text:
North Korea fires missiles into sea, fresh nuclear talks in doubt
North Korean leader Kim Jong Un (C) inspecting a newly built submarine at an undisclosed location on Tuesday. KCNA/AFP
North Korea fired two short-range missiles early on Thursday from its east coast, South Korea's military said, the first missile test since leader Kim Jong Un and US President Donald Trump agreed to revive stalled denuclearisation talks.
The missiles, launched from near the coastal city of Wonsan, flew about 430 km (267 miles) out over the sea, reaching an altitude of 50 km (30 miles), before splashing down, an official at South Korea's defence ministry told Reuters.
The firing of ballistic missiles will cast new doubt on efforts to restart denuclearisation talks after Trump and Kim met at the demilitarised zone (DMZ) between the two Koreas at the end of June.
The White House, Pentagon and US State Department did not immediately respond to requests for comment.
A US official, who declined to be identified, said according to initial information at least one short-range projectile was fired from North Korea. Further analysis was underway, the official said.
South Korea had detected related signs prior to the launch and was conducting detailed analysis with the United States, the presidential Blue House said in a statement.
South Korea's defence ministry urged the North to stop acts that are unhelpful for easing tension, saying the latest test posed a military threat.
Japanese Prime Minister Shinzo Abe said the test had no immediate impact on Japan's security, according to Kyodo News.
"We have confirmed that the situation is not one that impacts our country's national security. Going forward, we will work closely with the United States," Abe was quoted as telling reporters in a town west of Tokyo, where he is vacationing.
Trump's national security adviser John Bolton, who has taken a hardline towards North Korea, made no mention of the launches in a tweet on Thursday after a visit to South Korea. He said he had "productive meetings" with Seoul officials on regional security and building a stronger alliance.
TALKS IN DOUBT
After Trump and Kim met last month, the United States and North Korea vowed to soon hold a new round of working-level talks, but Pyongyang has since sharply criticised upcoming joint military drills by US and South Korean troops.
South Korea's ambassador to the United States, Cho Yoon-je, told reporters that Washington had offered to discuss the time and location of such talks but there had been no response from Pyongyang.
US Secretary of State Mike Pompeo and North Korea's foreign minister are expected to meet on the sidelines of a Southeast Asian security forum in Bangkok next week, but diplomatic sources said nothing had been decided.
North Korea's Foreign Ministry said this month that a US pattern of "unilaterally reneging on its commitments" by holding military exercises with South Korea was leading North Korea to reconsider its commitments to discontinue tests of nuclear weapons and intercontinental ballistic missiles.
North Korea's last weapons testing in May included short-range missiles as well as smaller rockets. At the time, Kim oversaw the first flight of a previously untested weapon - a relatively small, fast missile that experts believe will be easier to hide, launch and manoeuvre in flight.
On Tuesday, the North's KCNA news agency reported that Kim inspected a large, newly built submarine, accompanied by missile programme leaders, in a possible signal of the continued development of a submarine-launched ballistic missile programme.
"By firing missiles, taking issue with military drills and showing a new submarine, the North is sending one clear message: there might be no working-level talks if the United States doesn't present a more flexible stance," said Kim Hong-kyun, a former South Korean nuclear envoy.
Kim Dong-yup, a former navy officer who now teaches at Kyungnam University in Seoul, said the weapons tested on Thursday appeared to be the same as the ones tested in May, which were less of a challenge than long-range missiles but "enough to subtly pressure" the United States.
"North Korea is clearly upset that the US and South Korea are conducting joint military exercises," said Harry Kazianis of Washington's Center for the National Interest.
"We should not be shocked by this move and, in fact, we should have seen it coming."
Nuclear talks between North Korea and the United States stalled after a second summit between Trump and Kim in Vietnam in February broke down.
Trump has repeatedly stressed his good relationship with Kim and is keen for a big foreign policy win as he campaigns for re-election in 2020.
On Monday, Trump stressed North Korea's freeze in testing of nuclear weapons and long-range missiles, which has been in place since 2017, and positive recent exchanges.
"There was a little correspondence recently," he said. "We had very positive correspondence with North Korea. Again there's no nuclear testing, there's no missile testing, there's no nothing."
North Korea Missiles Kim Jong Un US Donald Trump
North Korea's ruling party to meet amid 'tense situation': state media
North Korea will hold a plenary session of its ruling party's central committee on Wednesday, a day after leader Kim Jong Un chaired a politburo meeting to discuss ways to make progress under the "prevailing tense situation," state media reported.
Trump invites Kim to DMZ meeting
US President Donald Trump on Saturday invited North Korean leader Kim Jong Un to meet for a historic handshake at the demilitarised zone (DMZ) that divides the Korean peninsula, and said he would have "no problem" stepping over the border.
US, North Korea agree at DMZ to resume stalled nuclear talks: Trump
After shaking hands with Kim over the line that marks where their two countries and their allies fought each other to a standstill in the 1950-53 Korean War, Trump walked for several steps into North Korean territory, before another handshake.
Xi urged Trump to ease North Korea sanctions in 'timely' fashion
Xi "pushed for the US to show flexibility and meet the DPRK (North Korea) halfway, including the timely easing of sanctions against the DPRK and finding a solution to each other's concerns through dialogue," Wang Yi told reporters.
UAE announces record 3,506 new coronavirus cases, six deaths in last 24 hours
The EU and the United States are the world's top trading powers, along with China, and have close cultural, historical, business and defence ties, but Donald Trump sought to sideline the EU, championing Britain's departure from the bloc.


OTTER SINGLES is a wonderful base of squishy, bouncy, soft yarn. The 100% Extra Fine Superwash Merino makes it next to skin soft and perfect for garment or shawl knitting.
While Otter Singles is superwash treated, and this yarn can withstand machine washing up to 30°C, we do advise you to hand wash all finished items with a mild wool-specific detergent (like Soak) to keep them in your life as long as possible. Otter Singles yarn is sourced from European non-mulesing breeders and is OEKO-TEX® Class I certified.


text:
Ormskirk, England
Edge Hill, ranked Gold in the Teaching Excellence Framework, is a campus university with a mission to create opportunity from knowledge.
St Helens Rd,
L39 4QP
About Edge Hill University
Factsheet about: Edge Hill University
Please provide us with a short blurb about the university. Edge Hill is a leading campus based University close to the vibrant city of Liverpool. We are proud to have won several prestigious awards such as 'University of the Year 2014/15' by the Times Higher Education, 'Gold' award for Teaching & Learning, 2017. Top 10 in the UK for teaching quality in the Times/Sunday Times Good University Guide 2017 and Winner of the What Uni Student Choice Awards for our accommodation 2017
Stuart Maconie, Jonathan Pryce, Kerry Howard
Our combination of beautifully landscaped grounds, state-of-the-art facilities, historic architecture, lakes and even a beach provides a unique and innovative place to study. Industry standard resources and cutting edge technology ensure a truly interactive student experience, complemented by 60 acres of sport and leisure facilities, more than 2,200 rooms in halls of residence, and plenty of places to study, socialise and relax.
Major campus developments completed in the last six years include a £13 million Technology Hub, £30 million Sports Centre, £17 million Creative Edge building, suites of brand new Biology and Geography laboratories, a newly developed Arts Centre and a £13.5 million Student Hub. Our halls of residence have also undergone significant expansion.
Work is currently getting underway on a £36 million development that will include a new Library and Student Services Centre, as well as dedicated accommodation for senior undergraduate (Year 2 upwards) and postgraduate students.
We also have a range of subject specific facilities which can be viewed on our website
Closest airport to the university? We are fortunate enough to be in close proximity to both Liverpool and Manchester airport. We are approximately 30 minutes from Liverpool airport and 45 minutes from Manchester airport. There are regularly scheduled flights between these airports
The Students' Union manages over 70 societies which bring a diverse, dynamic and fun variety of student-led activities to the campus.
Being a member of a society will give you the chance to meet likeminded people, make new friends and enrich your student life
With so many options to choose from, there really is something for everyone.
Examples of clubs include, Disney, Harry Potter, African & Caribbean, Music Clubs and Societies, LGBT Society, Murder Mystery and a huge variety of sports societies
We have a wide range of Bursaries and Scholarships. We are consistently reviewing our opportunities.
For the latest information please see our handy Money Matters guide: https://www.edgehill.ac.uk/study/money-matters/
Internships/Placement/Study abroad opportunities? We offer a huge range of on course placement opportunities as well and Study Aboard and Erasmus opportunities.
We have lots of accommodation options for our students including, catered and self-catered. Voted the best student accommodation in the UK (National Student Housing Survey Awards 2016), our halls of residence are at the heart of our vibrant on-campus community, providing a safe environment in which new students can live, study and socialise.
They offer excellent value for money, with a range of rooms and catering packages available depending on your requirements and your budget. You will find everything you need is just a few minutes' walk from your room.
All the costs and the different accommodation options can be found here: https://www.edgehill.ac.uk/study/accommodation/
Link to university website www.edgehill.ac.uk

