Ajout densité, test de Wald, paramètres RN et options Epps
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franc00018
parent
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commit
16722ab0e7
12 changed files with 1935 additions and 521 deletions
186
GAL-Buckle95.Rnw
186
GAL-Buckle95.Rnw
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@ -1,4 +1,5 @@
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\documentclass{report}
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\documentclass[letter]{report}
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\usepackage[margin=0.5in]{geometry}
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\usepackage{Sweave}
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\usepackage{graphicx}
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\usepackage[francais]{babel}
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@ -29,7 +30,6 @@ library(MASS)
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library(xtable)
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library(multicore)
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library(moments)
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library(TTR)
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library(FourierStuff)
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library(GeneralizedAsymmetricLaplace)
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library(GMMStuff)
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@ -50,6 +50,8 @@ alpha.test <- 0.05
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RETURNS <- head(read.csv("abbeyn.csv",sep="\t",header=TRUE)[,1],-1)
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#Taille de l'échantillon
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n <- length(RETURNS)
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#Nom de l'échantillon
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strData <- "Buckle95"
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@
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\section{Test de normalité}
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@ -166,7 +168,7 @@ optim7 <- optim.GMM(pt.depart,
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meanf=meanQEE,variancef=varianceQEE)
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pt.optim7 <- optim7$par
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cov.optim7 <- mean.variance.GMM.gradient.GAL(pt.optim7,sRET) %*%
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covariance.GMM(meanvariance.gmm.vector,pt.optim7,sRET,
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covariance.GMM(pt.optim7,meanvariance.gmm.vector,sRET,
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meanf=meanQEE,variancef=varianceQEE) %*%
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t(mean.variance.GMM.gradient.GAL(pt.optim7,sRET)) / n
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## GMM itératif
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@ -226,19 +228,19 @@ dist3 <- cbind(pGAL(xi,pt.optim1),
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\subsection{Graphiques}
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<<results=tex>>=
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for (i in 1:8)
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{
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file<-paste("dist-GAL-",i,".pdf",sep="")
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pdf(file=file,paper="special",width=6,height=6)
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plot.ecdf(sRET,main=paste("Fonction de répartition ",i))
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lines(xi,dist1[,i],col="green")
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lines(xi,dist2[,1],col="red")
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lines(xi,dist3[,1],col="pink")
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lines(xi,pnorm(xi),type="l",col="blue")
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dev.off()
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cat("\\includegraphics[height=2in,width=2in]{",
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file,"}\n",sep="")
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}
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for (i in 1:8)
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{
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file<-paste(strData,"-repart-",i,".pdf",sep="")
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pdf(file=file,paper="special",width=6,height=6)
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plot.ecdf(sRET,main=paste("Fonction de répartition ",i))
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lines(xi,dist1[,i],col="green")
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lines(xi,dist2[,1],col="red")
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lines(xi,dist3[,1],col="pink")
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lines(xi,pnorm(xi),type="l",col="blue")
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dev.off()
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cat("\\includegraphics[height=4in,width=4in]{",
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file,"}\n",sep="")
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}
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@
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\subsection{Statistiques}
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@ -248,29 +250,169 @@ chisquare.test1 <- function(param,DATA.hist,FUN,method)
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{
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chisquare.test(DATA.hist,FUN,param,method=method)
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}
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xtable(do.call(rbind,lapply(l.pts.estim,chisquare.test1,hist(sRET),cfGAL,"integral")),digits=6)
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xtable(do.call(rbind,lapply(l.pts.estim,chisquare.test1,hist(sRET),
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cfGAL,"integral")),digits=6)
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@
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Test du $\chi^2$, Méthode avec point de selle
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<<results=tex>>=
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xtable(do.call(rbind,lapply(l.pts.estim,chisquare.test1,hist(sRET),pGAL,"saddlepoint")),digits=6)
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xtable(do.call(rbind,lapply(l.pts.estim,chisquare.test1,hist(sRET),
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pGAL,"saddlepoint")),digits=6)
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@
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Statistique de Kolmogorov-Smirnov
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<<results=tex>>=
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ks.test1 <- function(param,x,y) ks.test(x,y,param)
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xtable(do.call(rbind,mclapply(l.pts.estim,ks.test1,sRET,"pGAL")),digits=6)
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ks.test1 <- function(param,x,y) ks.test(x,y,param)
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xtable(do.call(rbind,mclapply(l.pts.estim,ks.test1,sRET,"pGAL")),digits=6)
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@
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Statistique de distance minimale
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<<results=tex>>=
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tvariate1 <- seq(-.1,.1,by=0.01)
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xtable(do.call(rbind,mclapply(l.pts.estim,md.test,sRET,tvariate1,cfGAL,empCF)),digits=6)
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tvariate1 <- seq(-.1,.1,by=0.01)
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xtable(do.call(rbind,mclapply(l.pts.estim,
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md.test,sRET,tvariate1,cfGAL,empCF)),digits=6)
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@
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\section{Fonction de densité}
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Intégration de la fonction de densité approximée avec le point de selle, pour la
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normaliser en fonction qui intègre à 1.
