text:
\section{Introduction}
An American Digital Put (Am-DIP) with (lower) barrier B pays the amount of $1$ EUR at maturity $T$ in case that the underlying spot level $S_t$ has touched the barrier during the life of the contract, e.g.
\begin{equation}\label{eq:1}
Am - DIP(T,S_T,B,T) = \mathbf{1}_{\tau_B<T}
\end{equation}
where $Am - DIP(t,S_t,B,T)$ denotes the price of the Am-DIP at time $t$ and $\tau_B$ denotes the stopping time of the price process $S_t$ related to the barrier $B$. Standard option pricing theory assumes the existence of an equivalent martingale measure. This implies that the fair value of payoff \eqref{eq:1} is given by an expectation under the forward adjusted probability measure $Q_T$ \footnote{Throughout this paper interest rates are assumed non-stochastic so that the forward-adjusted and risk-neutral measure are used interchangeably in the sequel},e.g.
\begin{equation}\label{eq:2}
Am - DIP(t,S_t,B,T) = Df \; E^{Q_T}(\mathbf{1}_{\tau_B<T} | \mathcal{F}_t)
\end{equation}
where, as usual, $Df$ denotes the discount factor to maturity and $\mathcal{F}_t$ is the filtration in the probability triple $(\Omega,P,\mathcal{F})$.
\\
\\
In order to evaluate \eqref{eq:2}, standard modeling procedure requires the prior knowledge of the full dynamics of the spot process $S_t$. For example, in the case of a continuously trading economy where the filtration is generated by two Brownian motions $W_t$,$\tilde{W}_t$, a common class of processes have the following form
\begin{align}\label{eq:3}
\frac{dS_t}{S_t} &= \mu(t,\sigma_t)dt + \sigma_t dW_t \notag \\
d\sigma_t^2 &= \eta(t,\sigma_t)dt + \nu(t,\sigma_t)d\tilde{W}_t
\end{align}
where the correlation $\rho$ between the two Brownian motions is given by
\begin{equation}\label{eq:4}
<dW_t,d\tilde{W}_t> = \rho \ dt
\end{equation}
$S_t,\sigma_t,\mu(\dots),\eta(\dots),\nu(\dots)$ denote the spot, volatility, drift of the spot, drift of the volatility and vol-of-vol respectively.
\\
For example, if one sets $\eta(t,\sigma_t) = \kappa(\Theta-\sigma_t^2)$ and $\nu(t,\sigma_t) = \sqrt{\sigma_t^2}w$ for some level of the mean-reversion speed $\kappa$ and mean-reversion level $\Theta$ as well as a vol-of-vol parameter $w$, one obtains the Heston model of stochastic volatility in this case. Note that the dynamics defined in \eqref{eq:3} does not necessarily lead to an equivalent martingale measure. Without specifying the conditions in detail, for the purpose of this paper, we restrict the functions defined in \eqref{eq:3} such that the Novikov condition is fulfilled for the variance process at all times.
\\
\\
As far as the pricing of Am-DIP is concerned, \eqref{eq:3},\eqref{eq:4} can readily be integrated to obtain  the expectation value of \eqref{eq:2}. However even after a successful completion of this task the following questions remain:

\renewcommand{\labelenumi}{\roman{enumi}}
\begin{enumerate}
\item
How does the pricing of the American-DIP depend on the particular choice of the dynamics in \eqref{eq:3}?  If there were to exist two different models that both are consistent with the market prices for plain-vanilla options, which model should one prefer in practice and how can one specify the model-sensitivity more generally for the Am-DIP?
\item
How can one establish confidence in the parameterization of \eqref{eq:3} in situations where the barrier level B is below the traded strike range of the plain vanilla option market and hence no direct calibration of the parameters is possible?
\item
How can a conservative price be constructed in the pricing framework of \eqref{eq:3} and how can the hedges be best constructed and interpreted?
\end{enumerate}

In this paper we pursue an alternative pricing methodology for the American digital put option. Our approach utilizes a well-known intuitive relationship between American and European digital puts options in the Black-Scholes world and generalizes the latter to a situation where a volatility skew is present.
\\
\\
Hence our approach is primarily driven by hedging intuition of the American digital put and is, in this sense, conceptually different to the approach outlined above. In this paper we argue that the full knowledge of the dynamics is not required in order to solve the pricing problem of \eqref{eq:2}.  Hence our approach relies on fewer specific assumptions and can be viewed as a framework that simultaneously describes a wide range of different stochastic processes. This is in contrast to the standard option pricing philosophy of \eqref{eq:3} which requires the full \textit{a-priori} knowledge of the stochastic process.
\\
\\
Note that the idea of relating the valuation of knock-out options directly to the hedge is not a new idea. Under the special assumptions of driftless spot processes and symmetric distributions Carr et al \cite{Carr} describe how barrier options can be written as a portfolio of plain-vanilla options. In a later paper Carr and Lee generalize Put-Call Symmetry to a wider class of processes \cite{Carr2}. However two different pricing models that are both consistent with the plain-vanilla market will generally yield different values for knock-out options if these assumptions are relaxed. Hence knock-outs exhibit "`exotic risk"' that cannot be hedged into plain-vanilla instruments. As will be discussed in the paper such valuation differences can arise due to different dividend assumptions. In addition forward distributions for the spot are not uniquely determined by the plain-vanilla space either. As will be discussed in a later chapter this will lead to different unwinding costs of the hedge at the barrier which in turn will affect the price of the American digital put and hence give rise to model-risk.
\\
\\
The paper is outlined as follows:
\\
\\
Chapter 2 recaps a well-known approximate  relationship between American and digital puts in the case of a Black-Scholes world.
\\
\\
Chapter 3 derives an integral-equation for the stopping time density in the presence of a volatility skew.
\\
\\
Chapter 4 compares a specific instantaneous pricing model to our approach. We show how prices can be reconciled with our methodology once the forward volatility skew as well as the dividend assumptions are known at the barrier. Hence as a result one can think of our approach as a "pricing framework" that simultaneous comprises a large class of different pricing models.
\\
\\
Chapter 5 discusses the skew sensitivity of an American Digital puts.
\\
\\
Chapter 6 discusses an example for the conservative pricing of an equity default swap.

\pagebreak
\section{A "handy" relationship between American Digital Puts and European Digital Puts in a Black-Scholes world}
In contrast to an Am-DIP, European digital puts (Eur-DIP) pay an amount of 1 Euro in the case that the terminal spot price is below a barrier $B$ at the time of maturity, e.g
\begin{equation}\label{eq:5}
Eur-DIP(T,S_T,B,T) = \mathbf{1}_{S_T<B}
\end{equation}
where $Eur-DIP(t,S_t,B,T)$ denotes the price of a Eur-DIP at time $t$ with strike $B$. Hence
\[
Eur-DIP(t,S_t,B,T) = Df \; E^{Q_T}(\mathbf{1}_{S_T<B} | \mathcal{F}_t)
\]
Hence Eur-DIP are "non-exotic" as its price is a direct consequence of the plain-vanilla European option market. The relationship is given by
\begin{equation}\label{eq:7}
Eur-DIP(t,S_t,B,T) = \frac{dPut(t,T,K=B)}{dK}
\end{equation}
where $Put(t,T,K)$ denotes the value of a plain-vanilla European put of strike $K$ and is given by the Black-Scholes equation
\begin{equation}\label{eq:8}
Put(t,T,K) = Df \; (K \mathcal{N}(-d_2) - F \mathcal{N}(-d_1))
\end{equation}
where
\[
d_{1/2} = \frac{ln(\frac{F}{K})\pm \frac{1}{2} \sigma^2 (T-t)}{\sigma\sqrt{T-t}}
\]
In the particular case of a Black-Scholes world, the volatility does not depend on the strike and the rhs of \eqref{eq:7} simplifies to
\begin{equation}\label{eq:10}
\frac{dPut(t,T,K=B)}{dK} = Df \; \mathcal{N}(-d_2)
\end{equation}
Here $F,B,\sigma,T$ denote the forward, strike, volatility and maturity respectively.
\\
\\
Eq. \eqref{eq:7} states that the price of Eur-DIP is model-independent, given the derivative of the European Puts with respect to the strike.
\\
\\
Eq. \eqref{eq:10} allows one to derive an approximate relationship between the Am-DIP and the  Eur-DIP in a Black-Scholes world. In order to see this we note that at the time $\tau_B$ of hitting the barrier $B$, the forward price and the barrier price is approximately the same, e.g
\[
F_{\tau_B}(T) = S_{\tau_B}(1+\Delta) = B(1+\Delta)
\]
with a small correction $\Delta$. Hence the value of a Eur-DIP at the barrier is given by
\[
Eur-DIP(\tau_B,B,B,T-\tau_B) = Df \; \mathcal{N}(-\frac{log(1+\Delta)}{\sigma\sqrt{T-\tau_B}} + \frac{1}{2}\sigma\sqrt{T-\tau_B})
\]
In most cases one observes for sufficiently small values for $T-\tau_B $ that $-\frac{log(1+\Delta)}{\sigma\sqrt{T-\tau_B}}+\frac{1}{2}\sigma\sqrt{T-\tau_B} \approx 0$ and hence
\begin{equation}\label{eq:13}
Eur-DIP(\tau_B,B,B,T-\tau_B) \approx Df \; \frac{1}{2}
\end{equation}
On the other hand, at the time of hitting the barrier, the price of the Am-DIP put equals the discount factor to maturity so that the following approximate relationship is obtained
\begin{equation}\label{eq:14}
Am-DIP(t,S_t,B,T) \approx 2 \; Eur-DIP(t,S_t,B,T)
\end{equation}
In order to interpret \eqref{eq:14} intuitively, assume that one goes short an American Digital Put of notional $N$ at time $0$. As a hedge \eqref{eq:14} suggests to go long a European Digital Put option of notional $2N$ at the same time.
\\
\\
The following two scenarios are of relevance:

