(t,x,\sig_0 + \del) = \sum_{n=0}^\infty \frac{\del^n}{n!} \d_\sig^n u^{\BS}(t,x,\sig_0),
\end{align}
where
$
\d_\sig^n u^{\BS}(t,x,\sig_0)
= \frac{1}{2\pi} \int_\Rb \left.\(\d_\sig^n \E^{t \phi_0(\lam;\sig)} \)\right|_{\sigma=\sigma_0}
 \hh(\lam) \E^{\ii \lam x}\dd \lam_r.
$
The interchange of the derivative and integral operators is justified by Fubini's theorem.
If one observes the option price~$u$,
then the following proposition provides a way to compute the corresponding implied volatility.
\begin{proposition}
\label{thm:lagrange}
For any $t> 0$, $x\in\Rb$, let $u:(0,\infty)\to(0,\infty)$ be defined (as a function of $\sig$) by $u^{\BS}(t, x, \sig)=u$,
and let $\sigma_0$ be some strictly positive real number.
Then the following expansion holds:
\begin{align}
\sig
	&= \sig_0 + \sum_{n=1}^\infty \frac{b_n}{n!} (u - u^{\BS}(t, x, \sig_0))^n, &
b_n
	&:= \lim\limits_{\sig \to \sig_0} \d_\sig^{n-1} \( \frac{ \sig - \sig_0}{u^{\BS}(t,x,\sig)-u^{\BS}(t,x,\sig_0)} \)^n .
			\label{eq:inverse}
\end{align}
\end{proposition}
\begin{proof}
Since the function $u^{\BS}(t,x,\cdot)$ is strictly increasing on~$(0,\infty)$,
analytic in a neighbourhood of~$\sig_0$
and $\d_\sig u^{\BS}(\cdot,\cdot,\sig_0) \neq 0$,
the proposition follows from Lagrange Inversion Theorem~\cite[Equation 3.6.6]{as}.
\end{proof}
Proposition~\ref{thm:lagrange} shows that, for every fixed $t> 0$, $x\in\Rb$, $\sig_0>0$,
there exists some radius of convergence $R>0$ (depending on~$(t,x,\zeta)$) such that
$|u - u^{\BS}(t,x,\sig_0)|<R$
implies that $\sig$, defined implicitly through the equation $u^{\BS}(t,x,\sig)=u$, is fully characterised by~\eqref{eq:inverse}.
This result however seems to be only of theoretical interest.
Once the option value~$u$ is known, computing the implied volatility inverting the Black-Scholes formula is a simple numerical exercise.
Moreover, computing the implied volatility using~\eqref{eq:inverse} is not numerically efficient since
the option price~$u$ requires the computation of a (possibly highly oscillatory) Fourier integral.
One may wish to use~\eqref{eq:inverse} to deduce some properties of the implied volatility,
but then the proposition would benefit from precise error bounds when truncating the infinite sum.
The rest of the paper focuses on developing a similar expansion,
without the need for the (potentially computer-intensive) implementation of the value function $u$.

\section{Implied volatility expansions}
\label{sec:iv}

\subsection{Call prices as perturbations around Black-Scholes}
\label{sec:u.expand}
For any $\eps\in (0,1]$ and $\sigma_0>0$ define the function $\phi^\eps(\cdot,\cdot;\sigma_0):\Rb_+\times\Cb\to\Cb$ by
$$
\phi^\eps(t,\lam;\sig_0) :=t \, \phi_0(\lam;\sig_0) + \eps \, \phi_1(t,\lam;\sig_0) ,
$$
where $\ee^{t\phi_0}$
is the Black-Scholes characteristic function from Definition~\ref{def:BS} and
\begin{equation}\label{eq:phi1}
\phi_1(t,\lam;\sig_0) := \phi(t,\lam) - t \phi_0(\lam;\sig_0).
\end{equation}
Recall from Bochner theorem~\cite[Theorem 4.2.2]{Lukacs} that a complex-valued function~$f$
is a characteristic function if and only if it is non-negative definite and $f(0)=1$.
Therefore~$\E^{\phi^\eps}$ is a well-defined characteristic function for any $t\geq 0$, and
we can associate to it a (unique up to indistinguishability) stochastic process $(X_t^{\eps,\sigma_0})_{t\geq 0}$,
starting at $X_0^{\eps,\sigma_0}=x$, which is a true martingale.
The price $u^\eps$ of a call option written on~$X^{\eps,\sigma_0}$ thus reads
\begin{align}\label{eq:u.eps}
u^\eps(t,x,\sig_0) :=	\frac{1}{2\pi} \int_\Rb \dd \lam_r \, \E^{\phi^\eps(t,\lam;\sig_0)} \hh(\lam) \E^{\ii \lam x}.
\end{align}
Let $\sig^\eps$ denote the implied volatility corresponding to the option price~$u^\eps(t,x,\sig_0)$.
Since $\phi^\eps |_{\eps=1} = \phi$ and $u^\eps |_{\eps=1} = u$,
the implied volatility corresponding to the option price~$u$ is given by $\sig = \sig^\eps |_{\eps=1}$.
We now seek an expression for $\sig^\eps$.
The first step is to show that $u^\eps$ can be written as a power series in $\eps$,
whose first term corresponds to the Black-Scholes call price with volatility $\sig_0$.
To this end, we first expand $\E^{\phi^\eps(t,\lam;\sig_0)}$ as
$$
\exp\left(\phi^\eps(t,\lam;\sig_0)\right)
 = \E^{t \phi_0(\lam;\sig_0)} \sum_{n=0}^\infty \frac{1}{n!} \eps^n \phi_1^n(t,\lam;\sig_0),
$$
and deduce a series representation for $u^\eps$ in~\eqref{eq:u.eps}:
\begin{align}\label{eq:u.eps.expand}
u^\eps(t,x,\sig_0) = \sum_{n=0}^\infty \eps^n u_n(t,x,\sig_0) ,
\qquad\text{with}\qquad
u_n(t,x,\sig_0) := \frac{1}{n!} \frac{1}{2 \pi}
\int_\Rb \dd \lam_r \E^{t \phi_0(\lam;\sig_0)}  \phi_1^n(t,\lam;\sig_0) \hh(\lam) \E^{ \ii \lam x},
\end{align}
for any $n\geq 0$, where the application of Fubini's theorem is justified since
$\int_\Rb  \left|\E^{t \phi^\eps(\lam)} \hh(\lam) \E^{\ii \lam x}\right|\dd \lam_r$ is finite.
Note in particular that $u_0 \equiv u^{\BS}$.