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<<>>=
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f_integrale_saddle <- function(param,f,lower,upper)
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integrate(f,lower,upper,param)$value
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norm_int_saddle <- sapply(l.pts.estim,f_integrale_saddle,
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f=dsaddleapproxGAL,lower=-Inf,upper=Inf)
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@
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Séquence de points pour les graphiques
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<<>>=
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x_sRET <- seq(min(sRET)-sd(sRET),max(sRET)+sd(sRET),length.out=50)
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@
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Graphique de la fonction de densité
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<<results=tex>>=
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colors2=c("black","red","green","blue","grey")
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for (i in 1:dim(pts.estim)[2])
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{
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file=paste(strData,"-densite-", i, ".pdf", sep="")
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pdf(file=file, paper="special", width=6, height=6)
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plot(density(sRET),ylim=c(0,.7),type="l",
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main=paste("Densité de",strData, i),xlab=strData,
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ylab="f",lwd=2,lty=1)
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points(x_sRET,
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dGAL(x_sRET,pts.estim[,i]),
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type="b",ylim=c(0,4),col="red",pch=19,lwd=2,lty=2)
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points(x_sRET,
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dsaddleapproxGAL(x_sRET,pts.estim[,i])/norm_int_saddle[i],
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type="b",ylim=c(0,4),col="green",pch=20,lwd=2,lty=3)
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lines(x_sRET,dnorm(x_sRET),type="b",col="blue",
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pch=21,lwd=2,lty=4)
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points(seq(-2,4,length.out=1000)[seq(40,1000,by=40)],
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cftodensity.fft(cfGAL,1000,-2,4,pts.estim[,i])$dens[seq(40,1000,by=40)],
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type="b",col="grey",pch=23,lty=6)
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legend(quantile(sRET,0.9),0.7, c("emp","est.GAL","pt.selle","appx.nrm","fft"),
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cex=0.8, col=colors2, pch=c(NA,19:23), lty=1:6, title="Courbes")
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dev.off()
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cat("\\includegraphics[height=4in, width=4in]{"
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,file, "}\n", sep="")
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}
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@
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\subsection{Tests avec contraintes}
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Test de Wald
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<<>>=
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R <- matrix(c(0,0,1,0,
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0,0,0,1),ncol=4)
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r <- matrix(c(0,0),ncol=1)
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V <- lapply(l.pts.estim,covariance.GMM,meanvariance.gmm.vector,
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sRET,meanQEE,varianceQEE)
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D <- lapply(l.pts.estim,mean.variance.GMM.gradient.GAL,sRET)
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xtable(mapply(Wald.Test,l.pts.estim,n,list(R),list(r),V,D),
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caption="Test de Wald", digits=2)
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@
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\subsection{Vrais paramètres}
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Comme nous avons estimé avec des données centrées et réduites, nous utilisons
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une propriété de la distribution GAL qui nous permet d'obtenir les paramètres
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des rendements non réduits.
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<<>>=
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pts.estim.ns <- apply(pts.estim,2,scaleGAL,type="mu",
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mean(RETURNS),sd(RETURNS))
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@
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<<results=tex>>=
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xtable(pts.estim.ns,
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caption="Paramètres des données non centrées et réduites",
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digits=4)
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@
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\section{Prix d'options}
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\subsection{Données de base}
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<<>>=
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#Taux sans risque
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rfrate <- .05/365
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#Échéance
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T <- 30
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#Pas de discrétisation courbe des prix
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pas <- 0.005
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#Prix initial
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stock0 <- 299
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#Prix d'exercice dans le cours (put)
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strike1 <- stock0*seq(0.98,1,pas)
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#Prix d'exercice hors le cours (put)
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strike2 <- stock0*seq(1+pas,1.02,pas)
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#Prix d'exercice combinés
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strike <- c(strike1,strike2)
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#Damping parameter
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alpha <- 3
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@
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\subsection{Paramètres neutres au risque}
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<<>>=
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pts.estim.ns.rn <- apply(pts.estim.ns,2,riskneutralparGAL,rfrate)
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l.pts.estim.ns.rn <- as.list(data.frame(pts.estim.ns.rn))
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@
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<<results=tex>>=
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xtable(pts.estim.ns.rn,caption="Paramètres neutres au risque",digits=4)
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@
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\subsection{Méthode de Epps}
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<<>>=
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f_putEpps <- function(param,strikeprice,char.fn,eval.time,expiry.time,rate)
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putEpps(strikeprice,char.fn,eval.time,expiry.time,rate,param=param)
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prix_Epps <- as.data.frame(sapply(l.pts.estim.ns.rn,f_putEpps,strike/stock0,cfLM,0,T,rfrate))
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@
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<<results=tex>>=
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xtable(prix_Epps,caption="Prix unitaire de l'option de vente, Méthode de Epps",digits=6)
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@
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BIN
GAL-Buckle95.pdf
BIN
GAL-Buckle95.pdf
Binary file not shown.