\renewcommand{\labelenumi}{\arabic{enumi}}
\begin{enumerate}
\item
The spot never touches the barrier prior to maturity
\\
\\
In this case neither the American nor the European Digital Put are paying out.
Hence one breaks even in this case.
\item
The spot touches the barrier prior to maturity
\\
\\
The American Put is paying out the notional $N$ at maturity in this case. The
European-Digital-Put on the other hand is at the money when the barrier is
touched. This implies that the hedge is worth approximately $50\%$ of the notional
$2N$ at that time (see \eqref{eq:13}). Hence the money made by liquidation of the hedge at
the time of touching the barrier finances the Am-DIP position in this case.
\end{enumerate}
Hence the hedging argument presented above intuitively "explains" \eqref{eq:14}.
\\
\\
However, the precise relationship between Am-DIP and Eur-DIP depends on the exact value of $\mathcal{N}(-\frac{log(1+\Delta)}{\sigma\sqrt{T-\tau_B}}+\frac{1}{2}\sigma\sqrt{T-\tau_B})$ which does not equal $\frac{1}{2}$ even in a Black-Scholes world.
\\
\\
In reality also the price of a forward contract at time $\tau_B$ is of relevance in addition to the level of Black-Scholes volatility at that time.
\\
\\
In addition, when a volatility skew is present, Eq. \eqref{eq:7} implies an additional vega term such that  \eqref{eq:7} can be  written as
\begin{equation}\label{eq:15}
Eur-DIP(t,S_t,B,T) = Df \ \mathcal{N}(-d_2)+vega \; \sigma'(B)
\end{equation}
where $\sigma'(B)$ denotes the slope of the Black-Scholes implied volatility at the barrier $B$. Eq.\eqref{eq:15} also states that the price of the Eur-DIP decreases with the volatility-skew increasing. This observation will prove important in later sections.
\\
\\
The vega term in \eqref{eq:15} describes the contribution of the volatility skew to the price of the Eur-DIP. It becomes particularly important when the barrier is hit and the Eur-DIP hedge must be unwound. The vega term affects the price of the portfolio at that time and quantifies the price impact that is due to the deviation from log-normality. It is instructive to attach some numbers to a specific example in order to get a better understanding for the impact of the volatility skew.
\\
\\
Consider a one month European Put spread struck at the money. The European Put spread prices at $50.5\%$ if the vega term is ignored in \eqref{eq:15}. The correct value that includes the vega contribution is $44.7\%$. Hence on a notional of 800 Mio USD the pricing difference will be 46 Mio USD.
\\
\\
Hence one concludes that, in the presence of a forward-volatility skew, an additional deviation from the "unwind-factor" $\frac{1}{2}$ occurs that is due to the at-the-money slope of the forward volatility skew at the time of hitting.
\pagebreak
\section{Pricing methodology}
The valuation of a Am-DIP requires the knowledge of the stopping time density $\rho(\tau)d\tau$ which is the probability of first hitting the barrier between the time $\tau$ and $\tau+d\tau$.
\\
\\
However, the knowledge of $\rho(\tau)d\tau$ also allows to relate Eur-DIP at different valuation times: From
\begin{align*}
Eur-DIP(0,S_0,B,T) &=  E^\beta[\mathbf{1}_{S_T<B}| \mathcal{F}_0] =  E^\beta[\mathbf{1}_{S_T<B}\mathbf{1}_{\tau_B<T}| \mathcal{F}_0] \\
&= \int_0^Td\tau \; E^\beta[\mathbf{1}_{\tau_B \in d\tau}| \mathcal{F}_0]E^\beta[\mathbf{1}_{S_T<B}| \tau_B \in d\tau,  \mathcal{F}_0]
\end{align*}
where $E^\beta[\dots]$ denotes the expectation under the risk-neutral measure. Without loss of generality \footnote{Note that throughout this paper interest rates are assumed non-stochastic }we have set the discount factors to one in order not to unnecessarily complicate the equations.
It follows that
\begin{equation}\label{eq:16}
Eur-DIP(0,S_0,B,T) = \int_0^Td\tau \rho(\tau) \; EurDIP(F_\tau(T),B,T-\tau,\hat{\sigma}_{B,\tau,T-\tau},\hat{\kappa}_{B,t,T-\tau})
\end{equation}
\\
The variables $\hat{\sigma}_{B,\tau,T-\tau}$ describe the "forward - volatility" at the stopping time $\tau$ of an option with maturity $T$ when the spot price is first at the level $B$. Similarly $\hat{\kappa}_{B,\tau,T-\tau}$ describes the "forward-at-the-money-volatility-slope" at time $\tau$.
\\
Eq. \eqref{eq:16} defines the stopping time density
\[
d\tau \; \rho(\tau) \equiv E^\beta[\mathbf{1}_{\tau_B \in d\tau} | \mathcal{F}_0]
\]
and
\begin{equation}\label{eq:17}
EurDIP(F_\tau(T),B,T-\tau,\hat{\sigma}_{B,\tau,T-\tau},\hat{\kappa}_{B,\tau,T-\tau}) \equiv E^\beta[\mathbf{1}_{S_T<B}|\tau_B \in d\tau,  \mathcal{F}_0]
\end{equation}
\\
\\
where the explicit form of the lhs of \eqref{eq:17} follows  from \eqref{eq:15} and \eqref{eq:8}.
\\
\\
Eq.\eqref{eq:16} defines an integral equation for the unknown stopping time $\rho(\tau)$. It will play a crucial role in our methodology.
\\
\\
For a given complete set of plain vanilla option prices, the lhs of \eqref{eq:16} is fully specified. On the rhs, the value of  $Eur-DIP(\dots)$  only depends on the forward volatility $\hat{\sigma}_{B,\tau,T-\tau}$, and the forward-at-the-money volatility slope $\hat{\kappa}_{B,\tau,T-\tau}$ in conjunction with the forward price $F_\tau(T)$. In the case where these quantities are specified Eq.\eqref{eq:16} can be solved for $\rho(\tau) $ without the explicit knowledge of the stochastic process. This is the strategy followed in this paper.
\\
\\
Putting it another way, two different pricing models of the type outlined in \eqref{eq:3} that reproduce identical prices for the vanilla options, have different  stopping time densities if at least one of the following statements is correct:
\\
\\
\renewcommand{\labelenumi}{\roman{enumi}}
\begin{enumerate}
\item
The models disagree on the level of forward volatility of an at-the-money call at the time when the barrier is hit $\hat{\sigma}_{B,\tau,T-\tau}$.
\item
The at-the-money slope of the forward volatility surface is different at the time of hitting $\hat{\kappa}_{B,\tau,T-\tau}$.
\item
The forward price $F_\tau(T)$ is different at the time of touching the barriers.
\end{enumerate}
Note that case (iii) typically occurs when two models have different dividend assumptions despite the fact that $F_0(T)$ is the same in both cases: A proportional dividend model will generally exhibit a higher value for $F_\tau(T); \; \tau > 0$ compared to a model where dividend amounts are assumed to be independent of spot.
\\
\\
From this discussion it follows that, for the purpose of  pricing Am-DIPs, details of the stochastic process only matter to the extent that they produce differences in at least one of the quantities above. Should continuous pricing models produce the same values for $\hat{\sigma}_{B,\tau,T-\tau}$,$\hat{\kappa}_{B,\tau,T-\tau}$,$F_\tau(T)$ in addition to identical plain vanilla market prices, they also agree on the price of Am-DIP as well.
\\
\\
In order to solve \eqref{eq:16} we discretise the equation according to
\[
T_n = n\Delta T
\]
where $T_N = T$ and $T_0 = 0$ with the result
\begin{align}\label{eq:19}
&EurDIP(S_0,B,T_{n+1},\hat{\sigma}_{B,0,T_{n+1}},\hat{\kappa}_{B,0,T_{n+1}}) \notag \\
&=\int_0^{T_n}d\tau \rho(\tau) \; EurDIP(B,B,T_n-\tau,\hat{\sigma}_{B,\tau,T_n-\tau},\hat{\kappa}_{B,\tau,T_n-\tau}) \notag \\
&+ \Delta T \rho(T_n) \; EurDIP(B,B,\Delta T,\hat{\sigma}_{B,T_n,\Delta T},\hat{\kappa}_{B,T_n,\Delta T})
\end{align}
for $n=0,\dots,N-1$.
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\\
Eq. \eqref{eq:19} states the main result of this paper. It defines a recursive equation for $\rho(.)$ which can easily be solved numerically provided that the quantities outlined in (i),(ii),(iii) are known.
\\
\\
Note that \eqref{eq:19} relates the stopping time density directly to Eur-DIP-prices as well as the forward-vol and forward-vol-slope at the time of hitting. In the case where these values are provided, \eqref{eq:19} allows the calculation of $\rho(.)$ without the explicit prior knowledge of the full stochastic process for $S_t$. Even though the quantities $\hat{\sigma}_{B,\tau,T-\tau}$,$\hat{\kappa}_{B,\tau,T-\tau}$  are not explicitly traded, they represent "market-variables" \footnote{as opposed to model parameters}. Hence a trader should have good intuition about these values together with (conservative) bounds for them.
\\
\\
In the remaining chapters of this paper we will apply \eqref{eq:19} explicitly and discuss consequences.
\\
\\
Once the stopping time densities have been found, the American digital put can be valued according to
\begin{align}\label{eq:19a}
Am-DIP(B) = Df(T) \; \int_0^T d\tau\rho(\tau)
\end{align}
In cases where the payment is made at the time of hitting the price is given by
\[
Am-DIP(B) = \int_0^T d\tau \rho(\tau) Df(\tau)
\]
where $Df(t)$ denotes the discount factor at time $t$.
\pagebreak
\section{Relationship with standard Pricing models}
Eq.\eqref{eq:19} and Eq.\eqref{eq:19a} state that the stopping time densities can be determined if the cost of unwinding the hedge can be calculated. This is the case if the level and the slope of volatility is known at the time the barrier is first hit. This means that our pricing methodology in effect describes a whole class of specific diffusion models simultaneously.
\\
\\
In order to demonstrate this more explicitly let us price a one year Am-DIP on STOXX50E struck at $90\%$ of spot.
\\
\\
The Black Scholes Barrier Price is $64\%$ whereas the local vol price turns out to be $54.9\%$.
\\
\\
If one pre-calculates at-the-barrier-forward-volatilities together with its slope in the local-volatility model and subsequently uses these values in Eq.\eqref{eq:19} we obtain a value of $54.8\%$ in our approach.
\\
\\
Hence our pricing methodology coincides with local vol if one chooses the barrier vol as well as barrier vol slope obtained in this model.
\\
\\
The crux of our pricing methodology is the observation that different models can give rise to pricing differences only to the extent that their volatility slope or dividend treatment differ upon touching the barrier.
\\
\\
This offers a new way to stress the assumptions of a given model by bumping the vol and slope at the barrier calculated by the model.
\\
\\
It is well known that the local vol model underestimates the level of forward skew substantially. Our approach on the other hand allows the tuning of future skews explicitly in a realistic way.
\\
\\
\pagebreak
\section{Skew Risk in American Digital Puts}
It is very instructive to discuss some details of the skew risk in the American DIP explicitly.
\\
\\
In the following we graph the price of  a 6 month Am-DIP struck at $90\%$ of spot as a function of the barrier-skew at inception (spot-skew). The skew factor denotes the skew in units of the market volatility slope at the time of pricing. It shows that the price of an Am-DIP decreases with a steepening of the volatility skew.
\\
\begin{figure}[hptb]
\centering
\includegraphics[width=\textwidth,height=0.4\textheight,keepaspectratio=false]{fig1.png}
\caption{Price of an Am-DIP as a function of spot-skew. A "`skewfactor"' of 1 corresponds to the current market level of the vol-slope. The graph shows that Am-DIPs are short spot-skew. }
\label{fig:1}
\end{figure}
\\
As outlined in the introduction Am-DIP options can be approximately replicated by a EUR-DIP position with twice the notional of the Am-DIP (see \eqref{eq:14}). Hence the flatter the spot skew the more expensive the costs of putting on the initial hedge (see also  Eq. \eqref{eq:15}) and therefore the higher the fair value of the Am-DIP. This is reflected in Fig.\ref{fig:1}.