\subsection{Series expansion for implied volatility}
\label{sec:sig.expand}
From \eqref{eq:u.eps.expand}, it is clear that $u^\eps$ is an analytic function of $\eps$ (we have explicitly provided its power series representation).
Since the composition of two analytic functions is also analytic~\cite[Section 24, p. 74]{brown1996complex},
the expansion~\eqref{rmk:analytic} implies that $\sig^\eps = [u^{\BS}]^{-1}(u^\eps)$ is an analytic function and therefore has a power series expansion in $\eps$, which we write
$\sig^\eps := \sig_0 + \del^\eps$, where
$\del^\eps = \sum_{k\geq 1}\eps^k \sig_k$.
The following proposition provides an expansion formula for the coefficients~$\sigma_k$.
\begin{proposition}
Fix $\sigma_0>0$, $k\geq 1$, and let $R$ denote the radius of convergence of the expansion~\eqref{eq:inverse}.
If $\left|u(t,x)-u^{\BS}(t,x,\sig_0)\right|<R$ for all $(t,x)\in\mathbb{R}_+\times \mathbb{R}$, then the following expansion holds:
\begin{align}\label{eq:sig.k}
\sig_k  = \frac{1}{\d_\sig u^{\BS}(t,x,\sig_0)}
\( u_k - \sum_{n=2}^\infty \frac{1}{n!}\( \sum_{j_1+\cdots+j_n=k} \prod_{i=1}^n \sig_{j_i} \)  \d_\sig^n u^{\BS}(t,x,\sig_0)\).
\end{align}
\end{proposition}
The right-hand side only involves $\sig_j$ for $j \leq k-1$, so that the sequence can be determined recursively.
\begin{proof}
Let us fix some $t\geq 0$ and $x\in\Rb$.
Taylor expanding $u^{\BS}(t,x,\sig^\eps)$ around the point $\sig_0$ we obtain
\begin{align*}
u^{\BS}(t,x,\sig^\eps)
	&=	u^{\BS}(t,x,\sig_0 + \del^\eps)
	=	\sum_{n=0}^\infty \frac{1}{n!}(\del^\eps \d_\sig )^n u^{\BS}(t,x,\sig_0) \\
	&=	u^{\BS}(t,x,\sig_0) +	\sum_{n=1}^\infty \frac{1}{n!} \( \sum_{k=1}^\infty \eps^k \sig_k \)^n \d_\sig^n u^{\BS}(t,x,\sig_0) \\
	&=	u^{\BS}(t,x,\sig_0) + \sum_{n=1}^\infty \frac{1}{n!}
		\[ \sum_{k=1}^\infty \( \sum_{j_1+\cdots+j_n=k} \prod_{i=1}^n \sig_{j_i} \) \eps^k \] \d_\sig^n u^{\BS}(t,x,\sig_0) \\
	&=	u^{\BS}(t,x,\sig_0) +	\sum_{k=1}^\infty \eps^k
		\[ \sum_{n=1}^\infty \frac{1}{n!} \( \sum_{j_1+\cdots+j_n=k} \prod_{i=1}^n \sig_{j_i} \) \d_\sig^n \] u^{\BS}(t,x,\sig_0) \\
	&=	u^{\BS}(t,x,\sig_0) +	\sum_{k=1}^\infty \eps^k
		\[ \sig_k \d_\sig + \sum_{n=2}^\infty \frac{1}{n!}\( \sum_{j_1+\cdots+j_n=k} \prod_{i=1}^n \sig_{j_i} \)  \d_\sig^n \] u^{\BS}(t,x,\sig_0).
\end{align*}
In order to recover the implied volatility from Definition~\ref{def:imp.vol.def},
we need to equate the Black-Scholes call price above and
the option value~$u^\eps$ in~\eqref{eq:u.eps.expand}, and collect terms of identical powers of $\eps$:
\begin{align}
\Oc(1):&&
u_0(t,x,\sig_0) &= u^{\BS}(t,x,\sig_0) , \\
\Oc(\eps^k):&&
u_k(t,x,\sig_0)
	&=		\sig_k \d_\sig u^{\BS}(t,x,\sig_0)
				+ \sum_{n=2}^\infty \frac{1}{n!}\( \sum_{j_1+\cdots+j_n=k} \prod_{i=1}^n \sig_{j_i} \)  \d_\sig^n	u^{\BS}(t,x,\sig_0) , &
k & \geq 1 .
\end{align}
Solving the above equations for the sequence $(\sig_k)_{k\geq 0}$, we find
$\sigma_0=\sigma_0$ at the zeroth order and for any $k\geq 1$, the $\Oc(\eps^k)$ order is given by~\eqref{eq:sig.k}.
\end{proof}
\begin{remark}
Explicitly, up to $\Oc(\eps^3)$ we have
\begin{align}
\begin{aligned}
\Oc(\eps):&&
\sig_1
	&= 	\frac{1}{\d_\sig u^\BS} u_1, \\
\Oc(\eps^2):&&
\sig_2
	&= 	\frac{1}{\d_\sig u^\BS} \Big( u_2 - \tfrac{1}{2} \sig_1^2 \d_\sig^2 u^\BS \Big), \\
\Oc(\eps^3):&&
\sig_3
	&= 	\frac{1}{\d_\sig u^\BS} \Big( u_3 - \(\sig_2 \sig_1 \d_\sig^2 + \tfrac{1}{3!}\sig_1^3 \d_\sig^3 \) u^\BS \Big),

\end{aligned}
\label{eq:sigmas}
\end{align}
where all the functions $u_1,\ldots,u_5$ and $u^\BS$ are evaluated at $(t,x,\sigma_0)$.
\end{remark}
\begin{remark}
Having served its purpose, we now dial $\eps$ up to one.
The implied volatility is then given by
$\sig = \sum_{k\geq 0}\sig_k$,
where $\sig_0$ is a fixed positive constant and
where the sequence~$(\sig_k)_{k\geq 1}$ is given by~\eqref{eq:sig.k}.
\end{remark}

\subsection{Simplification of the expressions for $\sig_k$}
\label{sec:simple}
The expression for the coefficients $\sig_k$ ($k\geq 1$) in \eqref{eq:sig.k} is not straightforward to apply;
one needs to compute first the Fourier integrals $u_j$  ($j\leq k$) via~\eqref{eq:u.eps.expand},
then all the terms of the form $\d_\sig^j u^{\BS}$ ($j\leq k$).
We provide now a more explicit approximation---without integrals or special functions---for $\sig_k$.
The key to this simplification is that all the terms $\partial^i_\sigma u^{\BS}$ and $u_i$ ($i\in\mathbb{N}$)
in~\eqref{eq:sig.k} can actually be expressed in terms of derivatives of $u^{\BS}$ with respect to $x$,
the starting point of the log stock price process.
Indeed, the classical Black-Scholes relation between the Delta, the Gamma and the Vega for call options,
$\left.\d_\sig u^{\BS}(t,x,\sig)\right|_{\sigma=\sigma_0} = t \sig_0 ( \d_x^2 - \d_x ) u^{\BS}(t,x,\sig_0) $,
implies that the derivative~$\d_\sig^k u^{\BS}$ can be expressed as a sum of terms of the form
$a_{k_i} \d_x^{k_i} (\d_x^2 - \d_x) u^{\BS}$.
We shall also use the equality
$p(\lam) \E^{\ii \lam x} = p(- \ii \d_x) \E^{\ii \lam x}$, which holds for any polynomial $p$
(and actually for any analytic function---simply take $p$ to be its power series).
We first start with the following theorem, which provides an approximation for the coefficients~$u_n$ in~\eqref{eq:u.eps.expand}
as a differential operator acting on $u^{\BS}$.
\begin{theorem}\label{thm:SimpleUn}
Fix some $t\geq 0$ and $\sigma_0>0$.
If the power series
$\phi_1(t,\lam;\sig_0) = \sum_{k\geq 1} a_k(t;\sig_0) (\ii \lam)^k$
holds in a complex neighbourhood of the origin,
then for any integer $m\geq 2$, $u_n$ defined in~\eqref{eq:u.eps.expand} can be written as
$u_n(t,x,\sigma_0)  = u_n^{(m)}(t,x,\sigma_0) + \eps_n^{(m)}(t,x,\sigma_0)$,
where
\begin{align}
u_n^{(m)}(t,x,\sig_0)
	&=	\frac{1}{n!}\( \sum_{k=2}^m a_k(t,\sig_0) (\d_x^k - \d_x )\)^n u^{\BS}(t,x,\sig_0),
\label{eq:u.n.m}
\end{align}
and where $\varepsilon_n^{(m)}$ only contains derivatives (with respect to~$x$) of $u^{\BS}$ of order higher than~$n$.
\end{theorem}
\begin{remark}
Note that the power series for $\phi_1$ in the theorem starts at $k=1$, which
follows from the fact that the process $\exp(X^{\eps,\sig_0})$ is conservative.
This expansion holds as soon as
all the moments of $X_t$ exist and
$\lim_{k\uparrow \infty}|\lambda|^k\Eb\left(|X_t|^k\right)/k! = 0$
for $|\lambda|$ small enough, which is valid under Assumption~\ref{ass:Explosions}.
\end{remark}