redpajama_set_name: RedPajamaCommonCrawl


text:
46 Different Types of Democracy
December 16, 2020 April 15, 2020 by Jamie
For citizens of the United States, a representative democracy is all that many of us have known. But did you know that there are actually many different kinds of democracies in the world today and throughout history?
Types of Democracy
1. Direct Democracy
2. Representative Democracy
3. Liberal Democracy
4. Electoral Democracy
5. Dominant-party System
6. Parliamentary Democracy
7. Westminster Democracy
8. Presidential Democracy
9. Jacksonian Democracy
10. Soviet Democracy (Council Democracy)
11. Totalitarian Democracy
12. Demarchy (Lottocracy)
13. Non-Partisan Democracy (No-Party Democracy)
14. E-Democracy
15. Bioregional Democracy
16. Cellular Democracy
17. Workplace Democracy
18. Christian Democracy
19. Islamic Democracy
20. Jewish and Democratic State
21. Theodemocracy
22. Anticipatory Democracy
23. Associationalism (Associative Democracy)
24. Adversialism (Adversial Democracy)
25. Bourgeois Democracy
26. Consensus Democracy
27. Constitutional Democracy
28. Delegative Democracy
29. Deliberative Democracy
30. Democratic Centralism
31. Democratic Dictatorship
32. Democratic Republic
33. Economic Democracy
34. Ethnic Democracy
35. Grassroots Democracy
36. Guided Democracy (Managed Democracy)
37. Interactive Democracy
38. Jeffersonian Democracy
39. Market Democracy
40. Multiparty Democracy
41. New Democracy
42. Participatory Democracy
43. People's Democracy
44. Radical Democracy
45. Semi-Direct Democracy
46. Sociocracy
A direct democracy places all power in the hands of the individual. When political decisions have to be made, all people gather together and individuals cast a vote. In theory, this sounds like the ideal form of government but it fails in many areas.
As political communities alter and develop, so does our understanding of how democracy should be implemented. This political agreement establishes an intermediary political actor between the individual and the policy outputs of the state. In the case of the United States, elected officials represent groups of people whether it be on a local or national level.
A liberal democracy is a political ideology and a structure of government in which representative democracy operates under the principles of classical liberalism.
An electoral democracy is a kind of representative democracy based on election, on electoral vote, as modern occidental or liberal democracies. Dominant-party system – Democratic Party system where only one political party can rationally become the government, by itself or in an alliance government
A dominant-party system or one-party dominant system is a system where there is "a category of parties/political organizations that have successively won election victories and whose upcoming defeat cannot be envisaged or is improbable for the foreseeable future."
There are more parliamentary systems in the world than presidential democracies. As the name implies, parliamentary systems are distinct for the reason that of the power that they place in the hands of the legislative branch. Examples of this type of system are Germany and the United Kingdom.
The Westminster system is a parliamentary system of government modeled following that which developed in the United Kingdom. This name comes from the Palace of Westminster, the seat of the British parliament.
There are lesser presidential democracies in the world, and they are centrally placed in the Americas (North America, Central America, and South America). Scholars say that while parliamentary democracies are more representative, they are also fewer firms for many of the reasons cited above.
A Jacksonian democracy is the political movement throughout the Second Party System toward larger democracy for the frequent man symbolized by American politician Andrew Jackson and his supporters.
Soviet democracy (sometimes called a council democracy) was a political system in the Soviet Union, in which workers' councils named "soviets" (Russian for "council"), consisting of delegates, formed organs of legislative and executive power.
A system of government in which elected representatives make decisions on behalf of an entire country. Though granted the right to vote, citizens have little to no participation or voice in the decision-making course of the government and are simply followers.
Demarchy is a form of government in which the state is governed by randomly chosen decision makers who have been selected by sortition from a mostly inclusive pool of eligible citizens.
Nonpartisan democracy (also no-party democracy) is a system of representative government or organization such that universal and periodic elections take place without reference to political parties.
It is a form of government in which all adult citizens are supposed to be eligible to participate equally in the proposal, development, and creation of laws. An E-democracy encompasses social, economic and cultural conditions that allow the free and equal practice of political self-determination.
Bioregionalism is a political, cultural, and ecological system or set of views based on naturally defined areas called bioregions, like eco-regions. Bioregions are defined through physical and environmental features, such as watershed boundaries and soil and terrain characteristics.
As developed by geolibertarian political economist Fred E. Foldvary, cellular democracy is a model of democracy based on multi-level bottom-up structure based on either small neighborhood governmental districts or contractual communities.
A workplace democracy is the application of democracy in all its forms (including voting systems, debates, democratic structuring, due process, adversarial process, systems of appeal) to the workplace.
A Christian democracy is a political belief which emerged in nineteenth-century Europe under the influence of conservatism and Catholic social teaching.
An Islamic democracy is political beliefs that seek to apply Islamic principles to public policy within a democratic framework. Islamic political theory specifies three basic features of an Islamic democracy: leaders must be elected by the people, subject to sharia and dedicated to practicing "shura", a special form of consultation practiced by Prophet Muhammad, which one can find in various hadiths, with their community.
"Jewish and Democratic State" is the Israeli legal description of the nature and character of the State of Israel. The "Jewish" nature was first described within the Declaration of Independence of 1948.
Theodemocracy is a theocratic political system as well as elements of democracy, first theorized by Joseph Smith, founder of the Latter Day Saint movement (Mormonism), in the early nineteenth century.
Anticipatory democracy is a theory of civics relying on democratic decision making that takes into report predictions of future events that have some credibility with the electorate.
Associationalism is a political project where "human welfare and liberty are both best served when as many of the affairs of a society as possible are managed by voluntary and democratically self-governing associations."
The use of a voting system to decide candidates to hold political and military power is often necessarily adversarial. This process requires each candidate to convince voters that they are more trustworthy in the anticipated future circumstances, than their opponent.
A Bourgeois democracy is essentially a government that provides the interests of the bourgeois class.
A consensus democracy is the application of consensus decision-making to the process of legislation in a democracy.
A constitutional democracy is a system of government in which the confines of political authority are evidently stated and the electorate has the power to remove poor performing governments.
A delegative democracy, also named as liquid democracy, is a form of democratic control whereby an electorate vests voting power in delegates rather than in representatives. The word is a generic description of either already-existing or proposed popular-control apparatuses.
A deliberative democracy or discursive democracy is a form of democracy in which deliberation is central to decision-making. It adopts elements of together consensus decision-making and majority rule.
Democratic centralism is a Leninist organizational system in which policy is decided centrally and is required on all members.
"People's democratic dictatorship" is a saying incorporated into the Constitution of the People's Republic of China by Mao Zedong, leader the Communist Party of China.
A democratic republic is, firmly speaking, a country that is both a republic and a democracy. It is one where final authority and power is from the citizens, and the government itself is run through elected officials.
An economic democracy or stakeholder democracy is a socioeconomic philosophy that offers to shift decision-making power from corporate managers and corporate shareholders to a larger group of public stakeholders such as workers, customers, suppliers, neighbors and the broader public.
An ethnic democracy is a political system that joins a structured ethnic dominance with democratic, political and civil rights for all. Both the dominant ethnic group and the minority ethnic groups have citizenship and are capable to fully take part in the political process.
A grassroots democracy is a tendency towards designing political courses where as much decision-making authority as practical is transferred to the organization's lowest geographic or social level of organization.
A guided democracy, also known as managed democracy, is a democratic government with increased autocracy. Governments are legitimated by elections that are free and fair but emptied of substantive meaning in their ability to modify or change the state's policies, motives, and goals.
An interactive democracy is a kind of democracy that promotes direct interaction in order to create a fairer society according to the articulated will of the people. Interactive democracy is by its very nature 'interactive'.
A Jeffersonian democracy (occasionally capitalized), called after its advocate Thomas Jefferson, was one of two dominant political outlooks and movements in the United States from the 1790s to the 1820s.
A market democracy is not the democracy that Plato spoke of in his Republic as "a charming form of government, full of assortment and disorder, and providing a kind of equality to equals and uneven alike," nor that Aristotle in his Rhetoric chided as "when put to the strain, grows weak, and is supplanted by oligarchy."
A multi-party democracy is a system in which multiple political parties along the political spectrum run for national election, and all have the ability to get control of government offices, separately or in coalition.
A new democracy or the New Democratic Revolution is a idea based on Mao Zedong's "Bloc of Four Social Classes" theory.
A participatory democracy highlights the broad contribution of constituents in the direction and operation of political systems
A people's democracy (Marxism–Leninism), an ideological idea visualized by the Soviet Union in the aftermath of World War II
A radical democracy was expressed by Ernesto Laclau and Chantal Mouffe in their book Hegemony and Socialist Strategy: Towards a Radical Democratic Politics, written in 1985.
A semi-direct democracy is one of numerous systems in which direct democracy is moderated by mandatory formal mechanisms that force a degree of thought or expert input into the process of setting questions that are answered by votes.
Sociocracy is a system of governance using approval or consent in decision making and an organizational organization based on cybernetic principles.
Categories History & Culture


text:
NZ India clash in final T20 today
HAMILTON: India will look to end what has been a fine tour of New Zealand on a terrific high when the teams clash in the third and final Twenty20 International in Hamilton on Sunday.
The sides are locked 1-1 in the three-match series. India had a poor outing in Wellington, where they were bundled out for 139 chasing 220. They fought back in Auckland after all departments came together in a seven-wicket triumph.
They now have a chance to win a T20I series in New Zealand, having not even had a victory in the format in these parts till Friday.
That said, India's reaction to defeats have been particularly noteworthy so far this series. When they were bundled out for 92 in an eight-wicket loss in the fourth ODI, they managed to secure a fighting victory in the final ODI in Wellington.
Similarly, after going down in the first T20I, the team came together in the second match, winning quite comfortably in Auckland to level the series.
But what will particularly please the management is how the revival has been led by the players who needed to make their mark — Ambati Rayudu and Vijay Shankar starred in the victory in the final ODI and it was Krunal Pandya and Rishabh Pant, playing just his second match in the series, leading things on Friday.
That's already a lot of positives from the series, something especially pertinent given India have been experimenting with combinations and personnel ahead of the 2019 ICC Men's Cricket World Cup.
The visitors are unlikely to be satiated with that, though. They will want to bring an end to what has been a fine few months on the road with another series win.
That's easier said than done, of course. New Zealand have posed more of a threat in the latter part of India's tour, and have been a force in the shortest format.
Even in defeat in the second T20, New Zealand had some positives, particularly in the performance of Colin de Grandhomme, who scored a 28-ball 50, and Ross Taylor (42 off 36).
Furthermore, they will be aware India have struggled with the moving ball this series — that collapse for 92 in the fourth ODI came in Hamilton — and the likes of Tim Southee, Scott Kuggeleijn and de Grandhomme will be hoping to once again inflict some pain on the Indian batsmen on Sunday.
They will miss Lockie Ferguson — he makes way for the uncapped Blair Tickner for the final match of the series.
NZ India clash in final T20 today	2019-02-10
Pakistan vs England 4th ODI Match preview
$10 million prize pot for ICC Cricket World Cup 2019
The fans drive me to go on' Gayle on what pushes him to win the World Cup 2019
Pakistan prevent series whitewash win third T20 against South Africa
Leach tells England to improve not complain about pitches
Pakistan ODI squad named for Australia series in UAE
Islamabad vs Lahore Two-time champs take on three-time bottom dwellers in PSL 4 opener
Pak Vs Aus 1st ODI Dailymotion Full Highlights-22 March 2019
Highest wicket-taker in Pakistan Super League 2019
Pakistan India World Cup 2019 clash will go ahead as scheduled ICC
Shane Watson looks back at his winning over and batting for Quetta Gladiators in PSL 4
Mohammad Amir to undergo medical examination ICC Cricket World Cup 2019
London: Mohammad Amir was due to undergo a medical examination on Friday. Although uncertainty surrounds the ...