315
GAL-Buckle95.tex
315
GAL-Buckle95.tex
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@ -1,4 +1,5 @@
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\documentclass{report}
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\documentclass[letter]{report}
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\usepackage[margin=0.5in]{geometry}
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\usepackage{Sweave}
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\usepackage{graphicx}
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\usepackage[francais]{babel}
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@ -30,7 +31,6 @@
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> library(xtable)
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> library(multicore)
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> library(moments)
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> library(TTR)
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> library(FourierStuff)
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> library(GeneralizedAsymmetricLaplace)
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> library(GMMStuff)
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@ -53,6 +53,8 @@
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> RETURNS <- head(read.csv("abbeyn.csv",sep="\t",header=TRUE)[,1],-1)
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> #Taille de l'échantillon
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> n <- length(RETURNS)
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> #Nom de l'échantillon
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> strData <- "Buckle95"
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\end{Sinput}
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\end{Schunk}
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@ -255,7 +257,7 @@ $Reject
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+ meanf=meanQEE,variancef=varianceQEE)
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> pt.optim7 <- optim7$par
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> cov.optim7 <- mean.variance.GMM.gradient.GAL(pt.optim7,sRET) %*%
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+ covariance.GMM(meanvariance.gmm.vector,pt.optim7,sRET,
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+ covariance.GMM(pt.optim7,meanvariance.gmm.vector,sRET,
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+ meanf=meanQEE,variancef=varianceQEE) %*%
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+ t(mean.variance.GMM.gradient.GAL(pt.optim7,sRET)) / n
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> ## GMM itératif
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@ -337,28 +339,28 @@ $Reject
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\begin{Schunk}
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\begin{Sinput}
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> for (i in 1:8)
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+ {
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+ file<-paste("dist-GAL-",i,".pdf",sep="")
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+ pdf(file=file,paper="special",width=6,height=6)
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+ plot.ecdf(sRET,main=paste("Fonction de répartition ",i))
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+ lines(xi,dist1[,i],col="green")
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+ lines(xi,dist2[,1],col="red")
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+ lines(xi,dist3[,1],col="pink")
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+ lines(xi,pnorm(xi),type="l",col="blue")
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+ dev.off()
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+ cat("\\includegraphics[height=2in,width=2in]{",
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+ file,"}\n",sep="")
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+ }
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> for (i in 1:8)
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+ {
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+ file<-paste(strData,"-repart-",i,".pdf",sep="")
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+ pdf(file=file,paper="special",width=6,height=6)
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+ plot.ecdf(sRET,main=paste("Fonction de répartition ",i))
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+ lines(xi,dist1[,i],col="green")
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+ lines(xi,dist2[,1],col="red")
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+ lines(xi,dist3[,1],col="pink")
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+ lines(xi,pnorm(xi),type="l",col="blue")
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+ dev.off()
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+ cat("\\includegraphics[height=4in,width=4in]{",
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+ file,"}\n",sep="")
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+ }
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\end{Sinput}
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\includegraphics[height=2in,width=2in]{dist-GAL-1.pdf}
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\includegraphics[height=2in,width=2in]{dist-GAL-2.pdf}
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\includegraphics[height=2in,width=2in]{dist-GAL-3.pdf}
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\includegraphics[height=2in,width=2in]{dist-GAL-4.pdf}
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\includegraphics[height=2in,width=2in]{dist-GAL-5.pdf}
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\includegraphics[height=2in,width=2in]{dist-GAL-6.pdf}
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\includegraphics[height=2in,width=2in]{dist-GAL-7.pdf}
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\includegraphics[height=2in,width=2in]{dist-GAL-8.pdf}\end{Schunk}
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\includegraphics[height=4in,width=4in]{Buckle95-repart-1.pdf}
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\includegraphics[height=4in,width=4in]{Buckle95-repart-2.pdf}
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\includegraphics[height=4in,width=4in]{Buckle95-repart-3.pdf}
