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Ajout des fonctions EppsPulley.test, callCarrMadan

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François Pelletier 2014-02-22 13:29:17 -05:00
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4
.Rbuildignore
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^.*\.Rproj$
^\.Rproj\.user$
.gitignore
.project
.git
.settings

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DESCRIPTION
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@ -8,4 +8,6 @@ Description: This is a package gathering different functions to work with
option pricing
Suggests:
MASS
Depends:
multicore
License: LGPL-3

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LICENSE
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GNU LESSER GENERAL PUBLIC LICENSE
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R/EppsPulley.test.R Normal file
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# Approximate Epps-Pulley normality test
#
# Author: Francois Pelletier
#
# LGPL 3.0
###############################################################################
#' Approximate Epps-Pulley normality test
#'
#' An Approximation to the Limit Distribution
#' of the Epps-Pulley Test Statistic for Normality
#' By N. Henze
#' Metrika (1990) 37:7-18
#' @param x Sample
#' @param alpha Tolerance level
#' @return A list containing the test statistics
#'
#' @author François Pelletier
EppsPulley.test <- function(x,alpha=0.05)
{
## Statistics
n <- length(x)
if (n<10) stop("n doit être supérieur à 10")
xbar <- mean(x)
S <- sd(x)
## Constants
gamma <- 3.55295
delta <- 1.23062
lambda <- 2.26664
xi <- -0.020682
## Calculations
T <- 2/n*sum(outer(x,x,function(x,y) exp(-0.5*(x-y)^2 / S^2))*
outer(1:n,1:n,function(x,y) x<y)) -
sqrt(2)*sum(exp(-0.25*(x-xbar)^2/S^2))+
n/sqrt(3)+1
Tmod <- (T - 0.365/n + 1.34/n^2)*(1 + 1.3/n)
Z <- gamma+delta*log((Tmod-xi)/(xi+lambda-Tmod))
Pvalue <- 1-pnorm(Z)
reject <- Pvalue<alpha
cat(sprintf("\nTest de normalité de Epps-Pulley\n\n T: %f\n T*: %f\np-value: %f\n\n",T,Tmod,Pvalue))
list(Tstat=T,Tmod=Tmod,Zscore=Z,Pvalue=Pvalue,Reject=reject)
}

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R/callCarrMadan.R Normal file
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# Call price using the Carr-Madan damping parameter and FFT
#
# Author: Francois Pelletier
#
# LGPL 3.0
###############################################################################
#' Call price using the Carr-Madan damping parameter and FFT
#' @param strikeprice Vector of strike prices, relative to a unit stock price
#' @param char.fn Characteristic function of the log-price process
#' @param eval.time Evaluation time
#' @param expiry.time Expiry time
#' @param rate Continuously compounded interest rate (force of interest)
#' @param alpha Damping parameter
#' @param ... Parameters of the characteristic function
#' @param fft.control Control parameters list for the FFT discretization
#' @return A European call option price vector
#'
#' @author Francois Pelletier
callCarrMadan <- function(strikeprice,char.fn,eval.time,expiry.time,rate,alpha,
...,fft.control=list(N=2^14,eta=.1))
{
# Determine moneyness
moneyness <- strikeprice < 1
# Discretization step for Fourier transform
lambda <- lambda <- (2*pi) / (fft.control$N*fft.control$eta)
# Evaluation points of the damped characteristic function of the call option log-price
u <- seq(0,(fft.control$N-1)*fft.control$eta,fft.control$eta)
# Upper bound
b <- (fft.control$N * lambda)/2
# Vector of indices
jvec <- 1:fft.control$N
# Simpson's hypothesis
simpsonh <- ((dampedcfcallCarrMadan(u,char.fn,eval.time,expiry.time,rate,alpha,moneyness,param)*
exp(1i*u*b)*fft.control$eta)/3)*
(3+(-1)^jvec+((jvec-1)==0))
# Log-price vector
ku <- seq(-b,(fft.control$N-1)*lambda-b,lambda)
# Log-price of the call option vector
if(moneyness)
{
callvec <- Re((exp(-alpha*ku)*fft(simpsonh))/pi)
}
else
{
callvec <- fft(simpsonh)/(sinh(alpha*ku)*pi)
}
# Price vector
Ku <- exp(ku)
# Index to select subset of prices in the strikeprice vector
Kindex <- Ku>=(min(strikeprice)-1) & Ku<=(max(strikeprice)+1)
# We use a smooth spline to get the prices for the strikeprice vector
sp0 <- smooth.spline(x=Ku[indice],y=callvec[indice])
predict(sp0,strikeprice)$y
}

4
R/putEpps.R
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@ -8,14 +8,14 @@
#' European put option pricing using characteristic function
#'
#' As seen in Epps (2009)
#' @param strikeprice Strike price, relative to a unit stock price
#' @param strikeprice Strike price vector, relative to a unit stock price
#' @param char.fn Characteristic function of the price level at expiry time
#' @param eval.time Evaluation time
#' @param expiry.time Expiry time
#' @param rate Continuously compounded interest rate (force of interest)
#' @param ... Parameters of the characteristic function
#' @param int.bounds Integration bounds for the integrate() method used. Defaults to infinite bounds.
#' @return European put option price
#' @return European put option price vector
#'
#' @author Francois Pelletier
putEpps <- function(strikeprice,char.fn,eval.time,expiry.time,rate,...,int.bounds=c(-Inf,Inf))

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man/EppsPulley.test.Rd Normal file
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\name{EppsPulley.test}
\alias{EppsPulley.test}
\title{Approximate Epps-Pulley normality test}
\usage{
EppsPulley.test(x, alpha = 0.05)
}
\arguments{
\item{x}{Sample}
\item{alpha}{Tolerance level}
}
\value{
A list containing the test statistics
}
\description{
An Approximation to the Limit Distribution of the
Epps-Pulley Test Statistic for Normality By N. Henze
Metrika (1990) 37:7-18
}
\author{
François Pelletier
}

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man/callCarrMadan.Rd Normal file
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\name{callCarrMadan}
\alias{callCarrMadan}
\title{Call price using the Carr-Madan damping parameter and FFT}
\usage{
callCarrMadan(strikeprice, char.fn, eval.time, expiry.time, rate, alpha, ...,
fft.control = list(N = 2^14, eta = 0.1))
}
\arguments{
\item{strikeprice}{Vector of strike prices, relative to a
unit stock price}
\item{char.fn}{Characteristic function of the log-price
process}
\item{eval.time}{Evaluation time}
\item{expiry.time}{Expiry time}
\item{rate}{Continuously compounded interest rate (force
of interest)}
\item{alpha}{Damping parameter}
\item{...}{Parameters of the characteristic function}
\item{fft.control}{Control parameters list for the FFT
discretization}
}
\value{
A European call option price vector
}
\description{
Call price using the Carr-Madan damping parameter and FFT
}
\author{
Francois Pelletier
}

6
man/putEpps.Rd
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@ -6,8 +6,8 @@ putEpps(strikeprice, char.fn, eval.time, expiry.time, rate, ...,
int.bounds = c(-Inf, Inf))
}
\arguments{
\item{strikeprice}{Strike price, relative to a unit stock
price}
\item{strikeprice}{Strike price vector, relative to a
unit stock price}
\item{char.fn}{Characteristic function of the price level
at expiry time}
@ -25,7 +25,7 @@ putEpps(strikeprice, char.fn, eval.time, expiry.time, rate, ...,
method used. Defaults to infinite bounds.}
}
\value{
European put option price
European put option price vector
}
\description{
As seen in Epps (2009)