text:
Thought Broadcast
A Psychiatrist's Thoughts – Straight To Your Head
The Carlat Psychiatry Report
The Carlat Child Psychiatry Report
The Carlat Behavioral Health Report
Mental Illness and Social Realities
Does the definition of "mental illness" differ from place to place? Is there a difference between "depression" in a poor individual and in one of means? Are the symptoms identical? What about the neurobiology? The very concept of a psychiatric "disease" implies that certain core features of one's illness transcend the specifics of a person's social or cultural background. Nevertheless, we know that disorders look quite different, depending on the setting in which they arise. This is why people practice psychiatry, not computers or checklists. (Not yet, at least.)
However, sometimes a person's environment can elicit reactions and behaviors that might appear—even to a trained observer—as mental illness. If unchecked, this may create an epidemic of "disease" where true disease does not exist. And the consequences could be serious.
For the last three years, I have had the pleasure of working part-time in a community mental health setting. Our clinic primarily serves patients on Medicaid and Medicare, in a gritty, crime-ridden expanse of a major city. Our patients are, for the most part, impoverished, poorly educated, have little or no access to primary care services, and live in communities ravaged by substance abuse, crime, unemployment, familial strife, and a deep, pervasive sense of hopelessness.
Even though our resources are extremely limited, I can honestly say that I have made a difference in the lives of hundreds, if not thousands, of individuals. But the experience has led me to question whether we are too quick to make psychiatric diagnoses for the sake of convenience and expediency, rather than on the basis of a fair, objective, and thorough evaluation.
Almost predictably, patients routinely present with certain common complaints: anxiety, "stress," insomnia, hopelessness, fear, worry, poor concentration, cognitive deficits, etc. Each of these could be considered a feature of a deeper underlying disorder, such as an anxiety disorder, major depression, psychosis, thought disorder, or ADHD. Alternatively, they might also simply reflect the nature of the environment in which the patients live, or the direct effects of other stressors that are unfortunately too familiar in this population.
Given the limitations of time, personnel, and money, we don't usually have the opportunity for a thorough evaluation, collaborative care with other professionals, and frequent follow-up. But psychiatric diagnostic criteria are vague, and virtually everyone who walks into my office endorses symptoms for which it would be easy to justify a diagnosis. The "path of least" resistance" is often to do precisely that, and move to the next person in the long waiting-room queue.
This tendency to "knee-jerk" diagnosis is even greater when patients have already had some interaction—however brief—with the mental health system: for example, a patient who visited a local crisis clinic and was given a diagnosis of "bipolar disorder" (on the basis of a 5-minute evaluation) and a 14-day supply of Zyprexa, and told to "go see a psychiatrist"; or the patient who mentioned "anxiety" to the ER doc in our county hospital (note: he has no primary care MD), was diagnosed with panic disorder, and prescribed PRN Ativan.
We all learned in our training (if not from a careful reading of the DSM-IV) that a psychiatric diagnosis should be made only when other explanations for symptoms can be ruled out. Psychiatric treatment, moreover, should be implemented in the safest possible manner, and include close follow-up to monitor patients' response to these interventions.
But in my experience, once a patient has received a diagnosis, it tends to stick. I frequently feel an urge to un-diagnose patients, or, at the very least, to have a discussion with them about their complaints and develop a course of treatment—which might involve withholding medications and implementing lifestyle changes or other measures. Alas, this takes time (and money—at least in the short run). Furthermore, if a person already believes she has a disorder (even if it's just "my mother says I must be bipolar because I have mood swings all the time!!!"), or has experienced the sedative, "calming," "relaxing" effect of Seroquel or Klonopin, it's difficult to say "no."
There are consequences of a psychiatric diagnosis. It can send a powerful message. It might absolve a person of his responsibility to make changes in his life—changes which he might indeed have the power to make. Moreover, while some see a diagnosis as stigmatizing, others may see it as a free ticket to powerful (and potentially addictive) medications, as well as a variety of social services, from a discounted annual bus pass, to in-home support services, to a lifetime of Social Security disability benefits. Very few people consciously abuse the system for their own personal gain, but the system is set up to keep this cycle going. For many, "successful" treatment means staying in that cycle for the rest of their lives.
The patients who seek help in a community mental health setting are, almost without exception, suffering in many ways. That's why they come to see us. Some clinics do provide a wide assortment of services, including psychotherapy, case management, day programs, and the like. For the truly mentally ill, these can be a godsend.
For many who seek our services, however, the solutions that would more directly address their suffering—like safer streets, better schools, affordable housing, stable families, less access to illicit drugs, etc.—are difficult or costly to implement, and entirely out of our hands. In cases such as these, it's unfortunately easier to diagnose a disease, prescribe a drug which (in the words of one of my colleagues) "allows them to get through just one more night," and make poor, unfortunate souls even more dependent on a system which sees them as hopeless and unable to emerge from the chaos of their environment.
In my opinion, that's not psychiatry. But it's being practiced every day.
13 Comments | epidemiology, mental health | Tagged: community psychiatry, disability, society | Permalink
Posted by stevebMD
Steve Balt
All posts, unless otherwise noted, are written by Steve Balt, MD. Read more about Dr. Balt on his About Me page.
Get CMEs
Subscribe to The Carlat Psychiatry Report today for an easy, inexpensive way to fulfill your CME requirements.
If Medications Don't Work, Why Do I Prescribe Them Anyway?
Explain To Me Again Why Psychologists Can't Prescribe Meds?
My Own Bipolar Kerfuffle
Is James Holmes Mentally Ill? Does It Matter?
Turf Wars
What Adderall Can Teach Us About Medical Marijuana
The Evidence of the Anecdote
"Patient-Centered" Care and the Science of Psychiatry
Addiction Psychiatry and The New Medicine
Is The Joke On Me?
What's the Proper Place of Science in Psychiatry and Medicine?
Depression Tests: When "Basic" Research Becomes "Applied"
Yes, We Still Need Psychiatrists, But For What?
Did The APA Miss A Defining Moment?
The Problem With Organized Psychiatry
The Well Person
Is The Criticism of DSM-5 Misguided? Part II
1 Boring Old Man
Before You Take That Pill
Behavenet
Carlat Psychiatry Blog
David M Allen's blog
Health Care Renewal
Medscape Mental Health
NY Times Health Reform Blog
Placebo Journal
Shrink Rap
The Health Care Blog
The Last Psychiatrist
The Practical Psychosomaticist
The Sports Psychiatrist
The Trusting Heart
A blog about the practice of psychiatry... and all the things that make a thoughtful psychiatrist go hmmm...
psychiatry, medicine, health care


text:
\section{Introduction}

{}Foreign exchange (FX) rates in target zones have been studied extensively.\footnote{\, For a literature survey, see, {\em e.g.}, (Duarte {\em et al}, 2013). For a partial list (with some related literature, including on option pricing), see, {\em e.g.},
(Andersen {\em et al}, 2001),
(Anthony and MacDonald, 1998),
(Ayuso and Restoy, 1996),
(Ball and Roma, 1994),
(Bauer {\em et al}, 2009),
(Beetsma and Van Der Ploeg, 1994),
(Bekaert and Gray, 1998),
(Bertola and Caballero, 1992),
(Bertola and Svensson, 1993),
(Black and Scholes, 1973),
(Bo {\em et al}, 2011a, 2001b),
(Campa and Chang, 1996),
(Carr {\em et al}, 1998),
(Carr and Jarrow, 1990),
(Carr and Linetsky, 2000),
(Cavaliere, 1998),
(Chinn, 1991),
(Cornell, 2003),
(Christensen {\em et al}, 1998),
(De Jong, 1994),
(De Jong {\em et al}, 2001),
(Delgado and Dumas, 1992),
(Dominquez and Kenen, 1992),
(Driffill and Sola, 2006),
(Duarte {\em et al}, 2010),
(Dumas {\em et al}, 1995a, 1995b),
(Edin and Vredin, 1993),
(Edison {\em et al}, 1987),
(Flood and Garber, 1991),
(Flood {\em et al}, 1991),
(Garman and Kohlhagen, 1983),
(Grabbe, 1983),
(Harrison, 1985),
(Harrison and Pliska, 1981),
(Honogan, 1998),
(Hull and White, 1987),
(Kempa and Nelles, 1999),
(Klaster and Knot, 2002),
(Klein and Lewis, 1993),
(Koedijk {\em et al}, 1998),
(Krugman, 1991, 1992),
(Lai {\em et al}, 2008),
(Larsen and S{\o}rensen, 2007),
(Lin, 2008),
(Lindberg and S\"oderlind, 1994a, 1994b),
(Lindberg {\em et al}, 1993),
(Linetsky, 2005),
(Lundbergh and Ter\"asvirta, 2006),
(Magnier, 1992),
(McKinnon, 1982, 1984),
(Meese and Rose, 1990, 1991),
(Merton, 1973, 1976),
(Miller and Weller, 1991),
(Mizrach, 1995),
(Obstfeld and Rogoff, 1995),
(Rangvid and S{\o}rensen, 2001),
(Rose and Svensson, 1995),
(Saphores, 2005),
(Serrat, 2000),
(Slominski, 1994),
(Smith and Spencer, 1992),
(Sutherland, 1994),
(Svensson, 1991a, 1991b, 1992a, 1992b, 1993, 1994),
(Taylor and Iannizzotto, 2001),
(Torres, 2000a, 2000b),
(Tronzano {\em et al}, 2003),
(Veestraeten, 2008),
(Vlaar and Palm, 1993),
(Ward and Glynn, 2003),
(Werner, 1995),
(Williamson, 1985, 1986, 1987a, 1987b, 1989, 2002),
(Williamson and Miller, 1987),
(Yu, 2007),
(Zhang, 1994),
(Zhu, 1996),
and references therein.
}
Following Krugman (1991), the FX rate confined to a band with barriers is modeled as a stochastic process, where one needs to deal with the boundaries. There are essentially two choices: i) attainable boundaries, where the process is allowed to touch a boundary -- in this case the boundaries must be reflecting (see below); and ii) unattainable boundaries, where the process can get infinitesimally close to a boundary without ever touching it -- this is achieved by having the volatility of the process tend to zero (fast enough) as the process approaches a boundary. The unattainable boundary approach has been explored to a greater extent as dealing with reflecting boundaries can be tricky. However, with unattainable boundaries the underlying math typically is rather involved; {\em e.g.}, the pricing PDE for simple FX options (European call/put) either must be solved numerically or involves complicated special functions. Simply put, analytical tractability is challenging.

{}In this note we discuss -- in what is intended to be a pedagogical fashion -- FX option pricing in target zones with attainable boundaries. The basic idea behind option pricing in the presence of boundaries is no different than in the case without boundaries: we must construct a self-financing hedging strategy which replicates the claim at maturity. To do this, we must construct a discounted FX rate process and find a measure under which it is a martingale -- the risk neutral measure -- which is the requirement that there be no arbitrage. Then the option price is expressed via a conditional expectation of the discounted claim under this risk neutral measure, which leads to a Black-Scholes-like PDE. The key difference is that now, together with the terminal condition at maturity, we must also specify boundary conditions.