Graph Fig.\ref{fig:2} displays the dependence on the forward skew for a 6 month Am-DIP with barrier of $60\%$:
\\
\begin{figure}[hptb]
\centering
\includegraphics[width=\textwidth,height=0.4\textheight,keepaspectratio=false]{fig2.png}
\caption{Am-DIP sensitivity to the forward skew at the time of first hitting. A FwdSkewFactor of 1 corresponds to the spot-skew. The graph shows that Am-DIPs are long forward skew}
\label{fig:2}
\end{figure}
\\
One observes that, in contrast to the short spot-skew behavior, Am-DIP are long forward-skew instead. Intuitively this is obvious: the steeper the volatility-skew at the time of unwinding the hedge the less money is retrieved which results in a higher price of the AM-DIP in this case.

Hence we summarize that the price of an AM-DIP is short spot-skew but long forward-skew at the barrier. It is questionable whether, for the purpose of determining a conservative price for the Am-DIP, the stochastic class of models outlined in \eqref{eq:3} allows one to "`tune"' spot-skew and forward-volatility skew in opposite direction.
This is in contrast to our approach where spot-skew, forward-skew and forward vol can be tuned independently such that a conservative price can be obtained.
\\
\\
\\
Fig.\ref{fig:3} shows the result of an explicit calculation of the hitting time using Eq.\eqref{eq:19} for different assumptions of the forward-skew. The steeper the forward-skew, the higher the price of the Am-DIP and hence the higher the cumulative hitting probability that is obtained from \eqref{eq:19}.
\begin{figure}[hptb]
\centering
\includegraphics[width=\textwidth,height=0.4\textheight,keepaspectratio=false]{fig3.png}
\caption{Cumulative hitting probability for different assumption of the forward-skew as a function of time.}
\label{fig:3}
\end{figure}
\\
\\
\pagebreak
\section{A pricing example for an Equity-default swap}

In this section we discuss the pricing of a 6 month Equity default swap (EDS) on Commerzbank with a barrier of 70\% down as of the 15 Dec 2009.
As the share price at the time traded at 5.945 Euros this implies that the Equity default swap pays out if at any time between 15-Dec-2009 and 15-Jun-2010 the price drops
below 1.78 Euros. This price drop of 70\% may not result into default necessarily but would most likely result in serious distress of the company.
The at-the-money vol traded roughly at 52\% whereas our estimates for the vol at the barrier is about 80\%. The spot barrier slope could be around -11\% according to our estimates. If one were to assume the vol and slope upon touching to be the same one obtains a price of 165 basis points for the price of the EDS. However it is impossible to obtain plain-vanilla option quotes at strikes near the barrier level.  As one is short spot skew, for the purpose of obtaining a conservative price estimate, we take 80\% of our best estimate for this quantity and obtain a value of 180 basis points instead. In the case of the forward volatility skew we increase the original value by a factor of 2 in order to obtain a new estimate of 187 basis points. Similarly one can correct the price further if one bumps the best estimate for the spot barrier-vol up further to 86\% while bumping the forward vol at the barrier down by 5\%. In this case we obtain the conservative price of 281 basis-points. In a similar way different dividend assumptions
can be tested upon hitting the barrier in order to incorporate conservative dividend assumptions into the pricing. Note that even if the pricing was done more aggressively our approach is ideally suited for calculating reserves for this trade. Finally we remark that due to liquidity issues
as well as jump risk it may not be possible to unwind the trade at exactly the barrier level. An additional shifting of the barrier towards higher levels could take these effects into account.

\section{Acknowledgement}

I would like to thank Syed Aqeel and Alexander Kabanov for constructive comments on this paper.

\bibliographystyle{plain}

redpajama_set_name: RedPajamaArXiv


text:
During the 2001–02 English football season, Coventry City F.C. competed in the Football League First Division, following relegation from the FA Premier League the previous season.

Season summary
Despite the signing of prolific striker Lee Hughes from local rivals West Bromwich Albion, Coventry City were unable to make a genuine push for an immediate return to the Premier League and finished well away from promotion in 11th place. Manager Gordon Strachan had been sacked after five games with only one win and Coventry 19th; this heralded the beginning of an eleven-match unbeaten run which saw Coventry top the table with a third of the season gone, but from then three straight losses took them down to ninth. Coventry never regained the form from that unbeaten run, but with seven games left to play they stood fourth and appeared almost certain to gain a playoff place. Unfortunately, Coventry only gained one point from those last seven games and fell down to 11th place.

Final league table

 Pld = Matches ; W = Matches won; D = Matches drawn; L = Matches lost; F = Goals for; A = Goals against; GD = Goal difference; Pts = Points
 NB: In the Football League goals scored (F) takes precedence over goal difference (GD).

Results
Coventry City's score comes first

Legend

Football League First Division

FA Cup

League Cup

Squad

Left club during season

Reserve squad

Transfers

In
  Julian Joachim -  Aston Villa, 6 July, part-exchange
  Keith O'Neill -  Middlesbrough, 8 August, £750,000
  Lee Hughes -  West Bromwich Albion, 8 August, £5,000,001
  Youssef Safri -  Raja Casablanca, 11 August, £700,000
  Andy Goram - unattached (last at  Hamilton Academical), 24 August
  Lee Mills -  Portsmouth, 1 January, £250,000
  Paul Trollope -  Fulham, 22 March, free

Out
  Stephen McPhee - released (later joined  Port Vale on 24 June)
  Craig Bellamy -  Newcastle United, 25 June, £6,000,000
  John Aloisi -  Osasuna, 3 July, £1,200,000
  Mustapha Hadji -  Aston Villa, 6 July, £2,000,000 plus Julian Joachim
  John Hartson -  Celtic, 2 August, £6,000,000
  Chris Kirkland -  Liverpool, 31 August, £6,000,000
  Paul Williams -  Southampton, 31 October, free
  Paul Telfer -  Southampton, 31 October, free
  Carlton Palmer -  Stockport County, 6 November, free
  Tomas Gustafsson -  Copenhagen, 4 February, undisclosed
  Lee Carsley -  Everton, 8 February, £1,900,000
  Roland Nilsson - retired, 8 April
  Steve Froggatt - retired
  Andy Goram -  Oldham Athletic