\begin{proof}
Assume that the power series for $\phi_1(t,\cdot;\sig_0)$ holds around the origin,
where the coefficients read
\begin{align}\label{eq:Coefak}
a_k(t;\sigma_0) = \frac{(-\ii)^k}{k!}\left.\partial_\lambda ^k \phi_1 (t,\lambda;\sigma_0)\right|_{\lambda=0}.
\end{align}
The martingale condition implies
$\phi_1(t,-\ii;\sig_0) = \sum_{k\geq 1} a_k(t;\sig_0) = 0$, and hence
\begin{align}
\phi_1(t,\lam;\sig_0)  & = \sum_{k=1}^\infty a_k(t;\sig_0) (\ii \lam)^k
  = \ii \lam a_1(t;\sig_0) + \sum_{k=2}^\infty a_k(t;\sig_0)\left[ (\ii \lam)^k - \ii \lam \right] + \ii\lambda\sum_{k=2}^\infty a_k(t;\sig_0)\\
	&=	\sum_{k=2}^\infty a_k(t;\sig_0) \left[ (\ii \lam)^k - \ii \lam \right]. \label{eq:decomposition}
\end{align}
Let now $\phi_1^{(m)}(t,\cdot;\sigma_0):\Cb\to\Cb$ be the truncation of the series~\eqref{eq:decomposition} at the $m$-th order, i.e.
\begin{align}\label{eq:defPhi1m}
\phi_1^{(m)}(t,\lam;\sig_0) := \sum_{k=2}^m a_k(t;\sig_0) \left[ (\ii \lam)^k - \ii \lam \right],
\end{align}
and define the operator $\delta$ acting on $\phi_1^{(m)}$ by
\begin{align}
\del\phi_1^{(m)}(t,\lam;\sig_0)
	&:=	\phi_1(t,\lam;\sig_0) - \phi_1^{(m)}(t,\lam;\sig_0)
	= 	\frac{\lam^{m+1}}{2 \pi \ii} \int_{\d\Gam} \frac{\phi_1(t,z;\sig_0) \dd z}{z^{m+1}(z-\lam)}
 + \ii \lam \sum_{k=1}^{m} a_k,
\end{align}
where $\Gam$ is a closed set within the radius of convergence of $\phi_1$,
and the integral is nothing else than the remainder of the series expansion around the point $\lambda=0$.
Hence for any $n\geq 1$, $u_n$ in~\eqref{eq:u.eps.expand} can be written as
\begin{align}
u_n(t,x,\sig_0)
	&=	\frac{1}{n!} \frac{1}{2\pi} \int_\Rb \dd \lam_r \,
			\E^{t \phi_0(t,\lam,\sig_0)} \hh(\lam) \( \phi_1(t,\lam;\sig_0) \)^n \, \E^{ \ii \lam x} \\
	&=	\frac{1}{n!} \frac{1}{2\pi} \int_\Rb \dd \lam_r \,
			\E^{t \phi_0(\lam;\sig_0)} \hh(\lam)
			\( \phi_1^{(m)}(t,\lam;\sig_0) + \del \phi_1^{(m)}(t,\lam;\sig_0) \)^n \, \E^{ \ii \lam x} \label{eq:un.int} \\
	&=	\frac{1}{n!} \( \phi_1^{(m)}(t,-\ii \d_x;\sig_0) \)^n \frac{1}{2\pi} \int_\Rb \dd \lam_r \,
			\E^{t \phi_0(\lam;\sig_0)} \hh(\lam) \E^{ \ii \lam x} + \eps_n^{(m)}(t,x,\sig_0) \\
	&=	\frac{1}{n!} \( \phi_1^{(m)}(t,-\ii \d_x;\sig_0) \)^n u^{\BS}(t,x,\sig_0) + \eps_n^{(m)}(\sig_0)
	= 	u_n^{(m)}(t,x,\sig_0) + \eps_n^{(m)}(t,x,\sig_0),
\end{align}
where
\begin{align}
u_n^{(m)}(t,x,\sig_0)
	&:=	\frac{1}{n!} \( \phi_1^{(m)}(t,-\ii \d_x;\sig_0) \)^n u^{\BS}(t,x,\sig_0) , \\
\eps_n^{(m)}(t,x,\sig_0)
	&:=	\frac{1}{n!} \sum_{k=1}^n \binom{n}{k} \(\phi_1^{(m)}(t,-\ii \d_x;\sig_0)\)^{n-k} \(\del\phi_1^{(m)}(t,-\ii \d_x;\sig_0)\)^k u^{\BS}(t,x,\sig_0) .
\end{align}
From the decomposition~\eqref{eq:defPhi1m}, we can write
$\phi_1^{(m)}(t,-\ii \d_x;\sig_0) = \sum_{k=2}^m a_k(t;\sig_0) (\d_x^k - \d_x)$,
where the coefficients~$a_k$ are defined in~\eqref{eq:Coefak}.
We can now compute
\begin{align}
u_n^{(m)}(t,x,\sig_0) & = \frac{1}{n!} \( \phi_1^{(m)}(t,-\ii \d_x;\sig_0) \)^n u^{\BS}(t,x,\sig_0)
 = \frac{1}{n!} \left(\sum_{k=2}^m a_k(t;\sig_0) (\d_x^k - \d_x)\right)^n u^{\BS}(t,x,\sig_0) ,

\label{eq:un.m}
\end{align}
which is precisely the expression given in \eqref{eq:u.n.m}.
Regarding $\varepsilon_n^{(m)}$, since for any $z \in \Gam$, there exists $M>0$ such that $\left|\phi_1(t,z;\sig_0)/(z-\lam)\right| \leq M$, we have
$\left|\del\phi_1^{(m)}(t,\lambda;\sig_0) \right| \leq M \left(|\lam|/R \right)^{m+1} + |\lambda| \left|\sum_{k=1}^{m} a_k\right|$,
where $R$ denotes the radius of convergence of~$\phi_1$.
The sequence $(a_k)_{k\geq 1}$ is (eventually) decreasing and the sum tends to zero as $m$ tends to infinity,
so that the sum can be made arbitrarily small.
We then obtain
\begin{align}
\left|\eps_n^{(m)}(t,x,\sig_0)\right| &
\leq \frac{1}{n!} \sum_{k=1}^n \binom{n}{k} \left|\phi_1^{(m)}(t,-\ii \d_x;\sig_0)\right|^{n-k}
\left(M \left(|\lam|/R \right)^{m+1} + |\lambda| \left|\sum_{k=1}^{m} a_k\right|\right)^k u^{\BS}(t,x,\sig_0)\\
& \leq \frac{1}{n!} \sum_{k=1}^n \binom{n}{k} \left|\sum_{j=2}^m a_j(t;\sig_0) \left((\ii \lam)^j - \ii \lam \right)\right|^{n-k}
\left(M \left(|\lam|/R \right)^{m+1} + |\lambda| \left|\sum_{k=1}^{m} a_k\right|\right)^k u^{\BS}(t,x,\sig_0).
\end{align}
One can then readily check that the sum behaves as $\Oc\left(\lambda^n\right)$ as $\lambda$ tends to zero.
Therefore, $\varepsilon_n^{(m)}$ contains derivatives (with respect to~$x$) of $u^{\BS}$ of at least order $n$.
\end{proof}
\noindent
Expression \eqref{eq:u.n.m} motivates the following definition:
\begin{definition}
\label{def:sig.nm}
For any integers $n \geq 0$, $m \geq 2$ and for fixed $\sig_0 > 0$ we define the \emph{$(n,m)$-th order approximation of the implied volatility} as
\begin{equation}\label{eq:sig.n.m}
\sig^{(n,m)} := \sig_0 + \sum_{k=1}^n \sig_k^{(m)},
\end{equation}
where, for any $k=1,\ldots,n$, $\sig_k^{(m)}$ is defined as
\begin{align}
\sig_k^{(m)}
	&:= \frac{1}{\d_\sig u^{\BS}(t,x,\sig_0)} \( u_k^{(m)} - \sum_{n=2}^\infty \frac{1}{n!}
			\( \sum_{j_1+\cdots+j_n=k} \prod_{i=1}^n \sig_{j_i}^{(m)} \)
			\d_\sig^n u^{\BS}(t,x,\sig_0)\) . \label{eq:sig.k.m}
\end{align}
\end{definition}
Note that~$\sig_k^{(m)}$ is obtained from $\sig_k$ by replacing $u_k$ in~\eqref{eq:sig.k}
by its $m$th order approximation~$u_k^{(m)}$.
The following theorem, proved in Appendix~\ref{sec:proof}, is the main result of this paper
and provides and explicit expression (not involving the derivatives of Black-Scholes)
for the $(n,m)$-th order approximation of the implied volatility.
\begin{theorem}
\label{thm:main}
Fix $(t,x,\zeta,\sig_0)\in (0,\infty)\times\mathbb{R}\times\mathbb{R}\times(0,\infty)$, and define
\begin{equation}\label{eq:y0}
y_0 := \frac{1}{\sig_0\sqrt{2t}}\(x-\zeta-\frac{1}{2}\sig_0^2 t\).
\end{equation}
For $\phi(t,\lam)$, $\phi_0(\lam,\sig_0)$, $\phi_1(t,\lam;\sig_0)$ and $a_k(t;\sigma_0)$ defined respectively
in~\eqref{eq:char.form},~\eqref{eq:uBS},~\eqref{eq:phi1} and~\eqref{eq:Coefak},
the $(n,m)$-th approximation~\eqref{eq:sig.n.m} holds,
with $\sig_k^{(m)}=U_k^{(m)}-\Sigma_k^{(m)}$ and
\begin{align}
U_n^{(m)}
	& :=	\frac{1}{n! t \sig_0}  \sum_{k=2 n}^{n m}
			\sum_{\substack{j_1+\cdots+j_n = k \\ 2 \leq j_1,\cdots,j_n \leq m}}
			\( \prod_{i=1}^n a_{j_i} \) \sum_{k_1=2}^{j_1} \cdots \sum_{k_n=2}^{j_n}
			\binom{n-1}{m}(-1)^{n-1-m}
			\\ & \qquad \times
			\(-\frac{1}{\sig_0\sqrt{2t}}\)^{-n-1+m+\sum_{j=1}^n {k_j}}
			H_{-n-1+m+\sum_{j=1}^n {k_j}}(y_0) , \\
\Sigma_k^{(m)}
	& :=	\sum_{n=2}^\infty \frac{1}{n!}
			\( \sum_{j_1 + \cdots + j_n = k} \prod_{i=1}^n \sig_{j_i}^{(m)} \)