{}These boundary conditions must be reflecting, that is, they must be Neumann boundary conditions. This follows from the requirement that the identity process be a martingale under the risk neutral measure: simply put, the risk neutral measure must be normalized to 1 when summing over all possible outcomes, and this invariably forces reflecting boundary conditions. Put another way, if the boundary conditions are not reflecting, probability ``leaks" through the boundaries.

{}Reflecting boundary conditions imply that the differential short-rate -- the difference between the foreign and domestic short-rates -- cannot be constant; in fact, it cannot even be deterministic. This is a consequence of the requirements that: i) there be no arbitrage; ii) the FX rate be positive; and iii) the attainable boundaries be reflecting. Moreover, the requirement that the discounted FX rate be a martingale under the risk neutral measure fixes the differential short rate in terms of the functional form of the FX rate process as a function of the underlying Brownian motion together with the (generally, non-deterministic) drift and the volatility. This has a natural financial interpretation, to wit, as the Uncovered Interest Parity.

{}In most practical applications the width of the band is narrow\footnote{\, {\em E.g.}, the USD/HKD spread trades between 7.75 and 7.85, a band fixed by the Hong Kong Monetary Authority.}. This allows to take a pragmatic approach and pick the functional form of the FX rate process based on computational convenience. With a thoughtful choice, the FX option pricing problem can be solved analytically. In fact, the European call and put (and related) option prices are expressed via (fast converging) series of elementary (trigonometric) functions. We discuss the general approach to solving the pricing PDE and explicit examples. This includes analytically tractable models with (non-Ornstein-Uhlenbeck) mean-reversion, which are also solvable in elementary functions.

{}The remainder of this note is organized as follows. In Section \ref{sec3} we briefly review the general procedure for pricing FX options, with self-financing replicating strategies briefly reviewed in Appendix \ref{app.self-fin}. In Section \ref{sec4} we discuss pricing FX options in the presence of attainable reflecting boundaries, including hedging, European call and put options, explicit models, {\em etc.}, with some details relegated to Appendix \ref{app.0} and Appendix \ref{app.A}. We briefly conclude with some remarks in Section \ref{sec5}.

\section{FX Options}\label{sec3}

{}Let us assume that the domestic currency ({\em e.g.}, USD) is freely traded with no restrictions, whereas the foreign currency ({\em e.g.}, HKD) trades inside a target zone. We have a domestic cash bond $B^d_t$ and a foreign cash bond $B^f_t$. We also have the exchange rate $S_t$, which, for our purposes here, is the worth of one unit of the domestic currency in terms of the foreign currency ({\em e.g.}, in our USD/HKD example, $S_t$ is the HKD worth of 1 USD, whose target zone is 7.75 to 7.85). We will refer to tradables denominated in the foreign (domestic) currency as foreign (domestic) tradables. We are interested in pricing derivatives from a {\em foreign} investor's perspective. The foreign cash bond $B^f_t$ is a foreign tradable; however, $B^d_t$ and $S_t$ are not. We can construct another foreign tradable via
\begin{equation}
 {\widetilde S}_t \equiv B^d_t S_t
\end{equation}
(In our USD/HKD example above, this is the HKD value of the USD cash bond). The discounted process, which must be a martingale under the risk-neutral measure ${\bf Q}$ (see Appendix \ref{app.self-fin}), is given by
\begin{equation}\label{ZX}
 Z_t = (B^f_t)^{-1}{\widetilde S}_t = B_t^{-1} S_t
\end{equation}
where
\begin{equation}\label{eff.cash}
 B_t \equiv B^f_t / B^d_t
\end{equation}
The price of a claim $Y_T$ is given by (see Appendix \ref{app.self-fin})
\begin{equation}
 {\widetilde V}_t = B^f_t~\mathbb{E}\left((B^f_T)^{-1} Y_T\right)_{{\bf Q},{\cal F}_t}
\end{equation}
The foreign monetary authority, which confines the foreign currency to the target zone, (in theory) also adjusts the foreign interest rates based on the domestic interest rates and the FX rate. Therefore, we can assume that the domestic cash bond $B_t^f$ is deterministic within the (short enough) time horizons we are interested in for the purpose of pricing FX derivatives.\footnote{\, More generally, we can assume that any volatility in the domestic bond $B_t^d$ is uncorrelated with the volatility in the FX rate $S_t$ and the volatility in the foreign bond $B_t^f$, or, more precisely, any such correlation is negligible at relevant time horizons. This would not alter any of the subsequent discussions or conclusions, so for the sake of simplicity we will assume that $B_t^d$ is deterministic.}  For the claim price we then have
\begin{eqnarray}
 &&{\widetilde V}_t = B_t^d(B_T^d)^{-1}V_t\label{tildeV}\\
 &&V_t \equiv B_t~\mathbb{E}\left(B_T^{-1} Y_T\right)_{{\bf Q},{\cal F}_t}
\end{eqnarray}
Note that $B_t$ defined in (\ref{eff.cash}) is the ratio of the two cash bonds. We can define the corresponding differential (or ``effective") short-rate process via:
\begin{equation}
r_t \equiv {d\ln(B_t)\over dt} = r^f_t - r^d_t
\end{equation}
where $r^f_t$ and $r^d_t$ are the foreign and domestic short-rate processes:
\begin{eqnarray}
 &&r_t^f \equiv {d\ln(B^f_t)\over dt}\\
 &&r_t^d \equiv {d\ln(B^d_t)\over dt}
\end{eqnarray}
Note, however, that $r_t$ need not be positive. Also, here we are assuming that $r_t^d$ is deterministic; however, $r_t^f$ is not, nor is $r_t$. With this assumption, using (\ref{tildeV}), we can compute the actual price ${\widetilde V}_t$ of the claim $Y_T$ by computing the would-be ``price" $V_t$ of the claim $Y_T$ with $S_t$ and $B_t$ playing the roles of the tradable and the numeraire, respectively (see Appendix \ref{app.self-fin}). In the following, for the sake of notational and terminological convenience and brevity,\footnote{\, Alternatively, we can set $r_t^d$ to zero, so $B_t$ is the same as the foreign cash bond $B_t^f$, and restore the (deterministic) $r_t^d$ dependence at the end by multiplying all derivative prices by $B_t^d(B_T^d)^{-1}$.} we refer to $B_t$ as the cash bond, $r_t$ as the short-rate, and $V_t$ as the claim price; also, we refer to the FX rate $S_t$ as FXR.\footnote{\, FX has an analog in equities. Consider a stock with a continuous dividend rate $\delta_t$. Then the risk-free interest rate is analogous to the domestic short-rate, the dividend rate $\delta_t$ is analogous to the foreign short-rate, and the stock is analogous to the foreign currency (so the stock price is analogous to the worth of one unit of the foreign currency in terms of the domestic currency).}

\section{Pricing with Boundaries}\label{sec4}
\subsection{Martingales without Boundaries}

{}When we have no boundaries, typically we can construct a nontrivial martingale $Z_t$ other than the identity $I_t$. Thus, consider the transition density\footnote{\, {\em I.e.}, the probability density of starting from $W_t = z$ and ending at $W_{t^\prime} = z^\prime$, where $t^\prime > t$.}  for a ${\bf Q}$-Brownian motion $W_t$ (taking values on the entire real axis, $W_t\in {\bf R}$), which is the usual Gaussian distribution:
\begin{equation}
 P(t,z;t^\prime,z^\prime) = {1\over\sqrt{2\pi\left(t^\prime-t\right)}}~\exp\left(-{\left(z^\prime-z\right)^2\over 2\left(t^\prime-t\right)}\right)
\end{equation}
The identity $I_t$ is a martingale under this measure. However, there also exist other martingales, {\em e.g.}, $Z_t = W_t$ is a martingale, and so is
\begin{equation}\label{log.norm}
 Z_t \equiv S_0\exp\left(\sigma W_t - \sigma^2 t/2\right)
\end{equation}
where $S_0$ and $\sigma$ are constant.\footnote{\, In the log-normal Black-Scholes model the discounted process $B_t^{-1}S_t$ is given by (\ref{log.norm}).}

\subsection{Boundaries}

{}When boundaries are present, things are trickier. Thus, let us consider the process (here $W_t$ is a ${\bf Q}$-Brownian motion)
\begin{equation}\label{X}
 dX_t = \sigma(X_t) dW_t + \mu(X_t) dt
\end{equation}
where $\sigma(x)$ and $\mu(x)$ have no explicit time dependence.\footnote{\, We consider time-homogeneous dynamics so the problem is analytically tractable (see below).} In fact, for our purposes here, motivated by analytical tractability (see footnote \ref{foot.sigma}), it will suffice to consider constant $\sigma(x)\equiv\sigma$. However, for now we will keep $\mu(x)$ general (but Lipschitz continuous). We will now introduce barriers\footnote{\, With the view, {\em e.g.}, to have a function $S_t = f(X_t)$ with {\em attainable} barriers at $S_\pm = f(x_\pm)$. Also, note that, unless $\mu(x) \equiv 0$, this is not the same as having time-independent barriers for $W_t$.} for the process $X_t$ at $X_t = x_-$ and $X_t = x_+$ (see, e.g., \cite{Freidlin}). Below, without loss of generality, we will assume $x_- < x_+$.

{}We need to construct the measure ${\bf Q}$ under which the process $Z_t$ in (\ref{Z}) is a martingale. For our purposes here it will suffice to assume that\footnote{\, {\em I.e.}, i) $r_t$ is a {\em local} function of $X_t$ and $t$, and ii) $Y_T$ is independent of the history ${\cal F}_T$.} i) the short-rate $r_t = r(X_t, t)$ and ii) $Y_T = Y(X_T)$. Let us define the pricing function
\begin{equation}
 v(x, t, T) \equiv B_t~\mathbb{E}\left(B_T^{-1}Y_T\right)_{{\bf Q}, X_t = x}
\end{equation}
where $X_t$ is defined via (\ref{X}) (with constant $\sigma$). Note that $V_t$ in (\ref{E}) is given by $V_t = v(X_t, t, T)$. Since $E_t$ is a ${\bf Q}$-martingale, we have the following PDE for $v(x,t,T)$
\begin{equation}\label{PDE.v}
 \partial_t v(x,t,T) + \mu(x) \partial_x v(x,t,T) + {\sigma^2\over 2}\partial_x^2 v(x,t,T) - r(x,t) v(x,t,T) = 0
\end{equation}
subject to the terminal condition $v(x,T,T) = Y(x)$. Also, $r_t\equiv {d\ln(B_t)/dt}$.