Loan in
  Lee Mills -  Portsmouth, December, one month
  Horacio Carbonari -  Derby County, 22 March, one month
  Colin Healy -  Celtic, 29 January, 84 days
  Tim Flowers -  Leicester City

Loan out
  Carlton Palmer -  Sheffield Wednesday, 4 September, 46 days

References

Coventry City F.C. seasons
Coventry City

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Both accidents happened on the afternoon of February 5. At about 4:30 p.m., a bus with Chattooga County Schools in Georgia was traveling in the area of Highway 114 and Highway 100 in Summerville, Georgia. At the intersection of the two highways, a logging truck sideswiped the school bus.
The logging truck continued on the highway after the collision and did not stop. Authorities are wondering if the driver knew he hit another vehicle. Photos from the scene show a hole in the bus with wood debris hanging from it. It is not clear how many students were on board the bus at the time or whether anyone on the bus was injured.
At nearly the same time, a bus with Rhea County Schools in Tennessee was traveling on Highway 27 in Spring City, Tennessee. At the North red light, the school bus somehow collided with another vehicle. The make and model of the vehicle were not reported, and the circumstances of the collision were not provided in reports.
It is also not clear how many students were on this school bus at the time of the crash. Reports have not yet confirmed whether anyone was injured in this accident.
Authorities are investigating both accidents, and no further information has been released at this time.


text:
Biografia
Nato a Vienna il 13 febbraio 1823 in una famiglia aristocratica, figlio di un capitano della cavalleria dell'esercito austriaco.

Arruolatosi nell'esercito imperiale austriaco il 25 ottobre 1834, Pichler frequentò l'Accademia Militare Teresiana di Wiener Neustadt. Promosso tenente il 16 febbraio 1846, prestò servizio in Italia nel 59º Reggimento di fanteria "Arciduca Ranieri" e nel 3º Reggimento di fanteria "Duca Carlo". Combatté nelle guerre di indipendenza del 1848, 1849 e nel 1859, ove si distinse, con il grado di capitano,  nella battaglia di Montebello tale da essere decorato con la croce di guerra. Il 13 luglio 1859 fu promosso al grado di maggiore.

Nel 1866 con lo scoppio della terza guerra di indipendenza,  comandò le forze austriache che  contrastarono la colonna italiana del generale Giacomo Medici avanzante in Valsugana, ove rimediò, seppure in forte inferiorità numerica, tre pesanti sconfitte a Primolano il 22 luglio, a Borgo Valsugana il 23  e a Levico Terme il 23-24, quando fu rilevato nel comando dal generale Carl Kaim von Kaimthal sopraggiunto dalle Giudicarie con i rinforzi necessari.

Nel 1867 fu decorato della croce di cavaliere dell'ordine Imperiale di Leopoldo per essersi distinto nel corso delle operazioni militari in Tirolo.

Onorificenze

Note

Bibliografia
 Ugo Zaniboni Ferino, Bezzecca 1866. La campagna garibaldina dall'Adda al Garda, Trento 1966.
 R. Gasperi, Per Trento e Trieste. L'amara prova del 1866, 2 voll. Trento 1968.

Voci correlate
 Invasione del Trentino (Medici - 1866)

Persone della terza guerra d'indipendenza italiana


text:
All posts in olympic games
Home/Archive by Category "olympic games"
If you are going to Rio Olympics and don't have any mobile data tariff "Don't risk your money"
August 8, 2016 / in olympic games / by Cronos Team
mobile dataolympic gamesrioroaming
This summer the Olympic games in Rio are planning to be exciting, not just for the tournaments but for all the sport fans that are going to be filling up the big city of Rio. That's why they should be assured of what are going to be paying off for this holidays. The main concern? "Roaming mobile phone charges" which can be expected to be around $3,000 to $4,000.
América Móvil for instance, is a sponsor and official supplier of mobile services in Rio. For this event, the group will have a 'backbone' 374km fiber optic. With other networks such as Vodafone customers will be satisfied that the teleco's $5/day roaming deal will still work all around the country and during all year after the Olympics.
In the case of company Optus when travels to Brazil normally the cost for customers will be at $2/minute to make calls, $1 per SMS and $1 per MB. However, during the period of August 1st and September 28th 2016, this tariff will change to $10/day for the Travel Pack which will cover the Olympic host country as well. This means users will get unlimited local and international calls plus unlimited SMS whilst visiting the country for $10/day. Adding also a daily data allowance of 50MB, letting customers use it at their leisure across multiple days.
T-Mobile goes all in for the games. The carrier said "domestic customers traveling to the games will have access to unlimited "high-speed" data in Brazil throughout August, though with the fine print stating "primary usage must occur on the U.S. Sprint network" and "service may be terminated or restricted for excessive international use."
Also, customers must be on the Sprint Open World plan, which is available at no charge for postpaid customers, and have a roaming capable device. Those users also will have access to the plan's regular unlimited calling and text messaging features, with the data bonus over the standard 1 gigabyte of unthrottled usage.
On the other hand, another option for sports fans would be thinking of buying a Brazilian SIM card instead. This wouldn´t been allowed before programing the Olympic Games in Brazil, only residents were allowed to buy and register local SIM cards, basically the people who have a Brazilian CPF (the country´s version of a tax file number). Although that is possible now, the best option regardless a SIM card would be the TIM Visitor Prepaid ´chip´, which is fully designed for international visitors.
Therefore, if you are attending the games in Rio make sure you get an add-on roaming tariff, otherwise you will be overcharged and that could cost you at least $3,000 easily. Bear this in mind and enjoy the Olympics without paying too much.

redpajama_set_name: RedPajamaCommonCrawl


text:
Le elezioni regionali in Calabria del 1970 si tennero il 7-8 giugno.

Risultati elettorali

Collegamenti esterni

1970
Calabria


It was there from a unequivocally beginning, a thought of somehow stuffing scarcely dual dozen classical Midway games into a Lego Dimensions enlargement pack.
But primarily a developers during TT Games weren't utterly certain how they were going to do it.
What he and a rest of a group knew was that they had a permit to obey about 25 games. They knew that they were origination a diversion that was meant to be a arrange of vital creation, a height that could play horde to a broad, ever-increasing accumulation of properties recreated in Lego form and incited into levels, characters or gadgets that snap, brick-like, onto a categorical game.
Those properties enclosed films like The Wizard of Oz, The Lego Movie and The Lord of a Rings; radio shows like The Simpsons, Doctor Who and Scooby-Doo; DC Comics characters; and even toys like Ninjago.
But Lego Dimensions customarily had one diversion inside a game, Portal 2.
The group felt that a Midway Arcade pack, that was meant to come out as one of a final announced updates for Lego Dimensions, was a possibility to try games in a same proceed a group has been so successful exploring other facets of cocktail culture.
"We wanted to try and deliver all of these good classical games that some of us know to a new generation," Warburton said. "There's never been a good entrance to try classical games. Once a console dies it's kind of tough to get ahold of those classics.
Founded in 1958, Midway filed for failure in 2009, and Warner Bros. purchased many of a company's assets.
That meant that when Lego Dimensions came around, TT Games was means to get ahold of and use all of a strange Midway games and ROMs.
"They had entrance to a whole library," Warburton said.
But a group had to come adult with an proceed that would make sense.
"What we wanted to do in a categorical diversion was to reconstruct some of these classics in section form," he said.
The strange diversion enclosed a turn that overwhelmed on some of a Midway arcade themes, though didn't unequivocally excavate into all of those properties.
For this expansion, TT Games motionless to come adult with an engaging proceed to wobble a story around a need to hunt down and play a series of arcade games in their strange form, while also traffic with some of a Lego-ized versions of a diversion characters.
Much of a turn takes place inside an arcade left amuck, that spills all of a characters into an gullible city to wreak havoc.
Players take control of a Gamer Kid, a minifig that can serve special powers by swapping T-shirts and celebration an appetite drink.
Early on, players also clear a automobile from classical arcade diversion Spy Hunter and a enchanting Defender arcade machine, both of that come with a minifig as buildable Lego.
The rest of a add-on's debate has Gamer Kid elucidate puzzles inside a arcade to energy adult docks for a arcade machine. Once powered up, any plcae opens adult a specific classical game. To advance, we have to play a strange game, pulled directly from a ROM, and kick a high score.
After we do, a diversion lets we advance. But it also delivers a factoid or dual about a diversion we usually played. It's an engaging proceed to deliver people to games like Joust, Defender and Gauntlet.
Warburton pronounced there was early speak of holding a games and recreating them with Lego, though eventually a group motionless to say a strange demeanour and feel of those games by regulating a ROMs.
While a games we can play sojourn a originals, that doesn't meant a group didn't play with a art and characters from those games. Throughout your explorations, we run into Lego versions of characters from Gauntlet, Joust, Defender and other titles.
The open journey universe for Midway Arcade, that we can revisit any time, consists of a mashup of settings from a accumulation of those classical games, all recreated with Lego. So we can revisit a city in Rampage and assistance George destroy a buildings, try a Gauntlet obstruction from a top-down perspective, check out a 720° movement park, or travel opposite a Cyberball Stadium field.
Better still, a heart of a giveaway roaming universe is home to 23 Midway arcade games, any unbarred by finding them possibly in a Midway Arcade diversion turn or by sport by a rest of a diversion looking for dark machines. After we kick a level, we have entrance to about a half-dozen machines. Then we have to go, for instance, behind to a Yellow Brick Road in Oz to find Toobin', or The Simpsons' Springfield for Cyberball.
Once we clear a cabinet, we have full entrance to it forever, so Lego Dimensions radically becomes 23 games within a game.
While Warburton pronounced a group was means to embody many of a games they wanted to in a turn pack, during slightest dual games didn't make it in: APB and Mortal Kombat.
Now that Midway Arcade is out and customarily a few appendage packs are left from a strange announcement, a group is focusing on what it's going to do next.
"The cold thing is that we built something that we can do whatever we wish in," Warburton said. "At this indicate in time zero is off a table.