			\sum_{q=0}^{\left\lfloor n/2 \right\rfloor}\sum_{p=0}^{n-q-1}
			\binom{n-q-1}{p}c_{n,n-2q}\sig_0^{-(q+p)} t^{n-q-1}
			\left(\sqrt{2 t}\right)^{1-p-n+q} H_{p+n-q-1}(y_0).
\end{align}
Here, $H_n(y) \equiv (-1)^n \E^{y^2} \d_y^n \E^{-y^2}$ is the $n$-th Hermite polynomial,
the coefficients $(c_{n,n-2k})$ are defined recursively by
$c_{n,n}=1$ and $c_{n,n-2q} =(n-2q+1) c_{n-1,n-2q+1} + c_{n-1,n-2q-1}$,
for any integer $q \in \{ 1, 2, \cdots , \left\lfloor n/2 \right\rfloor \}$.
\end{theorem}
\begin{example}
\label{ex:computation}
To illustrate how the above theorem works in practice, we compute $\sig_2^{(3)}$ explicitly.
Fix $(t,x,\zeta,\sig_0)$ and write $a_k = a_k(t;\sig_0)$.
Equation~\eqref{eq:u.n.m} implies
\begin{align}
u_1^{(3)}(t,x,\sig_0)

	=	\Big\{a_3 \d_x + (a_2 + a_3) \Big\} (\d_x^2 - \d_x )  u^\BS(t,x,\sig_0),\\
u_2^{(3)}(t,x,\sig_0)

	=	\frac{1}{2} \Big\{a_3^2 \d_x^4 + (2 a_2 a_3 + a_3^2)\d_x^3 + (a_2^2-a_3^2)\d_x^2 + (-a_2^2-a_3^2-2 a_2 a_3)\d_x \Big\} (\d_x^2 - \d_x )  u^\BS(t,x,\sig_0).
\end{align}
Next, using Proposition \ref{prop2} we have
\begin{align}
\frac{u_1^{(3)}}{\d_\sig u^\BS}(t,x,\sigma_0)
	&=	\displaystyle \frac{1}{t \sig_0} \left\{
			a_3 \( \tfrac{-1}{\sig_0\sqrt{2t}}\) H_1(y_0) + (a_2+a_3)
			\right\}, \label{eq:ex1} \\
\frac{u_2^{(3)}}{\d_\sig u^\BS}(t,x,\sigma_0)
	&=	\displaystyle \frac{1}{t \sig_0} \left\{
			a_3^2 \( \tfrac{-1}{\sig_0\sqrt{2t}}\)^4 H_4(y_0) + (2 a_2 a_3 + a_3^2)\( \tfrac{-1}{\sig_0\sqrt{2t}}\)^3 H_3(y_0)\right.
			\\ &\qquad \qquad
			\displaystyle \left.+ (a_2^2-a_3^2) \( \tfrac{-1}{\sig_0\sqrt{2t}}\)^2 H_2(y_0) + (-a_2^2-a_3^2-2 a_2 a_3) \( \tfrac{-1}{\sig_0\sqrt{2t}}\) H_1(y_0)
			\right\}, \label{eq:ex2}
\end{align}
with $y_0$ defined in~\eqref{eq:y0}.
From Proposition~\ref{prop1} we then have
$\d_\sig^2 u^\BS =	\( \sig_0^2 \Lc^2 - \Lc \) u^\BS$, where
$\Lc = t (\d_x^2 - \d_x)$.
Therefore, recalling that $\d_\sig u^\BS = \sig_0 \Lc u^\BS$ we obtain
\begin{align}
\frac{\d_\sig^2 u^{\BS}}{\d_\sig u^{\BS}}(t,x,\sigma_0)
	&=	\frac{1}{t\sig_0} \( \frac{t^2\sig_0^2\d_x^2(\d_x^2-\d_x)u^\BS}{(\d_x^2-\d_x)u^\BS}
			- \frac{t^2\sig_0^2\d_x(\d_x^2-\d_x)u^\BS}{(\d_x^2-\d_x)u^\BS}
			+ \frac{t(\d_x^2-\d_x)u^\BS}{(\d_x^2-\d_x)u^\BS}  \)(t,x,\sigma_0)  \\
	&=	\frac{1}{t\sig_0} \(
			t^2\sig_0^2 \( \tfrac{-1}{\sig_0\sqrt{2t}}\)^2 H_2(y_0)
			- t^2\sig_0^2 \( \tfrac{-1}{\sig_0\sqrt{2t}}\) H_1(y_0)
			+ t \)
	=	\frac{(\zeta-x)^2}{t \sig_0^3}-\frac{t \sig_0 }{4} . \label{eq:ex3}
\end{align}
Lastly, from \eqref{eq:sig.n.m}-\eqref{eq:sig.k.m} we have
\begin{align}
\sig^{(2,3)}
	&=	\sig_0 + \sig_1^{(3)} + \sig_2^{(3)} , &
\sig_1^{(3)}
	&= 	\frac{u_1^{(3)}}{\d_\sig u^\BS} , &
\sig_2^{(3)}
	&= 	\frac{u_2^{(3)}}{\d_\sig u^\BS}
			- \frac{1}{2} \(\sig_1^{(3)}\)^2 \frac{\d_\sig^2 u^\BS}{\d_\sig u^\BS}  . \label{eq:ex4}
\end{align}
The explicit expression for $\sig^{(2,3)}$ can be obtained by inserting \eqref{eq:ex1}, \eqref{eq:ex2} and \eqref{eq:ex3} into \eqref{eq:ex4}.
\end{example}

\section{Numerical implementation: discussions and examples}
\label{sec:examples}
We now focus on the practical implementation of the results above, namely
Theorem~\ref{thm:main}.
Section~\ref{sec:SVI} proposes a smoothing procedure to further enhance the applicability of our methodology.
In Sections~\ref{sec:Levy} and~\ref{sec:Heston}, we implement our implied volatility expansion in two exponential L\'evy models (Merton and Variance Gamma) and one stochastic volatility model (Heston).

\subsection{Smoothing with the SVI parameterisation}
\label{sec:SVI}
Option data is often noisy and limited by the number of strikes at which options are liquidly traded.
In~\cite{gatheral2004parsimonious}, Jim Gatheral introduces the following \emph{Stochastic Volatility Inspired}
(SVI) parameterisation:
\begin{align}
\sig_t^{\SVI}(\zeta) &= \left\{ \frac{a}{t} + \frac{b}{t} \( \rho (\zeta-x-m) + \sqrt{(\zeta-x-m)^2 + \xi^2} \)\right\}^{1/2},
 \label{eq:SVI}
\end{align}
for any maturity $t>0$, where $a, b\geq 0$, $\xi>0$, $m\in\mathbb{R}$, $\rho\in [-1,1]$.
By fitting the SVI parameterisation to noisy option data, one is able to create a smooth implied volatility smile, which then can be used to interpolate implied volatility between strikes and extrapolate implied volatility to strikes which are not traded.
The density $p^\sig(t,x)$ corresponding to a given implied volatility parameterisation~$\sig(t,\zeta)$ can be computed via the Breeden-Litzenberger formula~\cite{breeden}:
$p^\sig(t,\zeta) = \d_K^2 u^\BS(t,x,\sig(t,\log K);\log K) \big|_{K=\E^\zeta}$.
An implied volatility smile $\zeta \mapsto \sig(t,\zeta)$ is said to be free of butterfly arbitrage
if the corresponding density is non-negative: $p(t,\cdot)\geq 0$.
Let $p_t^\SVI(\zeta)$ be the implied volatility smile corresponding to a given SVI parameterisation~\eqref{eq:SVI}.
In general, SVI parameterisation~\eqref{eq:SVI} is not guaranteed to be free of butterfly arbitrage.
However, for a given set of SVI parameters $(a,b,\rho,m,\xi)$,
one can easily verify that the corresponding density is non-negative, and therefore free of butterfly arbitrage.
This and recent arbitrage-free SVI parameterisations have recently been studied in~\cite{gatheral2012arbitrage}
and~\cite{JacquierMartini}, and we refer the interested reader to these papers for more details.
As we shall see in the examples considered in Section \ref{sec:examples},
for finite $(n,m)$, the approximate implied volatility $\sig^{(n,m)}$
derived in Section~\ref{subsec:imp.vol} has a tendency to oscillate around the true implied volatility
(see Figures~\ref{fig:Merton},~\ref{fig:VG} and~\ref{fig:Heston}).
Taking $\sig^{(n,m)}$ to be the true implied volatility could lead to arbitrage opportunities.
In order to prevent this, we propose to smooth the implied volatility approximation $\sig^{(n,m)}$
by fitting the SVI parameterisation to it.
That is, given a model for the underlying $X$ and a time to maturity $t$, we first compute the approximate implied volatility $\sig^{(n,m)}$ as a function of $\log$-strike $\zeta$,
and then fit an arbitrage-free SVI parameterisation $\sig_t^{\SVI}$ to $\sig^{(n,m)}$ over some range of strikes, usually chosen to be a symmetric interval around $\zeta=x$.