{}Consider a ${\bf Q}$-martingale of the form $M_t = w(X_t, t)$, where $w(x,t)$ is a deterministic function. We have the following PDE:
\begin{equation}\label{PDE.w}
 \partial_t w(x,t,T) + \mu(x) \partial_x w(x,t,T) + {\sigma^2\over 2}\partial_x^2 w(x,t,T) = 0
\end{equation}
We must specify boundary conditions for $w(x,t)$ at $x=x_\pm$. For the identity $I_t$ to be a martingale under ${\bf Q}$, we must have reflecting (Neumann) boundary conditions\footnote{\, Thus, Dirichlet or Robin boundary conditions would be inconsistent with $I_t$ being a martingale. See Appendix \ref{app.0} for the transition density and martingales for Robin boundary conditions.}
\begin{equation}
 \partial_x w(x_\pm,t) = 0
\end{equation}
The same boundary conditions must be imposed on the pricing function $v(x,t,T)$:
\begin{equation}\label{b.v}
 \partial_x v(x_\pm,t,T) = 0
\end{equation}
Then the claim $Y(x)$ must satisfy the same boundary conditions:
\begin{equation}\label{b.Y}
 \partial_x Y(x_\pm) = 0
\end{equation}
which are consistent with the claim $Y(x)\equiv 1$ for a zero-coupon $T$-bond.

{}We can now show that $r_t$ cannot be deterministic. First, note that we wish our FXR process $S_t$ to stay within a band with {\em attainable} boundaries $S_\pm$. This can be achieved by having $S_t = f(X_t)$, where $f(x)$ is a bounded {\em monotonic}\footnote{\, Monotonicity is assumed so we can price claims (see below).} function on $[x_-,x_+]$ such that $f(x_\pm)=S_\pm$. In this regard, $S_t$ cannot have any explicit $t$ dependence,\footnote{\, Otherwise, barring any contrived time dependence, $S_t$ generically will break the band.} {\em i.e.}, $S_t$ depends on $t$ only via $X_t$. Second, since the discounted FXR process $Z_t = B_t^{-1}S_t$ is a ${\bf Q}$-martingale, the function $f(x)$ satisfies the same PDE as $v(x,t,T)$. It then follows that $r(x,t) = r(x)$, so the short-rate $r_t$ cannot have any explicit $t$ dependence either. We thus have the following ordinary differential equation for $f(x)$:
\begin{equation}\label{f}
 \mu(x) f^\prime(x) + {\sigma^2\over 2} f^{\prime\prime}(x) - r(x)f(x) = 0
\end{equation}
subject to the boundary conditions
\begin{equation}\label{b.f}
 f^\prime(x_\pm) = 0
\end{equation}
where $f^\prime(x) \equiv \partial_x f(x)$. We must also have $f(x) > 0$; therefore, $r(x)$ cannot be constant.\footnote{\, For constant $r_t>0$ ($r_t<0$) we would have minima (maxima) at $x=x_-$ and $x=x_+$ with a maximum (minimum) located between $x_-$ and $x_+$, which is not possible for $f(x)>0$ on $[x_-,x_+]$.} So, we can {\em choose} $f(x) > 0$ satisfying (\ref{b.f}) and view (\ref{f}) as fixing $r(x)$:
\begin{equation}\label{r}
 r(x) = \mu(x) {f^\prime(x)\over f(x)} + {\sigma^2\over 2} {f^{\prime\prime}(x)\over f(x)}
\end{equation}
This relation has a natural financial interpretation in the FX context (see below).

\subsection{Pricing PDE}

{}We can now tackle the pricing PDE (\ref{PDE.v}). Let
\begin{eqnarray}\label{g}
 && g(x) \equiv \ln(f(x))\\
 && u(x,t,T)\equiv \exp\left({1\over\sigma^2}\int_{x_-}^x dy~\mu(y)\right) v(x,t,T)\label{u.1}
\end{eqnarray}
Then, taking into account (\ref{r}), we have:
\begin{equation}
 \partial_t u(x,t,T) + {\sigma^2\over 2}\left[\partial_x^2 u(x,t,T) - U(x) u(x,t,T)\right]= 0
\end{equation}
where the ``potential" $U(x)$ is given by
\begin{eqnarray}\label{U}
 &&U(x) \equiv h^2(x) + h^\prime(x)\\
 &&h(x)\equiv g^\prime(x)+ {\mu(x)\over\sigma^2}\label{h}
\end{eqnarray}
subject to the boundary and terminal conditions (note that $g^\prime(x_\pm)=0$ due to (\ref{b.f}))
\begin{eqnarray}\label{b.u}
 &&\partial_x u(x_\pm, t, T) = h(x_\pm) u(x_\pm, t, T)\\
 &&u(x,T,T) = \exp\left({1\over\sigma^2}\int_{x_-}^x dy~\mu(y)\right) Y(x)\label{term}
\end{eqnarray}
We have standard separation of variables and the solution is given by\footnote{\, We assume that $U(x)$ is bounded on $[x_-,x_+]$, so the spectrum $E_n$ is bounded from below.}
\begin{equation}\label{u.c}
 u(x,t,T) = \sum_{n=0}^\infty c_n~\psi_n(x)~e^{-E_n\left(T-t\right)}
\end{equation}
where $\psi_n(x)$ form a complete orthonormal set of solutions to the static Schr\"odinger equation ($\delta_{n n^\prime}$ is the Kronecker delta)
\begin{eqnarray}\label{psi}
 &&-{\sigma^2\over 2} \left[\psi^{\prime\prime}_n(x) - U(x)\psi_n(x)\right] = E_n\psi_n(x)\\
 &&\int_{x_-}^{x_+} dx~\psi_n(x)~\psi_{n^\prime}(x) = \delta_{n n^\prime}\label{ortho}
\end{eqnarray}
subject to the boundary conditions\footnote{\, Notice that $-{2\over\sigma^2}\left(E_n - E_{n^\prime}\right)\int_{x_-}^{x_+} dx~\psi_n(x)~\psi_{n^\prime}(x) = \int_{x_-}^{x_+} dx\left[\partial_x^2\psi_n(x)~\psi_{n^\prime}(x) - (n\leftrightarrow n^\prime) \right] = \left.\left[\partial_x\psi_n(x)~\psi_{n^\prime}(x) - (n\leftrightarrow n^\prime) \right]\right|_{x_-}^{x_+} = 0$ by virtue of (\ref{b.psi}), hence (\ref{ortho}) for $n\neq n^\prime$ as $E_n\neq E_{n^\prime}$.}
\begin{equation}\label{b.psi}
 \psi^\prime_n(x_\pm) = h(x_\pm)\psi_n(x_\pm)
\end{equation}
As above, $\psi^\prime_n(x) \equiv \partial_x\psi_n(x)$.

{}The coefficients $c_n$ in (\ref{u.c}) are fixed using the terminal condition (\ref{term}) and (\ref{ortho}):
\begin{equation}
 c_n = \int_{x_-}^{x_+} dx^\prime \exp\left({1\over\sigma^2}\int_{x_-}^{x^\prime} dy~\mu(y)\right)\psi_n\left(x^\prime\right)Y(x^\prime)
\end{equation}
The spectrum $E_n$ is nonnegative. For the eigenfunction ($a_0$ is fixed via (\ref{ortho}))
\begin{eqnarray}\label{psi.0}
 &&\psi_0(x) \equiv a_0\exp\left(\int_{x_-}^x dy~h(y)\right)\\
 &&a_0 \equiv \left[\int_{x_-}^{x_+} dx^\prime~e^{2\int_{x_-}^{x^\prime}dy~h(y)}\right]^{-{1\over 2}}
\end{eqnarray}
we have $E_0 = 0$. The other eigenvalues $E_1 < E_2 <\dots$ are all positive.\footnote{\, Indeed, from (\ref{ortho}) with $n>0$ and $n^\prime=0$ and the fact that $\psi_0(x) > 0$, it follows that $\psi_n(x)$ must flip sign on $[x_-,x_+]$, {\em i.e.}, $\psi_n(x)$ has at least one node. However, if any $E_n < 0$, then $\psi_{n_*>0}(x)$ corresponding to $E_{n_*} \equiv \mbox{min}(E_n) < 0$ would have to have at least one node, which is not possible.}

{}Putting everything together, we get the following formula for the pricing function:
\begin{eqnarray}\label{deriv.prc}
 &&v(x,t,T) = f(x) \left[{\widetilde c}_0 + {1\over\psi_0(x)} \sum_{n=1}^\infty {\widetilde c}_n~\psi_n(x)~e^{-E_n\left(T-t\right)}\right]\\
 &&{\widetilde c}_n \equiv \int_{x_-}^{x_+} dx^\prime~\psi_0\left(x^\prime\right)\psi_n\left(x^\prime\right) {Y(x^\prime)\over f(x^\prime)},~~n\geq 0
\end{eqnarray}
When $Y(x) = f(x)$, {\em i.e.}, $Y_T = S_T$, we have ${\widetilde c}_0=1$ and ${\widetilde c}_{n>0} = 0$, so $v(x,t,T) = f(x)$, as it should be since this is simply the pricing function for a forward.

\subsection{Hedging}

{}Above we imposed the boundary conditions (\ref{b.f}) on the FXR process. This implies that the local FXR volatility vanishes at the boundaries. However, unlike the case of unattainable boundaries, here the boundaries are {\em attainable}: the FXR process touches a boundary and is reflected back into the band. Furthermore, note that in any finite period, $S_t$ can touch a boundary multiple (unbounded number of) times.

{}Even though the local FXR volatility vanishes at the boundaries, the hedging strategy is well-defined. The number of the $S_t$ units held by the hedging strategy\footnote{\, The actual hedge (recall that we are operating from the foreign investor's perspective) consists of holding $\phi_t$ units of the domestic cash bond, and $\psi_t$ units of the foreign cash bond (which is the foreign investor's numeraire). As mentioned above, if we set the domestic short-rate to zero, $S_t$ (the worth of 1 unit of the domestic cash bond in the foreign currency) becomes a foreign tradable.}
\begin{equation}\label{phi.hedge}
 \phi_t = {\partial V_t\over \partial S_t} = {\partial_x v(x, t, T)\over f^\prime(x)}
\end{equation}
Since we have (\ref{b.v}), so long as $f^{\prime\prime}(x_\pm)$ are finite, $\phi_t$ is finite at the boundaries:
\begin{equation}
 \left.\phi_t\right|_{x = x_\pm} = {\partial^2_x v(x_\pm, t, T)\over f^{\prime\prime}(x_\pm)}
\end{equation}
Consequently, the cash bond holding $\psi_t$ is also well-defined at the boundaries.