This is being pushed by all Vendors.
Mgmt is G709. Which in time (I guess) will be replaced by GMPLS. It's not mature yet but I'm sold.
its all Ethernet from the router side..
It DOES look good and looks to me to be going in the right direction.. Just needs to mature as a IP Backbone technology.
ALU has been doing many things right in the past few years. It largely goes unnoticed, because ALU has *really* bad reputation with smaller ISPs and Telcos from the old days of Telephony world (in short, they would "talk" to incumbent only). They have been trying to get away with that and with some really great products. For example, their ESS switches are masterpiece that solves so many problems people using Cisco are facing every day.
This new launch is probably continuation of that policy and thinking. It remains to be seen how it does on the marked, dominated by C&J.
Sounds strangely familiar to the Newbridge IP-over ATM Convergence campaign (of which I was a part) in the late90's. Lets see.. lets move IP directly to ATM (over fiber) Converge Video, Image, Voice & Data on one medium and one transport.
Great Idea then, never quite made it.
What do you think about the Ciena strategy?
Come for a visit to this neck of the Kalahari and you can experiment with the DWDM kit we have acquired from them.
Give Martin a good reason to send me over 8-) I definitely won't object.


text:
Taiwan's CNFI releases 2019 White Paper
By Central News Agency
Wang Wen-yuan(王文淵). (CNA photo) Wang Wen-yuan(王文淵). (CNA photo)
The Taiwan-based Chinese National Federation of Industries (CNFI) released its 2019 White Paper Monday, which raised more than 200 suggestions to the government for a friendlier business environment amid global trade conflicts.
The 2019 CNFI White Paper makes 211 suggestions to the government in nine major fields, including industrial development, energy policy, taxation and financial policy, and cross-Taiwan Strait policy, Wang Wen-yuan (王文淵), chairman of the CNFI) and president of the Formosa Plastics Group, said at a Monday press conference.
The CNFI is a non-profit organization established in 1942 that currently consists of 159 member associations from a wide range of manufacturing industries in Taiwan, according to its website.
In order to attract more Taiwanese businessmen and foreign businessmen and encourage them to stay in Taiwan, Wang said, the government should create a friendly business environment and formulate pragmatic and effective policies in response to global uncertainties, including the heightening of the U.S.-China trade conflicts, and other trade disputes between Japan and Korea, as well as India and the U.S.
Meanwhile, Tsai Lien-sheng (蔡練生), secretary-general of the CNFI, said at the same press conference that the government should conduct an objective and comprehensive assessment on the impact of the U.S.-China trade war and find solutions to it.
In addition, the lack of electricity, water, land, workforce and talent, along with employers-worker relations, long-term care and environmental protection, are other imminent problems that require government attention, Tsai added.
He further recommended that the government should optimize tax collection and amend government revenue allocation laws to encourage private investment and promote economic growth and employment.
As for cross-Taiwan Strait relations, Tsai suggested that the government should lower cross-strait tension and hostility to foster trust and cooperation, while at the same time assisting Taiwanese businessmen in relocating or reallocating their investments globally.
Tsai said the government should strive for the country's inclusion in regional trade pacts such as the Comprehensive and Progressive Agreement for Trans-Pacific Partnership and the Regional Comprehensive Economic Partnership.
Meanwhile, the CNFI commended Chen Mei-ling (陳美伶), chief of the National Development Council, for resolving various industrial problems in inter-department coordinating meetings that she hosted personally.
Citing the results of a survey among its members, the CNFI said the acceptability of the government's responses to industrial problems is now 74.46 percent, a 12-year high compared to an average of only 60 percent in previous years.


I used to give people karma by clicking the thumbs up button at the bottom right of their forum posts. Today I tried this for the first time since the latest forum overhaul, and the button did nothing. This was in the GC3 forums. Did it get broken? Thanks.
So, it works here on Wincustomize Talk . Forum Issues.
Works for me on Wincustomize, too. Just not on the GC3 forums.
Could you please try hard refreshing the site, and if you still have problems let me know what browser you're using?
Tried it again this morning and it worked. BTW, I'm using the Pale Moon browser.
Broken again today on the GC3 forums. Still using the Pale Moon browser.


text:
As our nation works to strengthen our economy and to meet the significant transportation and energy challenges we face, we must encourage the use of a crucial tool: Telework.
Telework can reduce the cost of traffic congestion. According to the Texas A&M Transportation Institute, in 2011, traffic congestion cost the United States $121 billion in wasted time and fuel, not including the effect of longer delivery times, missed meetings and other negative consequences of congestion. By taking cars off the road, telework can cut such waste. Spared the drive, telecommuters can get to work faster. When highways hum, drivers can get to work faster and goods can reach customers sooner. Without the stress of daily gridlock, both telecommuters and office-based employees can work more efficiently and effectively. In addition, telecommuters can put the money they save on fuel back into the economy.
Telework can reduce the cost of transportation infrastructure. By decreasing the number of daily drivers and transit riders, telework reduces the wear and tear on the nation's existing roads and rails. It also reduces the need for additional construction. As a result, telework optimizes federal dollars spent on repairing and maintaining existing infrastructure and mitigates future costs.
Telework can assure business continuity. Powerful storms, pandemics, terrorist threats and major transit disruptions can slow or halt business operations. However, when employees are equipped and trained to telecommute, organizations facing such emergencies can continue functioning with no loss in productivity.
Telework can boost employment. By reducing recruitment, overhead and other business costs, telework makes it less expensive for companies to hire new staff. At the same time, it enables Americans who have lost their jobs to expand the region where they look for work. Further, according to the National Broadband Plan, increasing telework opportunities could enable 17.5 million non-workers, including retirees, homemakers and disabled Americans, to enter the workforce. These new teleworkers could produce significant revenue and disability savings for the federal government.
The Telecommuter Tax prevents businesses and individuals from adopting telework. Notwithstanding the critical benefits of telework, a harsh tax penalty thwarts its growth: the Telecommuter Tax. The tax derives from a state policy commonly referred to as the "convenience of the employer" rule. In a state applying this rule, nonresidents who work for in-state employers and choose to telecommute part-time must pay taxes to the state on 100% of their salary – not just the wages they earn when they work in the state, but also the wages they earn at home, in a different state. Because telecommuters' home states can also tax the income earned at home, workers are threatened with double taxation on that income.
The convenience rule is a strong deterrent to telework. Some workers are forced to reject telework because the rule creates too much confusion about where they owe taxes. Other workers are forced to reject telework because they cannot afford an extra state tax bill. The convenience rule also makes telework unaffordable for businesses: The administrative costs of figuring out where they must withhold for interstate telecommuters can be unmanageable.
The Multi-State Worker Tax Fairness Act would abolish the Telecommuter Tax. The legislation (H.R. 4085; S. 2347) provides that no state may tax income that nonresidents earn when they are physically present in a different state. It would eliminate the risk that workers will be double taxed for using the Internet to access an out-of-state job.
The National Broadband Plan called upon Congress to consider telework tax relief legislation, asserting that the "double taxation issue … is preventing telework from becoming more widespread." The Telework Coalition, the Association for Commuter Transportation, the National Taxpayers Union, the Small Business & Entrepreneurship Council, the Christopher & Dana Reeve Foundation and the American Legion are among the diverse group of stakeholders that have endorsed telecommuter tax relief legislation.
The Multi-State Worker Tax Fairness Act will strengthen our economy, transportation system, emergency preparedness and energy security. Please help make this essential measure law.


As we have learned to create a child theme in WordPress we may require some important work around to customize the child theme further. In this post, we are adding very useful and important functions for WordPress.
This entry was posted in Blog, Website Development. Bookmark the permalink.


If you like miniature tattoos, you will definitely love the art of Sol Tattoo, a tattoo artist based in Seoul, South Korea. Sol specializes in super cute cat tattoos, but realistic dog portraits and floral designs are also a big part of her portfolio.
Her subtle and delicate tattoos are often very small, yet highly detailed. You can see below a few of Sol's miniature designs and more on Instagram, where the artist regularly posts her exquisite creations.