\subsection{Exponential L\'evy models}\label{sec:Levy}
Suppose that $X$ is a L\'evy process with L\'evy triplet $(\mu,a^2,\nu)$.
Then its characteristic function reads
$$
\phi(t,\lam) = t\(\ii \mu\lam + \frac{1}{2} a^2 (\ii \lam)^2
 + \int_\Rb \nu(\dd z) (\E^{\ii \lam z} - 1 - \Ib_{\{|z| < 1 \}} \ii \lam z) \),
$$
where the drift $\mu$ is constrained by the martingale condition $\phi(t,-\ii) = 0$:
$\mu = - \frac{1}{2} a^2  - \int_\Rb \nu(\dd z) (\E^z - 1 - \Ib_{ \{|z| < 1 \}} z)$.
From the expansion $(\E^{\ii \lam z} - 1 ) = \sum_{n\geq 1} \frac{1}{n!} (\ii \lam z)^n$
we can write
$$
\phi_1(t,\lam;\sig_0)
\equiv	\phi(t,\lam) - t \, \phi_0(\lam;\sig_0)
\equiv t \( \mu + I_1 + \tfrac{1}{2} \sig_0^2 \) \ii \lam +  \frac{1}{2} t ( a^2 - \sig_0^2 ) (\ii \lam)^2 + t \sum_{n=2}^\infty \frac{1}{n!} I_n (\ii \lam )^n,
$$
with
$I_1 := \int_{|z| \geq 1 } \nu(\dd z) z$ and
$I_n  := \int_\Rb \nu(\dd z) z^n$,
for any $n\geq 2$.
The existence of~$I_n$ is equivalent to the finiteness of the $n$th moment of $X$
by~\cite[Theorem 25.3]{sato1999levy}, which is clearly satisfied under Assumption~\ref{ass:Explosions}.
Hence, the coefficients $a_n(t;\sig_0)$ in~\eqref{eq:Coefak} are given by
\begin{align}
a_2(t;\sig_0)
	&=	\frac{t}{2} (a^2 - \sig_0^2  + I_2 ) , &
a_n(t)
	&=	\frac{t}{n!}I_n , \quad n \geq 3 . \label{eq:Levy.a}
\end{align}
We examine two exponential L\'evy models in detail---the Merton model~\cite{merton1976option}
and the Variance Gamma model~\cite{madan1998variance}---whose L\'evy measures are given by:
\begin{align}
\text{Merton}:&&
\nu(\dd z)
	&= \frac{\alpha }{\sqrt{2 \pi s^2}}\exp \( \frac{-(z-m)^2}{2s^2} \) \dd z, \\
\text{Variance Gamma}:&&
\nu(\dd z)
	&= \alpha \( \frac{\E^{G z}}{-z} \Ib_{\{ z < 0\} } +  \frac{\E^{-M z}}{z} \Ib_{\{ z > 0\} }\) \dd z,
\end{align}
where $\alpha,s,G,M>0$, $m\in\mathbb{R}$.
The Merton model is a finite-activity L\'evy process ($\nu(\Rb)<\infty$),
whereas the Variance Gamma model has infinite activity ($\nu(\Rb)=\infty$).
For infinite activity L\'evy processes, one typically takes the diffusion component to be zero, namely $a=0$.
We now examine the accuracy of the implied volatility expansion above in these models:
the Merton model in Figure~\ref{fig:Merton} and the Variance Gamma in Figure~\ref{fig:VG}.
For each of these two sets of plots, we fix some parameters, and draw the implied volatility approximations~$\sig^{(n,m)}$
with $m=7$ for the Merton model and $m=8$ for the Variance-Gamma one, and $n\in\{1,2,3\}$.
We also plot the SVI smoothing of $\sig^{(3,m)}$ as well as the true implied volatility.
The true option price is computed by a quadrature of the inverse Fourier transform representation~\eqref{eq:InvFourierPrice},
and the true implied volatility is computed by numerical inversion of the Black-Scholes formula
(we use a simple Newton-Raphson algorithm).
We also plot the total errors between each approximation (and $\sigma^{(3,\cdot)}$ with SVI smoothing) and the true implied volatility.
As discussed above, the implied volatility approximation oscillates around the true implied volatility $\sig$.
However, the relative error corresponding to $\sig^{(3,m)}$ is less than one percent for nearly all log-moneyness to maturity ratios (LMMRs) satisfying
$|\zeta-x|/t<1.4$ for both models,
which is well within the implied volatility bid-ask spread of S\&P $500$ options.
Furthermore, the relative error of $\sig^{(3,m)}$ with SVI smoothing is about one half percent for all $|\zeta-x|/t<1.0$.
As a no-arbitrage consistency check, we also plot the density corresponding to the SVI fit.
The parameters for each model are as follows:
\begin{align}
\text{Merton model: } & &
\sig_0=0.55, a=0.25, m=-0.15, s=0.3, \alpha=1.5, t=1, x=0, \label{eq:paramMerton}\\
\text{Variance Gamma model: } &  &
\sig_0=0.55, a=0, M=7, G=6, \alpha=4.5, t=1, x=0.\label{eq:paramVG}
\end{align}

\subsection{The Heston model}\label{sec:Heston}
In the Heston model~\cite{heston1993}, the risk-neutral dynamics of $(X,Y)$ are given by
\begin{align*}
\dd X_t &= -\frac{1}{2} Y_t \dd t + \sqrt{Y_t} \dd W_t , &
\dd Y_t &= \kappa (\theta - Y_t) \dd t + \del \sqrt{Y_t} \dd B_t , &
\dd \< W, B \>_t	&=	\rho \, \dd t ,
\end{align*}
with $(X_0,Y_0) = (x,y)\in\mathbb{R}\times (0,\infty)$, $\kappa, \theta, \delta>0$, and where $W$ and $B$ are two standard Brownian motions
with correlation~$\rho\in [-1,1]$.
Its characteristic function reads $\phi(t,\lam,y) = C(t,\lam) + y D(t,\lam)$, where
\begin{equation*}
\left.
\begin{array}{rll}
C(t,\lambda) & := \displaystyle \frac{\kappa\theta}{\delta^2} \left((\kappa-\I \rho\delta\lambda - d(\lambda)) t
 -2\log\left[\frac{1-\gamma(\lambda) \E^{-d(\lambda)t}}{1-\gamma(\lambda)}\right]\right),
&
d(\lambda) := \displaystyle \left(\delta^2 (\lambda^2 + \I \lambda) +
(\kappa - \rho \I \lambda \delta)^2\right)^{1/2},\\
D(t,\lambda) & := \displaystyle \frac{\kappa - \I\rho \delta \lambda - d(\lambda)}{\delta^2}
 \frac{1-\E^{-d(\lambda)t}}{1-\gamma(\lambda) \E^{-d(\lambda)t}},
&
\gamma(\lambda) := \displaystyle \frac{\kappa - \I\rho \delta \lambda - d(\lambda)}{\kappa - \I\rho \delta \lambda + d(\lambda)}.
\end{array}
\right.
\end{equation*}
Unlike the exponential L\'evy setting, there is no simple general formula for the coefficients $a_n(t,\sigma_0)$
$(n \geq 2)$.
However, from~\eqref{eq:Coefak}, one can compute
\begin{align}
a_2(t;\sig_0) = & \frac{\E^{2 \kappa t}}{16 \kappa^3}
\Big(
 4 \E^{\kappa t} \left[2(\theta-y) \kappa^2+2(y+y \kappa t-\theta(2+\kappa t))\kappa\rho \del
 + (\theta + (\theta - y) \kappa t) \del^2\right] - (2 y-\theta ) \del^2
\Big) \\
 & + \frac{1}{16 \kappa^3}
\Big(
8\kappa^2(y+(\kappa t -1)\theta) - 8(y+\theta(\kappa t - 2))\kappa\rho\del - ((5-2\kappa t)\theta-2y) \del^2
\Big)
 - \frac{\sig_0^2 t}{2}.
\end{align}
Higher order terms $(3 \leq n \leq 6)$ are easily computed using any mathematical software,
and are omitted here for clarity.
In Figure~\ref{fig:Heston}, we plot the function~$\zeta\mapsto\sig_n^{(m)}(\zeta)$ with $m=6$ and $n\in\{1,2,3\}$,
a calibrated SVI to $\sig_3^{(6)}$ and the true implied volatility (computed exactly as for the L\'evy models above).
We also plot the relative errors between each approximation (and the SVI smoothing of $\sigma^{(3,6)}$) and the true implied volatility.
Again the approximation $\sig^{(n,m)}$ oscillates around the true implied volatility, but
the relative error of $\sig^{(3,6)}$ is less than two percent for nearly all LMMRs satisfying $|\zeta-x|/t<2.0$,
and that of $\sig^{(3,6)}$ with SVI smoothing is roughly one percent for all
$|\zeta-x|/t<2.0$.
As before, we also plot the density corresponding to the calibrated SVI parameterisation as a no-arbitrage consistency check.
We use the following set of parameters:
$\sig_0=0.95$, $\kappa=1$, $\theta=0.3$, $\del=0.7$, $\rho=-0.3$, $t=1$, $x=0$, $y=0.5$.