\subsection{Call and Put}

{}Consider claims of the form $Y^c_T(k) = (S_T - k)^+ = \mbox{max}(S_T - k, 0)$ (European call option with maturity $T$ and strike $k$) and $Y^p_T(k) = (k - S_T)^+ = \mbox{max}(k - S_T, 0)$ (European put option with maturity $T$ and strike $k$). We have
\begin{equation}
 Y^c_T(k) - Y^p_T(k) = Y^f_T(k)
\end{equation}
where $Y^f_T(k) = S_T - k$ is the claim for a forward with maturity $T$ and ``strike" $k$. We have the usual put-call parity: $V^c_t(k,T)-V^p_t(k,T) = V^f_t(k,T)$. The forward price
\begin{equation}
 V^f_t(k,T) = S_t - k~P(t,T)
\end{equation}
where $P(t,T) \equiv v^{bond}({\widehat x}_t,t,T)$ is a zero-coupon $T$-bond price (with $Y^{bond}_T = 1$), and the call price
\begin{eqnarray}\label{gen-call}
 &&V^c_t(k,T) = S_t \left[{\widetilde c}_0 + {1\over\psi_0({\widehat x}_t)} \sum_{n=1}^\infty {\widetilde c}_n~\psi_n({\widehat x}_t)~e^{-E_n\left(T-t\right)}\right]\\
 &&{\widetilde c}_n \equiv \int_{x_*}^{x_+} dx^\prime~\psi_0\left(x^\prime\right)\psi_n\left(x^\prime\right) \left[1 - {k\over f(x^\prime)}\right],~~n\geq 0
\end{eqnarray}
where\footnote{\, This is where the monotonicity of $f(x)$ is important.} $f(x_*)\equiv k$, $f({\widehat x}_t) \equiv S_t$ ($S_- < S_+$, $S_\pm \equiv f(x_\pm)$). For the binary option $Y^b_T = \theta(S_T-k)$ and $V_t^b(k, T) = -\partial V^c_t(k,T)/\partial k$ ($\theta(y)$ is the Heaviside step-function).

\subsection{FX Rate Process}

{}In most practical applications the band is narrow, so we can choose the FXR process based on computational convenience. Note that $\psi_1(x)$ has one node $x_1$ on $[x_-,x_+]$: $\psi_1(x_1) = 0$. In the cases where $\psi_1(x)/\psi_0(x)$ is a monotonic function on $[x_-,x_+]$, we can choose the FXR process as follows (note that $f^\prime(x_\pm) = 0$):
\begin{equation}\label{FXR.pr}
 f(x) = S_{mid}\left[1 + \gamma~{\psi_1(x)\over\psi_0(x)}\right]^{-1}
\end{equation}
Here $S_{mid} \equiv f(x_1)$. Without loss of generality we can assume $\psi_1(x_-)>0$ and $\psi_1(x_+) < 0$, so we have $S_- < S_+$ for $\gamma > 0$. Since the band is narrow, $\gamma\ll 1$.

{}For the FXR process (\ref{FXR.pr}) the zero-coupon $T$-bond price $P(t,T)$, for which $Y(x)\equiv 1$, simplifies. For this claim ${\widetilde c}_0=1/S_{mid}$, ${\widetilde c}_1 = \gamma/S_{mid}$ and ${\widetilde c}_{n>0} = 0$, so we have
\begin{equation}\label{T-bond}
 P(t,T) = {S_t\over S_{mid}} + \left[1 - {S_t\over S_{mid}}\right] e^{-E_1\left(T-t\right)}
\end{equation}
Note that $P(t,T)$ can be greater than 1 as the short-rate $r(x)$ need not be positive (recall that $r(x)$ is the differential short-rate). More on this below.

\subsection{Explicit Models}

{}We have two functions: $g(x)$ and $\mu(x)$. If we set $\mu(x) = 0$ (or some other constant), $X_t$ is a Brownian motion (with a constant drift). Then $U(x)$ is not that simple, albeit still tractable. Alternatively, we can take $g(x)$ and $\mu(x)$ such that $U(x)=0$.

\subsubsection{Vanishing Drift}

{}Let $\mu(x)\equiv 0$. Also, let $x_- = 0$, $x_+ = L$. Then we can take (note that this choice differs from (\ref{FXR.pr}))
\begin{equation}\label{quart1}
 g(x) = \gamma\left[3~{x^2\over L^2} - 2~{x^3\over L^3}\right] + \ln(S_-)
\end{equation}
where $\gamma>0$, so that $S_+ = S_-\exp(\gamma)$. We have a quartic potential
\begin{equation}\label{quartic}
 U(x) = {6\gamma\over L^2}\left[1-2~{x\over L} + 6\gamma\left({x\over L} - {x^2\over L^2}\right)^2\right]
\end{equation}
which is well-studied using perturbation theory. However, since $\gamma\ll 1$, we have simplifications. Recall that $E_0=0$ irrespective of $\gamma$. Also, $\psi_0(x) = a_0 f(x)/ f(0)\approx a_0 \approx 1/\sqrt{L}$. In the zeroth approximation, {\em i.e.}, in the limit $\gamma\rightarrow 0$ where $U(x)\rightarrow 0$, we have $E^{(0)}_n = \pi^2 n^2 \sigma^2/2L^2$ (see below). For the $n>0$ levels the corrections due to nonzero $\gamma$ are controlled by the ratio
\begin{equation}
 {\sigma^2 U(x)\over 2{E^{(0)}_n}} = {6\gamma\over \pi^2 n^2}\left[1-2~{x\over L} + 6\gamma\left({x\over L} - {x^2\over L^2}\right)^2\right]
\end{equation}
which is small for $\gamma\ll 1$. We can therefore set $U(x)\approx 0$. If we wish to account for the leading ${\cal O}(\gamma)$ corrections, we can drop the nonlinear term in (\ref{quartic}), which gives a linear potential
\begin{equation}
 U(x) \approx {6\gamma\over L^2}\left[1-2~{x\over L}\right]
\end{equation}
for which the solutions to the Schr\"odinger equation (\ref{psi}) are expressed in terms of the Airy functions $Ai(x)$ and $Bi(x)$. Alternatively, we can use the WKB approximation.

\subsubsection{Vanishing Potential}

{}We can set the potential $U(x)$ to zero without any approximations at the ``expense" (see below) of having nonvanishing $\mu(x)$:
\begin{equation}\label{mu.g}
 \mu(x) = -\sigma^2 g^\prime(x)
\end{equation}
Then, setting $x_-=0$ and $x_+=L$, irrespective of $g(x)$, we have $\psi_0(x) = 1/\sqrt{L}$ ($E_0 = 0$), and for $n>0$
\begin{eqnarray}
 &&\psi_n(x) = \sqrt{2\over L} \cos\left({\pi n x\over L}\right)\\
 &&E_n = {\pi^2 n^2\sigma^2\over 2L^2}\label{E_n}
\end{eqnarray}
The call price simplifies to
\begin{eqnarray}\label{call.cos}
 &&V^c_t(k,T) = S_t \left[{\widetilde c}_0 + \sqrt{L} \sum_{n=1}^\infty {\widetilde c}_n~\psi_n({\widehat x}_t)~e^{-E_n\left(T-t\right)}\right]\\
 &&{\widetilde c}_n = {1\over\sqrt{L}} \int_{x_*}^L dx^\prime~\psi_n\left(x^\prime\right) \left[1 - {k\over f(x^\prime)}\right],~~n\geq 0
\end{eqnarray}
where $f(x_*)\equiv k$, $f({\widehat x}_t) \equiv S_t$. Since $\psi_1(x)$ is monotonic on $[0,L]$, it is convenient to take $f(x)$ of the form (\ref{FXR.pr}):
\begin{equation}\label{cos}
 f(x) = S_{mid}\left[1 + \sqrt{2}\gamma\cos\left(\pi x\over L\right)\right]^{-1}
\end{equation}
We then have ($S_-\leq k\leq S_+$, $S_\pm = S_{mid}/(1\mp\sqrt{2}\gamma)$)
\begin{eqnarray}
 &&{\widetilde c}_0 = {\sqrt{2}\gamma k\over \pi S_{mid}}\left[(\pi - \phi_*)\cos(\phi_*) + \sin(\phi_*)\right]\label{c.0}\\
 &&{\widetilde c}_1 = -{\gamma k\over \pi S_{mid}}\left[\pi - \phi_* + \sin(\phi_*)\cos(\phi_*)\right]\label{c.1}\\
 &&{\widetilde c}_{n>1} = {\gamma k\over \pi S_{mid}}\left[{\sin((n+1)\phi_*)\over{n+1}} + {\sin((n-1)\phi_*)\over{n-1}}  - {2\cos(\phi_*)\sin(n\phi_*)\over n}\right]\label{c.n}\\
 &&\phi_*\equiv \arccos\left({1\over\sqrt{2}\gamma}\left[{S_{mid}\over k} - 1\right]\right)
\end{eqnarray}
In practical computations we would truncate the series in (\ref{call.cos}) at suitable finite $n$. Also, note that the $T$-bond price is given by (\ref{T-bond}).

{}Here the following remark is in order. As mentioned above, the local FXR volatility vanishes at the boundaries, which is due to (\ref{b.f}). There is no way around this: boundaries must be reflecting, and then we must have (\ref{b.f}). A simple way to see this is that otherwise (\ref{b.Y}) will not be satisfied for claims such as call $Y^c(x) = (f(x) - k)^+$ and put $Y^p(x) = (k - f(x))^+$, {\em i.e.}, we would not be able to hedge such claims. That the local FXR volatility vanishes at the boundaries in itself is not problematic. In fact, $p(x)\equiv g^\prime(x) = f^\prime(x)/f(x)$ is small compared with its maximal value $p_{max}$ on $[x_-,x_+]$ only in relatively small regions adjacent to the boundaries. Thus, in the model (\ref{cos}) we have
\begin{equation}\label{p}
 p(x) = {\sqrt{2}\gamma\over {1+\sqrt{2}\gamma\cos(\pi x/L)}} {\pi\sin(\pi x/L)\over L}\approx p_{max}\sin(\pi x/L)
\end{equation}
where $p_{max}\approx p(L/2) = \sqrt{2}\gamma\pi/L$, and we have taken into account that $\gamma\ll 1$. So, $p(L/6) \approx 0.5~p_{max}$, $p(L/10)\approx 0.31~ p_{max}$, {\em etc.}, {\em i.e.}, due to the nonlinearity of $p(x)$, even at $x=L/10$ the local FXR volatility is not too small (compared with $p_{max}$).\footnote{\, In the model (\ref{quart1}) we have $p(x)=4p_{max}(x/L - (x/L)^2)$, where $p_{max}=p(L/2)=3\gamma/2L$, so $p(x/10)=0.36~p_{max}$.}

\subsubsection{Nonvanishing Potential and Drift}

{}One ``shortcoming" of the model (\ref{cos}) is that, since we have (\ref{mu.g}), the drift $\mu(x) = -\sigma^2 p(x)$ is negative away from the boundaries, albeit it is small (compared with $\sqrt{2}\sigma^2\pi/L$) as it is suppressed by $\gamma\ll 1$. Therefore, in a long run, on average $X_t$ will slowly drift toward 0. This can be circumvented by considering models where both the potential $U(x)$ and the drift $\mu(x)$ are nonvanishing. Since $\gamma\ll 1$, with the appropriate choice of $h(x)$, to the leading order $\mu(x)\approx \sigma^2 h(x)$. Alternatively, we can take the desired drift and treat the terms in the potential stemming from $g^\prime(x)$ in (\ref{h}) as small. For our purposes here, the former approach is more convenient.