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Courts Government
DA Probing Borges Death
The Humboldt County District Attorney's Office has initiated a review of the June 13, 2014 in-custody death of Daren Borges, who died hours after being booked into the county jail by Eureka police officers.
Borges' sister, Stephany Borges, filed a federal wrongful death lawsuit last week, alleging officers acted negligently in booking him into jail without first having screened at a local hospital despite his "obviously experiencing a medical and psychiatric emergency."
Humboldt County District Attorney Maggie Fleming said Tuesday evening that, late last month, she received an email from Borges' family asking her office to review his death. Fleming said she agreed, and has requested reports from all involved agencies, including the Humboldt County Sheriff's Office, the Eureka Police Department and the coroner's office.
The purpose of the review, Fleming said, is to determine if there's any evidence of criminal conduct by anyone involved.
The protocol for county's Critical Incident Response Team (CERT) — a multi-agency group called to investigate critical incident, including officer-involved fatalities — allows for the team to assembled to investigate in-custody deaths, but leaves discretion over whether to initiate the team response with the agency of jurisdiction. In Borges' case, that would have been the sheriff's office, which did not initiate a CERT response. Under the protocol, all CERT investigations are forwarded at their conclusion to the district attorney's office for review.
Humboldt County Sheriff's Lt. Wayne Hanson said typically in-custody deaths are investigated by the sheriff's office and the coroner's office, with the help of an investigator assigned from the DA's office. Only in cases that appear suspicious or more complex would the office initiate CERT, Hanson said.
More information on Borges' death and the lawsuit can be found here and here, respectively.
Courts Government Daren Borges Maggie Fleming Wayne Hanson Humboldt County jail in-custody death Critical Incident Response Team Stephany Borges wrongful death lawsuit
'The Jury Heard It All'
Why a new trial won't change the outcome of the Borges wrongful death lawsuit
by Robert Poyourow | Jan 11, 2018
Federal Jury Hits County with $2.5 Million Wrongful Death Verdict 4
by Thadeus Greenson | Aug 28, 2017


Welcome to PureBeam Music - Pianist Ron Hart's indie label.
When using your android mobile phone, first expand each page slightly side-to-side, then scroll to the bottom of this page, which starts the automated music for this website.
Visit iTunes, Amazon.com, CDBaby.com, Tower.com, MTV.com, CDUniverse.com, TradeBit.com and other online music stores to download mp3 tracks or entire albums of pianist Ron Hart's music, such as "The Light Beyond the Atoms" and "April in Paris" CDs.
To find the online page links for these albums, please click on our LINKS TO BUY page.
I'd like to tell you about what is happening to creators of music in today's marketplace. Songwriters and composers register their works with licensing organizations such as ASCAP and BMI. These organizations collect license fees and distribute them as royalties to the creators of the music. In the past, the listening public would buy CDs or digitally download albums or songs from sites such as Amazon.com, iTunes, and many other online music stores. Now more and more people are choosing not to purchase music, but to listen to their favorite music on streaming sites such as Rhapsody, Spotify, Pandora, Apple Music, and Google Play Music.
Each "play" on Rhapsody pays the songwriter/performer $ 0.0006 cents, or 6/10,000th of a cent.
Each "play" on Spotify pays the songwriter/performer $ 0.0005 cents, or 5/10,000th of a cent.
In order to make $ 0.01 on Rhapsody, the song would need to get 16.67 "plays."
In order to make $ 0.01 on Spotify, the song would need to get 20 "plays."
In order to make $100 on Rhapsody, the song would need to get 166,167 "plays."
In order to make $100 on Spotify, the song would need to get 200,000 "plays."
These percentages are a pittance of what songwriters and composers used to make as a result of album and digital download sales. ASCAP and BMI are continuing to seek Congress to adjust these streaming music rates to benefit the creators of the music, not just the distributors which is now the case. The U.S. Legislature is unsympathetic due to the influence of lobbyists for the music streaming companies.
I'm bringing this to your attention so that you might decide to support your favorite musicians, songwriters and composers by going to iTunes, Amazon.com, etc., and purchasing their music online as downloads or CD sales. In this way, the creators of your favorite music can fairly benefit from their efforts.
Streaming jazz radio WGLT posted online a podcast with pianist Ron Hart featuring the careers of Ron and bassist Gary Fitzgerald, as well as selections from their jazz CD, "April in Paris."
The podcast lasts about 11 minutes and we invite you to follow this link and give a listen. Thanks for your support.
Pianist Ron Hart and upright bassist Gary Fitzgerald performed at the Arcosanti Jazz Festival near Prescott, Arizona during Father's Day weekend on June 15-16, 2013. During the two day festival the duo performed songs from their April in Paris CD as well as other jazz standards. Ron and Gary also had the pleasure of playing with alto sax jazz great Richie Cole on the main festival stage.
DownBeat Magazine, the world's foremost jazz magazine, in its September, 2012 issue included the "April in Paris" CD by pianist Ron Hart and upright bassist Gary Fitzgerald.
Cashbox Magazine listed the "April in Paris" CD by Ron Hart and Gary Fitzgerald in their "Jazz Top 50" airplay of new and current albums during April, May and June, 2012 by jazz stations in the U.S.
WUCF 89.9 FM in Central Florida added the "April in Paris" jazz CD by Ron Hart and Gary Fitzgerald into their rotation in March, 2012.
JazzReview.com, a major online site for reviews of jazz CDs, has given the "April in Paris" CD by pianist Ron Hart and bassist Gary Fitzgerald a very positive review. Go to our REVIEWS page to read the review, or go to our LINKS TO OTHERS page and click on the link to read the online review there.
Hearts of Space (www.hos.com) online radio featured a track from Ron's recent CD, "The Light Beyond the Atoms" on archived show 889, "Wistful, an ambient jazz reflection for autumn." Appearing on the show with Ron are jazz greats Chick Corea, Gary Burton, Herbie Mann and Jan Garbarek.
And please stop by the LINKS TO BUY page and click on one of the online stores that carry Ron's CDs.
The recording of the "April in Paris" CD has been a labor of love for pianist Ron Hart and upright bassist Gary Fitzgerald, and the overall effect of the music is joy, happiness and occasionally outright laughter. The style of playing on the album ranges from mainstream to progressive jazz, including six standards and five originals and features dynamic interplay between the grand piano and the upright bass. A uniquely playful jazz treatment of "Hit the Road, Jack" is the featured track on the CD.
The album is currently available at Amazon.com, CDBaby.com and iTunes, as well as most online music stores.
1 April in Paris (Vernon Duke / E.Y. Harburg) 8:34 – The title track has many unexpected moments in this popular standard.
2 Sidney's Soliloquy (Jimmy Wisner) 6:43 – This hauntingly beautiful song is one of Ron's favorites. It was recorded in the early 1960's by singer Mel Torme and again by pianist Teddy Wilson.
3 Night and Day (Cole Porter) 6:38 – This often-recorded standard is given a fresh treatment.
4 Hit the Road, Jack (Percy Mayfield) 3:54 – A completely new jazz rendition of this very popular song which highlights the rhythmic interplay between the bass and piano.
5 From the Heart (Gary Fitzgerald / Ron Hart) 9:47 – A result of allowing the music to play through them led the two musicians on a journey of deep peace and a sense of wonder and discovery.
6 The Sandbox (Gary Fitzgerald / Ron Hart) 4:26 – As the title implies, Gary and Ron put on display their inner kids, replete with buckets and shovels. WARNING: Outright laughter may occur.
7 Blues for Dr. Barcus (Ron Hart) 5:08 – Ron wrote this blues with an unusual time signature for his life-long friend, Bob Barcus.
8 Unshakeable Love (Gary Fitzgerald / Ron Hart) 4:43 – An expression of the longing for and pursuit of unconditional and eternal love.
9 Angel Eyes (Matt Dennis / Earl Brent) 6:05 – A beautiful standard saturated with sweet melancholy.
10 Middle East Solution (Gary Fitzgerald / Ron Hart) 9:37 – The timeless, undisturbed desert – people – the inevitable conflict – a hopeful resolution – the motionless desert.
11 My Romance (Richard Rodgers / Lorenz Hart) 6:27 – The duo express their romance with this great art form – jazz.
Ron Hart received his BFA in Music Composition from Ohio University and did his post-graduate work at UCLA in Film Scoring during the mid '70s. Ron has played with a variety of music artists, beginning at age 19 with Dionne Warwick. His work as a jazz pianist continued with saxophonists Sonny Stitt and Richie Cole, bebop guitarist Bill deArango (Dizzy Gillespie, Charlie Parker), trumpeter Harry "Sweets" Edison (Count Basie, Ben Webster), bassist Larry Klein (Herbie Hancock, Joni Mitchell, Freddie Hubbard), and drummer E.W. Wainwright (McCoy Tyner, Earl "Fatha" Hines). PureBeam Music released in 2008 the popular CD by Ron, "The Light Beyond the Atoms," a four-movement suite for grand piano with synthesizer orchestration.
Gary Fitzgerald began playing the upright bass while in the Air Force in 1963. He met Ron through jazz guitarist Bill deArango in 1971 and the two young men formed a jazz quartet and worked in clubs in Cleveland, Ohio. In 1972 Gary and Ron played in a trio with jazz drummer E.W. Wainwright and performed college concerts in Los Angeles. Gary later toured Europe with drummer Eddie Moore, violinist Michael White and woodwind player Russel Baba. He has also appeared with alto saxophonist Richie Cole, trumpeter Eddie Henderson, and was the bassist in African Roots of Jazz.