\subsection{Model-free calibration}\label{sec:Calibration}
As noted previously, the model-specific dependence of the approximate implied volatility expansion $\sig^{(n,m)}$ is entirely captured by the coefficients $a_i(t,\sig_0)$ $(2 \leq i \leq m)$.
This simple structure allows for a model-free calibration of the implied volatility surface.
Assume one observes implied volatilities for maturities~$(t_i)_{i=1,\ldots, n_T}$ and~$(k_j)_{j=1,\ldots,n_K}$,
where~$n_T$ and~$n_K$ are two integers.
We shall assume for simplicity that the number of available strikes is the same for each maturity.
We suggest the following procedure:
\begin{itemize}
\item[(i)] Let $\sig_{i,j}:=\sig(t_i,k_j)$ be the quoted implied volatility for an option with maturity $t_i$ and $\log$ strike $k_j$.
\item[(ii)] Let $\sig_{i,j}^{(n,m)}:=\sig^{(n,m)}(t_i,k_j;\sig_0)$ be the approximate implied volatility for an option
with maturity $t_i$ and $\log$ strike $k_j$ computed using the approximation~\eqref{eq:sig.n.m}.
\item[(iii)] At each maturity $t_i$, leave $\sig_0$ and $a_q(t_i;\sig_0)$ $(2\leq q \leq m)$ as free parameters.   Fit $\sig^{(n,m)}(t_i,\cdot)$ to the market's $t_i$-maturity implied volatility smile $\sig(t_i,\cdot)$ by minimising
$\sum_{j=1}^{n_K} \left|\sig^{(n,m)}(t_i,k_j) - \sig_{ij}^{(n,m)}\right|^2$.
\item[(iv)] As an initial guess, use the largest quoted implied volatility at each maturity for $\sigma_0$,
and $a_q(t_i,\sig_0)=0$.
\end{itemize}
\begin{remark}
With $n=3$ and $m=8$, step~(iii) is instantaneous using Mathematica's {\tt FitTo} or Matlab's {\tt lsqnonlin} for instance.
\end{remark}
We test this procedure on SPX index options from January 4, 2010 with $n=3$ and $m=8$.
The results for three separate maturities ($t=0.033$, $t=0.70$, $t=1.45$ years)
are given on Figure~\ref{fig:SPX-FIT}.
The calibrated parameters are ($a_i$ is a shorthand notation for $a_i(t;\sig_0)$):
\begin{center}
  \begin{tabular}{ l | c c c c c c c c }
 & $\sigma_0$ &  $a_2$ &  $a_3$ & $a_4$ & $a_5$ & $a_6$ & $a_7$ & $a_8$\\
\hline
$t=$0.033 & 0.382 &  -1.64E-3 & -1.00E-6 & 1.64E-6 & 1.89E-8 & 8.62E-10 & 5.22E-12 & 1.40E-13\\
$t=$0.70 & 0.659 & -1.31E-1 & -5.00E-3 & 2.40E-3 & 4.24E-4 & 6.96E-5 & 2.88E-6 & 4.83E-7\\
$t=$1.45 & 0.436 & -8.35E-2 & -1.22E-2 & 1.68E-3 & -6.26E-5 & 3.42E-5 & -1.77E-6 & 3.96E-7
  \end{tabular}
\end{center}

\begin{remark}
If the stock price is an exponential L\'evy model, then~\eqref{eq:Levy.a} implies that
$\frac{1}{2} \sig_0^2 + \frac{1}{t_i} a_2(t_i,\sig_0)=\frac{1}{2}(a^2 + I_2)$
and $\frac{1}{t_i}a_q(t_i) = \frac{1}{q!}I_q$ $(3\leq q \leq m)$ should be constant.
If this is not so, then exponential L\'evy models are probably not the best dynamics to describe the underlying.
\end{remark}

\begin{remark}
Our whole methodology is based on approximating the characteristic function of a process by a truncated version
of its expansion with respect to some small parameter.
In essence, this truncation tends to ignore the tail behaviour (high-order terms in the expansion) of the process,
and hence, even though the resulting volatility expansion is accurate around the money,
there is no reason why it should be so in the tails.
The latter, however, are usually not observable in practice, so that this should be of lesser concern for practical implementation.
This in particular means that, should one plot the densities corresponding to the fit in Figure~\ref{fig:SPX-FIT},
the latter may become negative in the tails (hence allowing for arbitrage opportunities).
In our calibration example (Figure~\ref{fig:SPX-FIT}), the density does remain non-negative though.
If however it was to become negative, one could perform an SVI fit, as explained in Section~\ref{sec:SVI}, or, even better,
use the fully no-arbitrage SVI version developed in~\cite{gatheral2012arbitrage}.
\end{remark}

\subsection*{Acknowledgments}
M.~Lorig acknowledges financial support from Imperial College London, and both authors are grateful to Claude Martini and Zeliade Systems for their useful comments and for indicating to us the availability of CBOE data.  The authors would also like to thank an anonymous referee, whose suggestions improved both the mathematical quality and readability of this manuscript.

redpajama_set_name: RedPajamaArXiv


SALT LAKE CITY, March 20, 2013 /PRNewswire via COMTEX/ --inContact (NASDAQ: SAAS), the leading provider of cloud contact center software and contact center agent optimization tools, today announced the findings of their February 2013 survey, that examined the current state of customer service and the changing preferences of consumers.
The study, conducted online by Harris Interactive among 2,191 U.S. adults aged 18 years or older shows that consumers are making less of their buying decisions based on brand loyalty, but rather on which companies can match their desired experience, at a time of their choosing. According to the findings, more than half (56%) of U.S. adults would be at least somewhat likely to switch to another brand or company if it offered more options and channels to connect with them than they were currently using. Further, younger consumers aged 18-44 (64%) indicated this was true significantly more than their counterparts aged 55 or older (45%), showing a major shift among the younger consumer base in terms of how they're making decisions.
Based on the findings, this generation of consumers, who are used to lots of information and being presented with a myriad of choices, showed a desire for options that allow for a tailored experience in their interaction with brands, and is demanding more options and availability to handle these interactions when and how they see fit. The survey results clearly show that consumers are demanding control of their experience, and companies are at risk of losing customers if they neglect to accommodate customer preferences or adopt evolving channels of communication in providing service.
"The survey results are clear: consumers expect more choices and more ways to interact with business today. The smartest companies are quickly adapting to changing consumer behaviors and needs, extending customer service beyond just phone and email to mobile apps, text messaging, chat and social media." said Paul Jarman, CEO of inContact. "At inContact, we believe that offering a personalized customer service experience is at the forefront of success for brands today. We have added significant new features to our own platform to help our users adapt to new channels and new ways of communicating."
This survey was conducted online within the United States by Harris Interactive on behalf of inContact via its Quick Query omnibus product from February 11-13, 2013 among 2,191 adult ages 18 and older.
inContact (NASDAQ: SAAS) is the cloud contact center software leader, helping organizations around the globe create high quality customer experiences. inContact is 100% focused on the cloud and is the only provider to combine cloud software with an enterprise-class telecommunications network for a complete customer interaction solution. Winner of Frost & Sullivan 2012 North American Cloud Company of the Year in Cloud Contact Center Solutions, inContact has deployed over 1,300 cloud contact center instances. To learn more, visit www.inContact.com.
866.965.7227 | © 2013 inContact Inc.