{}Thus, one evident choice is $h(x) = \alpha(\theta - x)/\sigma^2$, where $\theta$ and $\alpha$ are constant. Then $\mu(x)\approx \alpha(\theta - x)$, so $X_t$ (approximately) follows the mean-reverting Ornstein-Uhlenbeck (OU) (Uhlenbeck and Ornstein, 1930) process, $\alpha$ is the mean-reversion parameter, and $\theta$ is the long-run expected value of $X_t$ (which we can set to $L/2$). In this case we have a quadratic potential and $\psi_n(x)$ in (\ref{psi}) are expressed via the parabolic cylinder functions.

{}However, with an appropriate choice of $h(x)$, we can also have a solution expressed purely via elementary functions. Thus, consider
\begin{equation}\label{tan}
 h(x) = -\nu\tan\left(\nu\left[x - {L\over 2}\right]\right)
\end{equation}
where $0 < \nu < \pi/L$ is a constant parameter. Then we have a constant potential $U(x) \equiv -\nu^2$. The eigenfunctions $\psi_n(x)$ read ($n=0,1,2,\dots$):
\begin{eqnarray}
 &&\psi_n(x) = a_n\cos\left(\lambda_n\left[x - {L\over 2}\right] + {\pi n\over 2}\right)\\
 &&a_n = \left({L\over 2}\left[1 + (-1)^n{\sin(\lambda_n L)\over\lambda_n L}\right]\right)^{-1/2}\label{a.n.tan}
\end{eqnarray}
where $\lambda_n$ are the positive roots of the following equation (which follows from (\ref{b.psi})):
\begin{equation}\label{lambda.n.tan}
 \lambda_n\tan\left([\lambda_n L - \pi n]/2\right) = \nu\tan(\nu L/2)
\end{equation}
The smallest root is $\lambda_0=\nu$, and $\lambda_0<\lambda_1<\lambda_2<\dots$ (Note that $E_n = \sigma^2(\lambda_n^2-\nu^2)/2$.)

{}The call option price is given by (\ref{gen-call}) with ${\widetilde c}_n$ defined in Appendix \ref{app.A}. The zero-coupon $T$-bond price is given by (\ref{T-bond}). If $\nu\sim\pi/L$ (although recall that $\nu<\pi/L$),\footnote{\, In fact, here we assume that $\nu$ is not too close to $\pi/L$ or else the drift becomes large near the boundaries. In the $\nu\rightarrow \pi/L$ limit the boundaries are no longer attainable.} then, assuming $\gamma \ll 1$, the drift $\mu(x)\approx-\sigma^2\nu\tan(\nu(x-L/2))$ and we have positive drift for $x<L/2$ and negative drift for $x>L/2$, so we have a mean-reverting behavior.\footnote{\, Near $x=L/2$ the drift is approximately linear as in the OU process: $\mu(x)\approx \sigma^2\nu^2(L/2-x)$; however, away from the long-run value ({\em i.e.}, $L/2$), the nonlinear effects become important. Unlike the OU case with reflecting boundaries, the model (\ref{tan}) is solvable via elementary functions.} The $g^\prime(x)$ contribution into $\mu(x)$ via (\ref{h}) introduces a small asymmetry into $\mu(x)$ but does not alter the qualitative picture.

\subsection{Differential Rate}

{}The meaning of (\ref{r}), which stems from the requirement that there be no arbitrage ({\em i.e.}, that the discounted process (\ref{ZX}) be a martingale under the risk-neutral measure ${\bf Q}$), has a natural financial interpretation as the Uncovered Interest Parity. To illustrate this, let us momentarily step away from the target zone case and consider the case where neither the domestic nor the foreign currencies are constrained in any way. Then, if we take a familiar ``log-normal" form for the FX rate via $S_t = \exp(X_t)$, from (\ref{r}) we have
\begin{equation}\label{UIP}
 r_t = r^f_t - r^d_t = \mu(X_t) + {\sigma^2\over 2}
\end{equation}
Recalling that $dX_t = \sigma dW_t + \mu(X_t)dt$, (\ref{UIP}) is indeed the Uncovered Interest Parity.\footnote{\, The $\sigma^2/2$ shift is due to the log-normal form of the FX rate. {\em E.g.}, if $\mu(X_t) \equiv \mu=\mbox{const.}$, the expectation $\mathbb{E}\left(S_T\right)_{{\bf Q},{\cal F}_t} = \exp((\mu+\sigma^2/2)(T-t))$.}

{}In fact, there is a simple formula for the differential short-rate $r_t$. Using (\ref{r}), (\ref{g}), (\ref{h}), (\ref{psi}), (\ref{psi.0}) and (\ref{FXR.pr}), we have
\begin{equation}\label{r.1}
 r_t = E_1\left[1 - {f(X_t)\over S_{mid}}\right] = E_1\left[1 - {S_t\over S_{mid}}\right]
\end{equation}
so $r_t$ is positive (negative) at the lower (upper) barrier, which is a consequence of the requirement that there be no arbitrage.\footnote{\, If the domestic short-rate is low, $r_t^d < E_1\left(S_+/S_{mid} - 1\right)$, then the foreign short-rate would become negative for $S_t > S_{mid}\left(1 + r_t^d / E_1\right)$. Theoretically this would appear to imply arbitrage. However, in practice the short-rate is not a tradable instrument and this situation may not be arbitrageable as the tradable bonds (for the actually available maturities) may still have well-behaved yields despite the negative underlying short-rate (for a recent discussion, see, {\em e.g.}, (Kakushadze, 2015) and references therein). Also note that (\ref{r.1}) simply follows from $r_t = f(t,t)$ and (\ref{T-bond}), where $f(t, T) = -\partial_T \ln\left(P(t,T)\right)$ is the forward rate.}  Note that (\ref{r.1}) does not explicitly depend on $U(x)$ so long as we have (\ref{FXR.pr}).\footnote{\, And $r_t$ is continuous even if $U(x)$ contains $\delta$-functions, {\em i.e.}, when $\mu(x)$ is discontinuous.}

\section{Concluding Remarks}\label{sec5}

{}As we saw above, with a thoughtful choice of the FX rate process -- which choice, from a practical viewpoint, exists because the band is narrow and said choice does not affect quantitative results much -- we can solve the FX option pricing problem in the target zone analytically, in fact, via elementary functions. This is assuming attainable barriers.\footnote{\, Hence our choice of a constant diffusion coefficient $\sigma(x)\equiv\sigma$. When the band is narrow, there is little benefit to having nonconstant $\sigma(x)$ as the boundaries are reflecting. This is to be contrasted with the case of unattainable boundaries where $\sigma(x)$ tends to zero near the boundaries.\label{foot.sigma}} For unattainable barriers the math typically is more involved. Also, in practice the exchange rates in target zones frequently attain the boundaries, so attainable boundaries are also appealing from this viewpoint. In fact, in some cases the FX options markets imply a future expectation that the FX rate will break the band. Models accommodating band breaking are outside of the scope of this note; however, the fact that the markets sometimes price band breaks further indicates appealability of models with attainable boundaries.

\subsection*{Acknowledgments}
{}ZK would like to thank Eyal Neuman for discussions on Brownian motion with reflecting barriers, which prompted him to think about this topic. We would also like to thank Travis Fisher for discussions.

redpajama_set_name: RedPajamaArXiv


text:
Nebraska 150 Celebration
Celebrating Nebraska Statehood Board
Nebraska Sesquicentennial Commission
All Events & Programs
For Official Status
NE150 License Plates
Commemorative Trees
Primo Virtuosi – Young Artist Winners
« Nebraska Sesquicentennial Anniversary Celebraton QSO Party
League of Nebraska Municipalities 2017 Midwinter Conference »
As we welcome winners of the Nebraska High School Young Artist Competition, we also celebrate our State's 150th Birthday with a performance of Symphony No. 2 ("Romantic") by Wahoo-born composer, Howard Hanson. The biennial competition for high school juniors and seniors is held in January 2017; generally two winners are selected to perform with the Hastings Symphony. Howard Hanson was a major figure in the orchestral world of the 1920s-1960s, having headed the Eastman Conservatory of Music for 40 years and won a Pulitzer Prize for Music in 1944. A Nebraskan native who went on to achieve great acclaim as a composer and administrator. He was the recipient of the Distinguished Nebraskans Award in 1976. Our concert is open to everyone: Tickets are $15 and $12; all students admitted free. The Hastings Symphony Orchestra is celebrating its 91st Season of continuous music in south central Nebraska.
Hastings Symphony Orchestra
Masonic Center Auditorium
411 N Hastings Ave
Hastings, NE 68901 United States + Google Map
201 N 8th St Suite 215 Lincoln, NE 68508
Copyright © – Celebrating Nebraska Statehood
social_facebook	social_twitter	social_youtube


vco action on & off the courts!
Young tennis players take a clinic on center court!
Speed painter Christopher Johnson drew a crowd of observers as he painted this young Michael Jackson portrait in about five minutes while jamming to the King of Pop's music. For more information visit kolpeace.com.
Will Ramey of Daniel Island drew a chip during the Draw Party at Dockery's on Saturday.
Pam Whytcross of the WTA, players Christina Mchale and Kiki Bertens, and VCO tournament executives Bob Moran and Eleanor Adams gather at the conclusion of the official draw.
Kyle Kotic, aka Superman, flips over the Easter Bunny and members of the crowd for the finale of the strongman and break dance show the crew performed over Family Weekend at the VCO.
Easter Sunday at the VCO! Fans played some tennis, enjoyed the holiday spirit, and saw the pros in action during the qualifying rounds.