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Final Fate/stay night: Heaven's Feel anime film delayed due to COVID-19
Official website announced delay as several Japanese cinemas announced that they're temporarily closing down due to COVID-19.
The third Fate/Stay Night film, Fate/stay night: Heaven's Feel III. spring song, was supposed to premiere on 28th March. However, it seems that it's the latest victim Japan's COVID-19 outbreak. This is because the anime's official website has now announced that the film is now delayed. It will instead premiere in Japan on 25th April.
Prior to the delay, the film has been selling out tickets despite threats of infection from the COVID-19 virus. The announcement came after TOHO Cinemas announced that it will close all its theatres in Tokyo, Kanagawa, and Saitama. They also announced the cancellation of all screenings which start at 8:00pm or later every Monday, staring 30th March. Other theater chains have announced temporary closures thanks to the outbreak as well.
ufotable will once again be animating the film, much like the two previous ones. Its story will pick up where the second film, lost butterfly, left off. The trilogy adapts the original Fate/Stay Night visual novel's Heaven's Feel storyline, which is of course Sakura Matoh's route.
Source: Heaven's Feel film official website
Categories: ANIME & MANGA Tags: COVID-19, Fate, heaven's feel, Toho


Hello darlings! Can you believe it's Thanksgiving week already? I've been a bit busy with a few different projects but today I'm excited to bring you another "Style & The Bar Cart." If you're not familiar with this series let me quickly break it down for you.
For this Bar Cart I wanted to create a simple Thanksgiving themed cart but with a bit of a topical twist because that's just how I roll. For the cocktail I made a Mango Mint Aperol Spritz and included other mango-flavored beverages such as juice and seltzer water on the cart. I also baked (via Trader Joe's, lol) a delicious Pumpkin Spice Pie because what's Thanksgiving without one?
Ice cream, how I love thee!
It's no secret, I L-O-V-E ice cream! I eat ice-cream almost every week (more like every other day,shhh) and it's my guiltiest of pleasures. I couldn't imagine a world without it and with Summer fast approaching, I thought it would be fun to share some of my favorite ice cream shops in NYC. Below is a little gallery and if you click on each photo, you'll get all the deets! Be sure to let me know if you try any of my reccomendations below and enjoy a little sweet treat this Summer!
Weeeee! It's almost that time of year to celebrate L-O-V-E and I am pumped! I love celebrating love and my love language is that of giving and receiving gifts, mostly receiving (lol). Don't take my word for it though, this quiz confirmed what I'd known for years. Honestly, truly!
So with that being said, I bring you my annual love language guide full of gifts in shades of my favorite color, pink! So show your sweethearts, galentines, sisters and Moms just how much you care unless they speak a diff love language and in that case I can't help you cus I'm all about the gifts.
With the Summer coming to an end and my family visiting, I decided to take a break from work and the blog to enjoy some downtime.
We've been having a lot of fun exploring the city and over the weekend we took my niece to have tea at Ladurée in SoHo. She was super excited and enjoyed every moment of it. Everything was delicious and the hot chocolate was so rich it tasted like we were drinking melted chocolate.
It's 2002, I'm 15, my lipgloss is poppin' and my glitter-game is on point. Okay not quite but back in my teen and early adult years I loved me some lipgloss & shimmer. I had the roller-ball gloss, ones that tasted like "fruit" and I felt extra fancy when I got ahold of the Victoria Secret ones with gold shimmer in them. I mean who couldn't resist a shiny pout? I would slather it on but being careful not to look like I ate greasy chowmein as we say in Guyana. There was an art to wearing gloss and glitter or at least I liked to think that as a teen.
Oh how I love a good shimmer. My most prized glitter was one I received as part of a perfume set. It was called Fetish (very suitable for an early teenager, don't you think?) and was a sort of golden body glitter. I would rub it on my collar bones aka decolletage and arms when going out and you couldn't tell me anything! I had glitter gel for my hair as well and even sneaked my sister's shimmer powder (she still gives me the side-eye about it) because I was all about that JLO glow!


text:
A Finding Aid to the Lucinda H. Gedeon Research Material on Charles W. White, 1940-1997, bulk 1980-1981, in the Archives of American Art
Documentation of Lithograph Prints
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Gedeon, Lucinda H.
The collection is in English.
The Lucinda H. Gedeon research materials on Charles W. White measure 1.4 linear feet and date from 1940 to 1997, with the bulk of the materials dating from 1980 to 1981. This research material was compiled for a catalogue raisonné at UCLA and includes correspondence with collectors and institutions; a card file catalogue of works by Charles White; photographs and negatives; printed material; transcripts of interviews; bibliographic information; and writings.
The Lucinda H. Gedeon research materials on Charles W. White measure 1.4 linear feet and date from 1940 to 1997, with the bulk of the materials dating from 1980 to 1981. This research material was compiled for a catalogue raisonné at UCLA and includes correspondence with collectors and institutions regarding Charles White works in their collections; a card file catalogue of works by White; photographs and negatives of works by White; printed material including exhibition materials and magazine and newspaper clippings; transcripts of interviews with White and other individuals; bibliographic information; and writings about White.
Due to the small size of this collection, the papers are arranged in one series.
Series 1: Lucinda H. Gedeon Research Material on Charles W. White, 1940-1997, bulk 1980-1981 (Boxes1-2; 1.4 linear feet)
Lucinda H. Gedeon is a retired art historian in Vero Beach, Florida. Previously the director of the Neuberger Museum at the State University of New York, Purchase, and later of the Vero Beach Museum of Art, Gedeon earned both a master's degree and a doctorate at UCLA. She completed her master's thesis on the work of Charles White.
Charles W. White (1918-1979) was an African American painter. White was born in Chicago and attended the Art Institute of Chicago. He worked as an artist for the Works Progress Administration and later taught first at Dillard University, then at Otis Art Institute from 1965 until his death in 1979.
White exhibited widely and his work is held at a number of institutions. He was elected to the National Academy of design in 1972.
Rayna Andrews
The Lucinda H. Gedeon research materials on Charles W. White were donated to the Archives of American Art by Lucinda H. Gedeon in 2007.
The collection was minimally processed and a finding aid prepared by Rayna Andrews with funding from the Henry Luce Foundation in 2018.
Use of original papers requires an appointment and is limited to the Archives' Washington, D.C. Research Center.
Lucinda H. Gedeon research material on Charles W. White, 1940-1997, bulk 1980-1981. Archives of American Art, Smithsonian Institution.
Also found in the Archives of American Art are the Charles W. White papers, circa 1930-1982, and an oral history interview with Charles W. White conducted by Betty Hoag, March 9, 1965.
Art historians -- Florida Occupation Search Smithsonian Collections Search ArchiveGrid
Museum directors -- Florida Occupation Search Smithsonian Collections Search ArchiveGrid
Women art historians Topical Search Smithsonian Collections Search ArchiveGrid
Painters -- California -- Los Angeles Occupation Search Smithsonian Collections Search ArchiveGrid
Muralists -- California -- Los Angeles Occupation Search Smithsonian Collections Search ArchiveGrid
African American artists Topical Search Smithsonian Collections Search ArchiveGrid
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Women muralists Topical Search Smithsonian Collections Search ArchiveGrid
White, Charles, 1918-1979 Personal Name Search Smithsonian Collections Search ArchiveGrid
University of California, Los Angeles Corporate Name Search Smithsonian Collections Search ArchiveGrid


I'd been a pastor's wife for less than a year when I began preparing my exit strategy. I'd unknowingly slipped on the pastor's wife persona when we arrived at our church, bright-eyed and bushy-tailed, and had been attempting to live up to its clawing expectations ever since. I wanted so badly to be a good pastor's wife, to have the answers when asked, to serve up profound wisdom, and to love people well. However, preparing my exit strategy highlighted what it is that I really wanted so badly: to be liked, to be approved of, to be appreciated, to be thought of as a "good" pastor's wife.
I was going on as if everything was perfectly fine, but, inside, I was all knots and confusion. Condemning thoughts lurked behind every conversation, every Sunday morning, every word that spilled from my mouth. Privately, I cried and cried as I evaluated and wished back every mis-step.
Hiding my insides from others wasn't the worst of it. I also hid myself from God, so sure that I was failing Him. I didn't dare cast my cares on Him, because I felt certain He'd throw them back in my face, disappointed about all the things I had yet to get together. So I tried harder--smile, hug, serve, minister--as if I was a single performer under the stage's harsh spotlight, feet tapping ever faster, trying to win the smile of God. Yes, He was my audience of One, but my audience appeared, in my own estimation, completely unmoved.
Life moved slowly, or perhaps it was just me moving slowly, weighed down, heavy, trudging along.
Less than a year in and I was already so.very.tired. I didn't cry out, not to anyone, least of all my God. I simply gave myself a pep talk, swung the weight once again on my back, and took a step.
The thing I didn't yet understand about God is that we don't move toward Him, but rather He comes to us. He is a pursuer, a wooer, an initiator. With me, He waited until I had only fumes of self-effort left, and then He came. Because, as I can see now, He knew I needed to understand my need, because only then could I understand the extent of His grace toward me.
Sitting across from two college girls, I attempted to explain how God works by starting with "if". If I obey Him, then He will approve and act. Did that not sum up everything I'd believed and everything that formed the foundation of my Christian life?
Respectfully, one of the girls said, "Christine, I don't think that's right." And God came. There in my heart, I knew instantly that things were changing, that God wanted to show me some things, some things about His true character, about grace.
And God came, specifically through the book of Galatians. I discovered that, because I am in Christ, I am holy and righteous before God, and nothing I do or don't do can change my status before Him. I discovered that He's given me a Helper, the Holy Spirit, to help me, guide me, and convict me. I don't have to lead and convict myself but can depend fully on God to do so. I discovered that my external behaviors are not what make me loved and approved by God, but that once I receive the love of God given through Jesus, it will compel me to love Him back. What I'm saying is that I discovered grace and my whole life flipped on its head because of it.
As I received this great grace, I finally understood why Jesus said His yoke is easy and His burden is light. Because He carries the burden of my sin, my ministry, my life. I am loved, so I am freed to love.
The posture of the Christian is not performing in order to receive, which bears bitter fruits of pride and condemnation. The posture of the Christian is primarily receiving, because we're receiving something that wells up in us and compels us to joyfully respond.
God came. That exit strategy? It's long forgotten, because He still comes. He is still guiding my exploration of His love and grace, and all that I uncover becomes another building block in my enduring hope.