The perfect base for exploring the grand city of Rome!
Historical center of Rome, 10-minute walk from the Colosseum and the Roman Forum.
Easy access to major tourist destinations. Metro and bus stop 50 mt.
Stylish, comfortable, cozy. rooms with ensuite bath, a / c, LCD TV, free Wi-Fi internet.
In the hearth of Rome, easy access to tourist must-see-sights. The bed & breakfast Brilli offers great value for money!
Stylish, comfortable, spacious, cozy rooms, quiet and freshened up each day, with a clean, private bathroom. Free Wi-Fi, for relaxing after a long day in Rome.
The B&B Brilli is a recent opened bed and breakfast inaugurated last July 2012. It is located inside an historic building of the end of 19st Century, opposite the old building of the former Ministry of Post. The district Esquilino, where the B&B Brilli is located, is in the center of the Eternal City of Rome, close to many tourist sites, with easy access to Rome must-see-sights, just a few stops away by bus, tram or by Metro station. Buses and metro stops are less than 50 mt. from the b&b Brilli.The district "Esquilino" is very nice, safe and noiseless , safe neighborhood with a police station beside the B&b and another one just around the corner. You won't have any troubles walking around at 1am.
The famous Coliseum and the Roman Forum are very close to us, just 10 minutes walk , crossing the lovely and ancient "Colle Oppio" Park where is located also the renowned Domus Aurea. You can reach 15 minutes walking also the Papal Basilica of Saint Mary Major, the largest Roman Catholic Marian church in Rome.
It is possible to arrange your transfers to and from the airport. For more than half a century this house, has been owned by the Brilli family. Recently opened last July 2012, and managed by Alexandra, a family member, who lives inside the B & B, taking care of every detail and welcoming the guests with her good humor and good spirits.
Alexandra, immediately make you feel at home, with a warm welcome and great advice about what to see and where to eat, restaurant choices, sightseeing idea, to providing you with all the information you need to make your stay in Rome perfect, with a priceless tips about the eternal City, definitely will make your visit memorable and unforgettable!
The b and b Brilli is cheap, very clean, with a friendly atmosphere, a very good budget accommodation in Rome near the Colosseum.


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Overview of Sales Transaction Entry window Integration.


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On May 1st 2009, I officially moved aboard my sailboat 'TIE Fighter' fulltime.
People often ask about the name; there are two distinct reasons for naming her 'TIE Fighter'. The first, of course, is the 'Star Wars' reference. I have always been a rabid fan of science fiction, but alas, having been born about a century too soon, I have been forced to come to terms with the fact that I will never have my own spacefaring vessel. At the current rate of progress, there is a strong possibility that I will never even leave this planet in my lifetime! This boat is the closest thing to a spaceship that I will ever call my own, and the ocean is really the only frontier left to us right now.
The second reason I chose the name 'TIE Fighter' is the pun - by moving aboard and shifting my life to a technomadic existence, I have removed the need for a cubicle job. If I play my cards right, I may never have to wear a necktie again. 'Tie fighter'. Get it?
She is a Brown Searunner 37, a sailing trimaran eleven meters (37') long and seven meters (23') wide, and yet she only drafts about one meter (3') with her swing keel up. She has a center cockpit, and she is 'cutter rigged', meaning her mast is closer to the middle of the boat than your typical sailboat and she flies three sails rather than the usual two. She has somewhere around a hundred and fifty square meters of deck space, enough to comfortably host fifteen or more people for summer sunset cruises.
Dual cabins, fore and aft, dual diesel furnaces for warmth, a 27-horsepower Yanmar inboard diesel engine, and oodles of space for storage. Outfitted for offshore sailing, she can easily support a crew of five for a month or more.
That's not to say she came without problems - a boat of this size and pedigree should cost somewhere between $75k and $150k, whereas I got her for - oh, just around the price of a Volkswagen Jetta. I think that's actually pretty appropriate given that I'm thirty-four years old and have never owned a car, and at this rate it's starting to look like I never will. The guy I bought her from had only had her a year, with the intention of fixing her up from the previous owner's complete lack of upkeep, but he decided that he didn't have the time or energy to pour into her. At least, that's what he told me - the past few years I've poured my heart, soul and wallet into her, getting her up to the point where I'm now comfortable taking her far out into the open ocean. There are always more projects to tackle, but the lists of "needs" is now pretty much non-existent and we're left with just a shorter list of "wants".
She is a wooden boat, built of marine-grade plywood and cedar stringers, skinned with epoxy and fiberglass. There is a great deal of controversy around wooden boats vs. the more modern fiberglass hulls, with each side having valid points. Some of the more nostalgic (or perhaps senile) old salts claim that wooden boats, being made from living material, have a soul. I would scoff, but for the sense of safety and well-being I get when I am aboard her.
I have literally put my blood, sweat and tears into this vessel - the work has been physically and mentally exhausting, but it has also been incredibly rewarding. For instance, in the past fifteen years of my professional career, I cannot point to a single thing that I have built that is older than three years. Hundreds or thousands of hours poured into projects, each slowly becoming obsolete and retired or deleted. Working on the TIE Fighter has been incredibly empowering - there has been a hugely steep learning curve, but the more I learn, the more I realize that there is not a system on this vessel that I cannot become the master of. I never thought I'd be a diesel engine guy, nor did I ever really feel a drive to be (pardon the pun), but I know that with effort I will be able to learn. I have become quite proficient with epoxy and fiberglass repairs, 12V electrical systems design and maintenance, and my wood shop classes from junior high have come back to me, albeit slowly.
Ever since moving aboard, my life has been a constant running adventure. I am in love with my ship.
That is an awesome story! You should be extremely proud of yourself. I myself am saving up to buy a trimaran to live aboard. ENJOY YOURSELF!