At NC Farm Bureau, Helping You is What We Do Best. Nathan's specialty is helping individuals, businesses, and families protect their assets, paychecks, and maintain their standard of living as live events occur.
In today's World, mistakes, accidents, untimely deaths, and other peoples' decisions that are often out of our own control can quickly turn a bad day into a bad life. Everyone has a story that includes different situations and priorities. Understanding the risks to a client's livelihood and family's standard of living are paramount in creating a proper insurance program. Additionally, having an expert be transparent in explaining cost versus coverage's/benefits will help maximize insurance dollars for benefits that most suit the client's particular needs.
With experience as an investment adviser, financial planner, and business owner, Nathan has the knowledge base to help clients incorporate their insurance program into the 'overall picture' as well as highlight areas of potential risks and propose appropriate solutions.


text:
Volunteer Spotlight: Cory
Networking with professionals and rapport-building are integral aspects of any job-searching strategy. Hire Heroes USA volunteer Cory Hamma takes pride in each and every conversation he has with clients and spends just as much time actively listening as he does providing guidance for next best steps.
"The experience of meeting that first client, and all the subsequent clients, has truly been heartwarming and rewarding. I cannot overstate how thankful the clients are for my time and advice, whether I am helping them revise their resume, reviewing their LinkedIn profile, or generally helping them find a direction that suits their personality, interests and experience."
Cory enjoys frank and honest dialogue with clients about their career path and exploring career options that may not have been on a veteran's radar. He works to provide them direction based on his expertise in information security, digital forensics and information technology. His strong and robust professional background that he's built over the years gives him the ability to relate to clients and understand the reality of charting a successful career path.
"We talk candidly about networking, education options, certifications, pay expectations, and the difference between what you see on TV and movies versus the actual job experience. It is incredibly rewarding to receive a follow-up email from a client proudly announcing that they interviewed and were hired for a job in their interest area."
Cory's genuine approach to serving his clients and meeting them where they're at is evident in his client's gratitude. We are incredibly thankful for Cory's dedication, commitment and the heart he leads with on the Hire Heroes USA volunteer team.
If you would like to make a difference in the lives of veterans and military spouses, please click here to learn more about volunteering with Hire Heroes USA.
Hire Heroes USA
Latest posts by Hire Heroes USA (see all)
Volunteer Spotlight: Dan - January 26, 2023
Top Jobs & Training Programs for January 2023 - January 9, 2023
10 Tips for Professional Communication - January 6, 2023


Hammocking is arguably the best way in the world to be lazy. Not only are they incredibly comfortable, but hammocks can but put up almost anywhere. Therefore, hammocks are an unbeatable way to recline in the backcountry. Camping with a hammock adds an extra element of relaxation to the great outdoors.
Camping hammocks are almost as comfortable as regular hammocks and are lightweight and portable—far lighter than camping chairs. The downside is that there are limited places to set them up. There are a couple types of camping hammocks.
First and foremost, there are single hammocks and multiple-person hammocks. Multi-person hammocks can be uncomfortable for a single occupant. There are tents with mosquito netting, which is nice for when you're in a buggy area.
There are also hammock tents. These are especially useful during ultra-light backpacking, and they come with a rain fly and tent stakes. REI even offers a three person hammock tent. You can also sleep pretty comfortably in a regular hammock if you have wind protection over your sleeping bag and it is clear outside.
If you're hammocking, you need to think about hammock straps. Make sure your straps are long enough and can handle the weight that you're putting on it. Also, if you're hammocking between trees, make sure that you bring something to put between the hammock strap and the tree so that you don't damage the bark of the tree. Cardboard works great.
If you don't have access to cardboard, tarps or t-shirts will do the trick during backpacking. In addition, be sure not to get the hammock wet. Wear and tear on your hammock will have you falling out of the hammock bottom pretty quickly. Be sure to put a camping hammock away if it starts raining.
It is important that before you get in your hammock, you make sure that your beer is in arm's reach from within the hammock. Get in the hammock, stretch out your arms, get out, and place the beer a little closer.


Very excited to announce Locals SHY NATURE as headliner. Think anthemic, bold indie that manages to stay well away from the 'landfil'l tag that such a description might suggest. Catch them in our intimate surroundings because they're destined for bigger things, having released a string of critically acclaimed singles in the last six months.


text:
Denton Artist Zeke Forever Has Bops That Would Make Lady Gaga Proud
by Miguel Perez 26 Aug 2021 3:52 PM
From Gaga to gospel music, the 24-year-old singer drew from every corner of pop culture to craft his latest album, "Kryptonite."
CTA TBD
Kenan Mcwilliams and Zeke Forever go way back. The two have been friends ever since the Denton musician first conjured up Zeke in his mind in elementary school.
"When I was a kid, I didn't have many friends. I felt really alone to the point where I made up imaginary friends," he said. "There was a point in high school where I decided to give that up, but one of my favorite people was Zeke. That's where my name comes from."
Mcwilliams has spent years transforming that old imaginary friend into a very real (and very talented) musical persona. Now, Zeke Forever is gearing up for the release of his second album on Aug. 30. A slickly-produced pop and R&B record, "Kryptonite" explores the ebb and flow of young adulthood with "a side of Black Boy Joy," he says.
Photo courtesy of Zeke Forever
The 24-year-old artist pulled from a deep pool of past and present influences to create "Kryptonite." The result sounds like an exuberant reclamation of life for a young man who has been through it.
"I'm black and gay, and I grew up in a super religious family," Forever said. "I felt like I was wrong. I was never really happy with myself because I didn't really have a voice … The mission for me is to make sure that no one has to go through the things that I went through as a kid."
Some moments on the record call to mind R&B greats like Aaliyah and Solange. At other times, Forever looks to his biggest musical hero for inspiration.
"Lady Gaga was one of the first people that made me feel OK with being me," he said. "I literally ride or die for her. That is my queen."
Zeke Forever broke down the album's many influences.
What were your sonic inspirations for this record?
It's kind of all over the place. I live my life by albums. "Chromatica" by Lady Gaga, obviously. "Future Nostalgia" by Dua Lipa. "When I Get Home" by Solange. But also, "Incredible" by Mary Mary, which is a gospel duo that I listened to when I was a kid. A lot of their songs I didn't understand then, but I understand now, because life sucks.
Those were the sounds that I grabbed from and that really inspired me and pushed me to do something that I felt was very different for me.
I also hear a little bit of Kaytranada in songs like "Wonderland," which is an incredible album opener.
Yes, I love me some Kaytranada. Pop music has always been a way for me to escape my world. In my world, everything was church 24/7, and pop music was frowned upon. I remember I was grounded for a year for listening to Lady Gaga, which is crazy. I would still sneak. I took a computer class in middle school just so I could go online and download songs and burn them onto CDs that I would buy at the Dollar Tree. Pop music and R&B music has always just been that escape for me.
How did you start making your own music?
At first, it was Windows Movie Maker. "High School Musical 2: The Soundtrack" had just come out, and I was so excited. We had gotten this huge Dell desktop computer, and I would spend all day with this [Nintendo] Wii microphone that came with the "High School Musical 2" video game. I would connect it to my laptop and just layer and layer vocals.
That progressed into a random program I found called Mixcraft, which I still use now. I found that in sixth grade, and I hadn't ever seen an eight-track program before. My mind exploded.
Zeke, do you write and produce all your work?
I produced the whole album. I use Splice loops, but I did the tempos and put it all together. I have to because … I'm broke. Hopefully one day, I'll have the budget, but I'm just not there yet. I see other people with teams and backing, and I'm like, "I wish I could do that." That's why I'm really inspired by artists like Tinashe. She just released an amazing record, and it's getting me through a lot right now.
You grew up in a musical family. Did that influence the record?
I'm good with harmonies because of my mother. My mother is the music director at my church. I remember she had us writing songs and performing them when I was young. That main choir chorus on "Kryptonite" was heavily influenced by Fred Hammond and Kirk Franklin. That's what I listened to a lot of when I was younger.
Photo courtesy of Zeke Forever.
The interludes on the album are pulled from interviews you did with family. They immediately brought to mind Blonde and CTRL. Tell me more about why you decided to incorporate them into the record.
My biggest inspiration for that is Solange's "A Seat At The Table." I think that that taught me that I don't have to over explain lyrics. I can just use the interludes to talk about my story.
I interviewed all of the people in my room. I felt alone during this time writing this album, but they were the ones that were checking up on me.
It's crazy because me and my family, I always thought that we would never be close. My dad has kind of been one of my biggest cheerleaders. I feel like a lot of great things that happened in my life happened after feeling the worst. What I really wanted to tell anyone that listens is that you're not alone and your nights won't last always.
Was there anything non-musical that was a big influence for you during the making of the album?
A lot of these songs are also inspired by TV shows that I binge-watched. "Kryptonite" is a song about loneliness. I was kind of dealing with this weird friendship situation, and they kind of just ghosted me. Instead of dealing with that loneliness, I had started watching "The Get Down." I loved the disco music that was coming along. "Fade" is a song that kind of references Issa and Molly's relationship [on "Insecure"] and how they were falling apart this season. But, also my friendship was falling apart at the same time. It was just really inspired by a lot of things that I was watching and listening to in the pandemic, which was kind of cool.
Toward the end of the album, your father is heard saying "greatness comes from great struggle." How does that line resonate in your life?
You have to struggle to get to a point where you're learning lessons. I'm becoming more intuitive because for me in my whole life, loneliness has been one of my biggest struggles. I have tried to avoid loneliness.
The pandemic was a blessing and a curse. Obviously, it's a curse because COVID-19 has killed so many people, but during the lockdown, I couldn't not be alone. I had to learn a lot about my reactions, and that was a really big struggle. I mean, I still hate loneliness. It's literally my kryptonite, but after that struggle, you find different ways to deal with it and to become stronger. If you're able to take that and make something out of it, then everything will be OK. Everything will be OK.
Got a tip? Email Miguel Perez at [email protected]. You can follow him on Twitter @quillindie.
Art&Seek is made possible through the generosity of our members. If you find this reporting valuable, consider making a tax-deductible gift today. Thank you.
Kaytranada
Zeke Forever
About Miguel Perez
Miguel Perez is an arts reporter and digital producer for Art&Seek. Before he joined KERA's arts and culture team, Miguel was helping put together newscasts as an assistant producer for the stations local Morning Edition broadcast. View more about Miguel Perez.
Music of La Convivencia
@ Zion Lutheran Church
Sat, Jan 29 at 7 pm Zion Lutheran Church 6121 East Lovers Lane, Dallas, ...
Music: World
Pyre Blend at Fort Brewery & Pizza
Free local music at the new Fort Brewery & Pizza. No cover. Seating is...