Though people know that metal is a regularly used material in construction, some may be surprised at the degree to which metal is utilized by individuals throughout everyday life. Take a look at what life would be like without the use of metal.
Housing. Without metal, you would most likely live in a wooden home. Plumbing is comprised of metal, so you would have to haul water for cooking and cleaning purposes. You would also lack many appliances, such as sinks, tubs and toilets.
Food. You would not have a refrigerator or cooler, so you would need to be careful not to let your food go to waste. Even gas stoves are structured of some form of metal, so you would also have to use a fire for heating and meal preparation, while utilizing wooden utensils.
Transportation. On the upside, you would get your daily cardio from your commute to work. Without metal you would not have vehicles, trains, airplanes or even bicycles.
Communication. Computers, laptops and phones all have some form of metal in them. Without metal, you have the option of regular postal mail or word of mouth. These slower methods of communication are effective, however the length of time it takes could prove to be less efficient.
Clearly, metal is a key component in the functioning of society today.
For more information on how metal is used in everyday life, check out the fun infographic below!


Description: Ethan Tate's photographs of Pine Bluff, Arkansas, reflect a complicated homecoming; Tate had lived in the community when he was young and wasn't entirely happy to return as an adult. He took long drives through the Delta as a way of re-acclimating to the place and, along the way, taught himself to use a 4x5 view camera. The images he produced arose out of an interest in interventionist photography that blurs "the lines between staged, editorialized images and traditional photojournalism," coupled with an investment in the way rural America "has suffered disproportionately" under the pressures of capitalism: "its resources stripped bare and its people disenfranchised." The landscapes, as they're captured, seem at once "battered" and in motion, Tate's fingerprint on the photographs mirroring the cumulative impact of humanity on the land.
Ethan Tate is an artist who splits his time between Los Angeles, California, and Pine Bluff, Arkansas. His photography occasionally appears in the New York Times. Currently he is working on a public art program in Southeast Arkansas.


Tune into Part II of this webinar series highlighting insights from the newly released book, The Growing Out-of-School Time Field: Past, Present, and Future, which delves into the ways in which the out-of-school time (OST) field has matured over the past two decades as a partner in helping children and youth reach their full potential.
This second webinar will feature leaders in the OST field who authored chapters in the book focused on the professional development of the OST field, the role of federal policy in supporting OST programs, and what the future holds for the OST movement.
Join us for an engaging webinar that will both reflect back on the progress made in the OST field, as well as look at what is ahead for this growing field's future. If you missed Part I of this webinar series, a recording is now available on our website.


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Rays need Charlie Morton to save their season
After dropping Game 2 the Tampa Bay Rays will turn to their ace Charlie Morton to save their season in Game 3.
The Houston Astros have dominated the first two games of the ALDS thanks in large part to their two aces in Justin Verlander and Gerrit Cole. The duo has combined to throw 14.2 innings of scoreless baseball while striking out 23 batters, effectively shutting down the Tampa Bay offense.
But if there is something to take away from these first two games for Tampa Bay it's that Houston's bullpen is hittable, scoring all three of their runs in the series off relievers. The Astros are sending veteran Zack Grienke to the mound in Game 3, who allowed five runs to the Rays in their last meeting back on Aug. 29th where OF Austin Meadows and C Travis d'Arnaud both homered.
However, the Rays have yet to hit a home run this the postseason, maybe their fortune changes back home in Tampa Bay. But the Rays were able to push Grienke out of that Aug. 29th game after 93 pitches in 5.2 innings, so seeing pitches and working Grienke's pitch count may be the gameplan. However, Grienke does lead all Astro starters in first-pitch strikes, getting ahead early in counts 67.3 percent of the time.
But the Rays best chance to beat the Astros is a great game from Charlie Morton, who's coming off a five-inning shutout win over the Athletics in the AL Wild Card game. Morton has been the rock of this Tampa Bay rotation, putting together an AL Cy-Young worthy season while teammates Blake Snell and Tyler Glasnow spent extended time on the IL.
Morton's been the Rays go-to guy all season and with his impressive postseason resume, Tampa Bay manager Kevin Cash wouldn't want anyone else on the mound in a must-win game. The 35-year-old ace did have a rough outing against Houston back on Aug. 27th, allowing six runs in just 4 innings of work, but in the postseason "Ground Chuck" always ramps it up to another level.
If the Tampa Bay fans can show up to Tropicana Field and the offense can get to Grienke early in Game 3, Morton has the dominating stuff to take over a game and hopefully swing some momentum back towards his ballclub. But for a team that has baseball's lowest payroll and has been compared to the Island of Misfit Toys, the Rays are no stranger to overcoming the odds.
And with the Rays backs' against the wall, it just feels like destiny that Charlie Morton would add another incredible postseason performance. This time, against his former team.
Next: Gerrit Cole nearly unhittable as Astros win Game 2
MLB Power Rankings: The biggest Hall of Fame snub for every team
Ronald Acuña drama in Venezuela: Everything to know about fight, retirement and more
MLB world reacts to Angels announcement that team won't be sold


In short, we can't imagine life without him.
4 Responses to He's One!
Happy Birthday to Mark from us also!
Happy birthday mark! We love having you in the family! Our girls are similar, Kaitlyn will tell Maria "you are my best friend." It is so cute!


Go-Chiktsa Seminar and Naadi Parikshan Camp; Bangluru.
series of camp throughout the nation.
conserve the Indian 'Desi' breeds of cows.
Gau-Bhakta without whose collaboration this mission would not have become successful.
We pray to Gau-Mata to shower her blessings on Gau-Bhaktas and on us too to make our service a successful one.
Special Thanks to our Inspiration DS Satyajitkumar S Khachar (Jasdan State Saheb Sri), Banglore organizers team and All Gau Bhata.


A man on an epic journey across America with his family. Riding his bicycle from YorkTown, Virginia to Astoria, Oregon in 66 days over 4,228 miles. Summiting mountain passes, crossing deserts, and passing through multitudes of National Forests/Parks. Join him as he recounts the tale from his resignation as a Director of IT Services to his final dip of the front tire in the Pacific Ocean. This is a story for those who need to disconnect from our hectic society and get back in touch with the natural world that surrounds them. Go seek nature!


At Seeds Church we know that we are better together including this team that God has assembled. We get the privilege of leading together and serving alongside of our amazing Dream Team to make this dream a reality: To see thousands of men, women, and children in Middle Tennessee equipped and empowered to BUILD THE KINGDOM Of God on Earth as IT is in heaven.
Believers who invest their hearts, time, families, and finances in the building of a local church deserve to have confidence in church leadership. People are looking for leaders who conduct themselves with integrity and respect when making decisions that affect their lives.
The Pastoral staff team is led by the Lead Pastor. This team will oversee the day-to-day ministry and operations of the church. These staff pastors will serve the congregation and are responsible for the development of the spiritual life of the church.
The Trustees will be members of the congregation who will oversee the finances and direct the provision of the facilities needed by the church. They will provide counsel to the Lead Pastor and pastoral team regarding the major financial commitments of the church. The Trustees will serve as Non-staff Elders.
The Overseers are pastors of respected congregations and ministries who love Seeds Church and are willing to provide spiritual protection to the church. They may be called in to help in accountability matters relating to the Lead Pastor if requested by the Pastors or Trustees. The Overseers serve as Apostolic Elders.


During the summer, it is wonderful to go out in short sleeves. But hanging skin in the upper arms sometimes prevents us from wearing the clothes we would like to wear. Hanging skin maybe due to excessive weight loss, aging or loss of muscle mass. An arm lift surgery can help to tighten the upper arm area to give you the confidence to wear short sleeves again. The medical term for Arm Lift Surgery in India is Brachioplasty. In this surgery, excessive skin can be removed by either a small incision which runs from the mid upper arm to the under arm area, or by an under arm incision, which is not noticeable. Brachioplasty can be combined with liposuction to remove excess fat and tighten the skin at the same time.
Best candidates for the procedure are those who have hanging and redundant skin because of weight loss can opt for this surgery to help tighten and give shape to their upper arm area; people whose arms are not in proportion with other parts of the body are also the right candidates for brachioplasty.
Even though, recuperation after the surgery depends on the condition of the candidate, it usually takes two to three weeks to do routine work. You can resume light work within span of a couple of days. You will be recommended to wear compression garment that is especially designed for the the procedure. It will allow your to heal quicker and help reduce the swelling faster. If you have hanging skin on the upper arms, then Brachioplasty is your solution.
You can find the Best Arm Lift surgeon in Delhi at our facility, Dr. Ajaya Kashyap, MD, FACS. Best candidates for arm lift surgery in Delhi are those who have hanging and redundant skin because of weight loss or the aging process and who are in good health. Recovery after the surgery depends on the of the candidate, but usually takes two to three weeks to get back to routine work. You can resume light work within span of a couple of days. You will be recommended to wear compression garment that is especially designed for the procedure. It will allow you to heal quicker and help reduce the swelling faster. If you have hanging skin on the upper arms, then Brachioplasty is your solution at our arm lift surgery clinic in Delhi. We are always happy to give you a quote for your Arm Lift surgery cost in Delhi or Brachioplasty surgery cost in India with the best Arm lift surgeon in Delhi.