text:
The True Net
Home NEWS Dr M May Issue Ultimatum Tonight
Dr M May Issue Ultimatum Tonight
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Tonight's Pakatan Harapan pre-presidential council meeting is expected to witness an "ultimatum" laid out by Tun Dr Mahathir Mohamad, on the heels of detractors calling for him to step down as prime minister.
The 94-year-old leader is also expected to "seal the deal" that might see him remain in office, as sources in the ruling coalition have revealed to the New Straits Times that Dr Mahathir has secured a two-thirds majority support in the Dewan Rakyat.
Having such considerable support might mean having the power to jolt naysayers with an ultimatum; that is, the discretion to form a unity government should they disagree with him.
One source said the pre-council meeting today would be an avenue for the top six PH leaders to set the tone of the evening, while the second session would be more of an "announcement meeting".
The six are PH chairman Dr Mahathir, PH president Datuk Seri Dr Wan Azizah Wan Ismail, PKR president Datuk Seri Anwar Ibrahim, Parti Pribumi Bersatu Malaysia president Tan Sri Muhyiddin Yassin, DAP secretary-general Lim Guan Eng and Parti Amanah Negara president Mohamad Sabu.
They are scheduled to meet at 8.30pm at Dr Mahathir's Perdana Leadership Foundation in Putrajaya, while about 20 other PH leaders from PKR, Bersatu, DAP, and Amanah are expected to attend the main presidential council meeting after that.
"A pre-council (meeting) is normal, but this one won't be. We can expect either something juicy or nasty to happen.
"Dr Mahathir is going to seal the deal by telling the other five that he is to remain as prime minister.
"If they disagree, we can expect Dr Mahathir to announce something big," the source said.
It is understood that Dr Wan Azizah does not usually attend the pre-council meeting but would do so this time.
Recently, the Malaysiakini portal quoted a source as saying that Dr Mahathir "wanted" Dr Wan Azizah to be around this time for the meeting as she was considered an "important factor".
As the PH president and deputy prime minister, Dr Wan Azizah carries a lot of weight in the ruling pact and whatever decision she makes on the succession plan will invite controversy, a source said.
"If Dr Wan Azizah chooses Anwar, people will say it's nepotism. If she supports Dr Mahathir, people will say she has family issues.
"Either way, it doesn't look good for Dr Wan Azizah," the source said.
Another source claimed that Anwar and his allies in the PH presidential council are planning to remind Dr Mahathir of the succession plan during the pre-council meeting, in line with the consensus reached by PH leaders before the 14th General Election.
The source said a proposal will be presented at the pre-council meeting to Dr Mahathir, which will cover, among others, Dr Mahathir's role when he passes the baton to Anwar.
"They will try to use the pre-council meeting to confirm Dr Mahathir's resignation. However, if Dr Mahathir declines the proposal, it will then turn into a nasty pre-council meeting.
"Remember, Dr Mahathir already has the two-thirds majority support. The question now is, who will support Anwar?" the source said.
If the claim that Dr Mahathir has secured a two-thirds majority support is true, another source said no one in PH can force the prime minister to resign.
"In fact, I think he (Dr Mahathir) will be happy if anyone from PH tries to propose a vote of no confidence against him in Parliament.
"It's like getting a free ride, or as the perumpamaan (idiom) goes, umpama orang mengantuk disorongkan bantal (getting help at the right time).
"Dr Mahathir has the numbers. He has the support needed. He has promises yet to be fulfilled and he plans on delivering them.
"This is not a man you want to give an ultimatum to. Remember, he was once an activist. You won't see him waving the white flag without putting up a good fight."
A PH leader, who spoke on condition of anonymity, hinted at the possibility of "another big thing" during the first week of this year's Dewan Rakyat session, which will run from March 9 to April 16.
Asked if it involved a cabinet reshuffle or a vote of no confidence, the leader said: "It may be both. It will be huge, nothing you've seen before."
With all the controversies relating to the power transition reaching a boiling point, members of the press are expected to ask hard questions at the media conference after the meeting today.
If their questions remain unanswered, the first week of the Dewan Rakyat sitting might become a platform for Dr Mahathir to reaffirm his stay as prime minister. – NST
Dr Mahathir may issue ultimatum tonight
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PERSPECTIVE January 17, 2021
How many Datuks have been jailed for punching people, for stealing taxpayers' money and committing crimes?
Ten former Bar presidents: PN govt's Emergency laws "dangerous precedent", table in Parliament first...
ISSUES January 17, 2021
The current Emergency on Malaysia is a "dangerous precedent".
PPBM-friendly Umno bigwigs drumming up enough support among leaders to force Zahid to "step...
Some Umno bigwigs are believed to be wooing other supreme council members into supporting PPBM.
Johor Bahru MP Akmal Nasir has urged Muhyiddin Yassin to postpone projects to build three halls in his Pagoh constituency and nearby areas.
Last-minute decision makes it difficult for many parties, especially parents, teachers and students to prepare.
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text:
You Can't Take It With You BROADWAY REVIEWS
Theater: Longacre Theatre / 220 West 48th Street, New York, NY, 10036
Family can do crazy things to people. And the Sycamore family is a little crazy to begin with. Come join 2-time Tony Award winner James Earl Jones as the head of the wackiest household to ever hit Broadway in Kaufman and Hart's Pulitzer Prize-winning classic You Can't Take It With You. He plays wily Grandpa Vanderhof, leader of a happily eccentric gang of snake collectors, cunning revolutionaries, ballet dancers and skyrocket makers. But when the youngest daughter brings her fiancé and his buttoned-up parents over for dinner, that's when the real fireworks start to fly.
NEW YORK TIMES REVIEW OF You Can't Take It With You
Screwball Magic Does the Trick 'You Can't Take It With You,' Handled Properly, Ages Well
September 28, 2014: The only downside to the unconditional upper called You Can't Take It With You, which wafted open last night at the Longacre Theater, is that it may strain previously underused muscles around your mouth. That can happen when you spend two-and-a-half hours grinning like an idiot. A lot of shows can make you laugh. What's rare is a play that makes you beam from curtain to curtain. Such is the effect of Scott Ellis's felicitous revival of Moss Hart and George S. Kaufman's 1936 comedy about one improbably happy family during the Great Depression, which stars a haloed James Earl Jones as the wise old leader of the clan. This is, frankly, surprising news to me. Though it won the Pulitzer Prize for drama, the very mention of You Can't Take It With You is known to elicit shivers of revulsion among people who saw or appeared in high school productions.
NBC NEW YORK REVIEW OF You Can't Take It With You
A Joyous "You Can't Take It With You," with James Earl Jones
Robert Kahn
September 28, 2014: James Earl Jones, more often a lion who roars, instead brings a soft steadiness to his role as the family patriarch in You Can't Take It With You, the Moss Hart-George S. Kaufman comedy—a perennial favorite that first arrived during the Great Depression—now enjoying a revival at the Longacre Theatre. You Can't Take It With You still feels like the perfect escapist comedy for tough times, in spite of its creaky references to "the 48 states" and Eleanor Roosevelt. For that, you can thank a top-notch ensemble that includes Rose Byrne, in an impressive Broadway debut, as well as helmsman Scott Ellis ("Drood"), whose zippy direction brings the play's three acts in at 2 hours and 20 minutes. Byrne, a star of TV's Damages and the foil to Kristen Wiig in Bridesmaids, is Alice, the only conventional member of the happy-go-lucky Sycamore clan. How the Sycamores pay for their magnificent house near Columbia University is anyone's guess, because the family patriarch, Martin Vanderhof—or just "Grandpa" (Jones)—hasn't worked in 35 years.
ASSOCIATED PRESS REVIEW OF You Can't Take It With You
'You Can't Take It With You' Crazy, Uneven
September 28, 2014: You know the play you're watching might be a little long in the tooth when there are jokes about Eleanor Roosevelt, the Works Project Administration and Calvin Coolidge, and it makes reference to the nation's 48 states. As in not 50 yet. The Great Depression was still palpable when Moss Hart and George S. Kaufman wrote their Pulitzer Prize-winning comedy You Can't Take It With You in 1936, some 23 years before Alaska and Hawaii joined the Union. A sweet revival opened Sunday at the Longacre Theatre with a perfectly picked cast but offering little reason why this old chestnut needs to be seen again. It stars a remarkable ensemble that includes such stage luminaries as James Earl Jones, Elizabeth Ashley and Byron Jennings, the British actress Rose Byrne, seasoned veterans Kristine Nielsen and Reg Rogers, rising star Annaleigh Ashford and TV favorite Mark Linn-Baker.
HUFFINGTON POST REVIEW OF You Can't Take It With You
You Can't Take It With You' Takes You With It Merrily
September 28, 2014: On the way into You Can't Take It With You, the revival at the Longacre of the 1936 George S. Kaufman-Moss Hart comedy, I ran into Anne Kaufman Schneider. For those who don't know, Schneider is Kaufman's daughter and the primary keeper (now that Kitty Carlisle Hart is gone) of the collaborators' flame. Since I know her slightly, I said hello and reminded her where we'd met, et cetera. Well worth understanding about Schneider -- at least from what I've picked up in our brief acquaintance -- is that she has inherited two traits from her father: his sense of humor and his suffer-no-deficient-production-gladly attitude. I asked her if she'd seen the new production. (She recalled that she saw the original production when she was nine or so.) She said she'd already attended this one more than once and would be at the opening. Then she said, "It's good."
HOLLYWOOD REPORTER REVIEW OF You Can't Take It With You
Chock full o' nuts and still a delicious treat
David Rooney
September 28, 2014: With its spirited defense of lives lived for sheer joy rather than for achievement, ambition, financial gain or rank, the 1936 play You Can't Take It With You proved an escapist tonic in the midst of the Great Depression. It has remained irresistible in the decades since, in particular to anyone ambivalent about that overrated concept of the work ethic. The prototype for countless comedies about wacky families blithely out of step with the world around them, this giddy romp by Moss Hart and George S. Kaufman is a perennial favorite of high school and community theaters but has been absent from Broadway for 30 years. So it's time to give it a warm welcome back. The deluxe revival is directed with unflagging energy and an assured grasp of the play's shifting rhythms by comedy pro Scott Ellis. This is a work that champions the individualist, and the director follows suit by marshaling his impeccable cast to create loopy characterizations. Yet in what might be the most crucial requirement, they all inhabit the same universe, banding together in defiance of the hard times blighting the nation. That applies whether they are charter members of the eccentric Vanderhof-Sycamore clan or figures drawn either voluntarily or haplessly into the family's chaotic orbit.


Some people love nothing more than giving a good gift. Not just something thoughtful but something unique, rare, and—when it comes to fashion—in season. After all, there's no better feeling than watching your friend or family member's face light up when unwrapping your present, especially when it's in a Gucci box. This year, instead of sifting through hundreds of options, save yourself time and stress and go right to Gucci's latest holiday collection. Filled with updated takes on its classic silhouettes, the brand's bags, jewelry, shoes, and more are sure to catch the eye of your fashion-forward friends. Whether you're opting for the classic GG Marmont Matelassé Leather Bag or something a bit more eye-catching in the form of the Sparkling Swimsuit With Zebra Print, prepare for excessive thank-yous.


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