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\includegraphics[height=4in,width=4in]{Buckle95-repart-4.pdf}
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\includegraphics[height=4in,width=4in]{Buckle95-repart-5.pdf}
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\includegraphics[height=4in,width=4in]{Buckle95-repart-6.pdf}
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\includegraphics[height=4in,width=4in]{Buckle95-repart-7.pdf}
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\includegraphics[height=4in,width=4in]{Buckle95-repart-8.pdf}\end{Schunk}
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\subsection{Statistiques}
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Test du $\chi^2$, Méthode avec intégration
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@ -368,10 +370,11 @@ Test du $\chi^2$, Méthode avec intégration
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+ {
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+ chisquare.test(DATA.hist,FUN,param,method=method)
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+ }
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> xtable(do.call(rbind,lapply(l.pts.estim,chisquare.test1,hist(sRET),cfGAL,"integral")),digits=6)
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> xtable(do.call(rbind,lapply(l.pts.estim,chisquare.test1,hist(sRET),
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+ cfGAL,"integral")),digits=6)
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\end{Sinput}
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% latex table generated in R 3.0.2 by xtable 1.7-1 package
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% Sat Mar 15 11:38:58 2014
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% latex table generated in R 3.0.3 by xtable 1.7-3 package
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% Sat Mar 29 12:42:33 2014
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\begin{table}[ht]
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\centering
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\begin{tabular}{rrrr}
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@ -393,10 +396,11 @@ pt.optim1 & 5.473824 & 6.000000 & 0.484626 \\
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Test du $\chi^2$, Méthode avec point de selle
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\begin{Schunk}
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\begin{Sinput}
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> xtable(do.call(rbind,lapply(l.pts.estim,chisquare.test1,hist(sRET),pGAL,"saddlepoint")),digits=6)
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> xtable(do.call(rbind,lapply(l.pts.estim,chisquare.test1,hist(sRET),
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+ pGAL,"saddlepoint")),digits=6)
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\end{Sinput}
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% latex table generated in R 3.0.2 by xtable 1.7-1 package
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% Sat Mar 15 11:38:58 2014
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% latex table generated in R 3.0.3 by xtable 1.7-3 package
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% Sat Mar 29 12:42:33 2014
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\begin{table}[ht]
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\centering
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\begin{tabular}{rrrr}
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@ -418,11 +422,11 @@ pt.optim1 & 9.293574 & 6.000000 & 0.157728 \\
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Statistique de Kolmogorov-Smirnov
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\begin{Schunk}
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\begin{Sinput}
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> ks.test1 <- function(param,x,y) ks.test(x,y,param)
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> xtable(do.call(rbind,mclapply(l.pts.estim,ks.test1,sRET,"pGAL")),digits=6)
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> ks.test1 <- function(param,x,y) ks.test(x,y,param)
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> xtable(do.call(rbind,mclapply(l.pts.estim,ks.test1,sRET,"pGAL")),digits=6)
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\end{Sinput}
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% latex table generated in R 3.0.2 by xtable 1.7-1 package
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% Sat Mar 15 11:38:58 2014
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% latex table generated in R 3.0.3 by xtable 1.7-3 package
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% Sat Mar 29 12:42:33 2014
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\begin{table}[ht]
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\centering
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\begin{tabular}{rrrrrr}
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@ -445,11 +449,12 @@ Statistique de distance minimale
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\begin{Schunk}
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\begin{Sinput}
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> tvariate1 <- seq(-.1,.1,by=0.01)
|
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> xtable(do.call(rbind,mclapply(l.pts.estim,md.test,sRET,tvariate1,cfGAL,empCF)),digits=6)
|
||||
> tvariate1 <- seq(-.1,.1,by=0.01)
|
||||
> xtable(do.call(rbind,mclapply(l.pts.estim,
|
||||
+ md.test,sRET,tvariate1,cfGAL,empCF)),digits=6)
|
||||
\end{Sinput}
|
||||
% latex table generated in R 3.0.2 by xtable 1.7-1 package
|
||||
% Sat Mar 15 11:38:58 2014
|
||||
% latex table generated in R 3.0.3 by xtable 1.7-3 package
|
||||
% Sat Mar 29 12:42:33 2014
|
||||
\begin{table}[ht]
|
||||
\centering
|
||||
\begin{tabular}{rrrr}
|
||||
|
|
@ -468,6 +473,240 @@ pt.optim1 & 0.000422 & 21.000000 & 0.000000 \\
|
|||
\end{tabular}
|
||||
\end{table}\end{Schunk}
|
||||
|
||||
\section{Fonction de densité}
|
||||
|
||||
Intégration de la fonction de densité approximée avec le point de selle, pour la
|
||||
normaliser en fonction qui intègre à 1.
|
||||
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> f_integrale_saddle <- function(param,f,lower,upper)
|
||||
+ integrate(f,lower,upper,param)$value
|
||||
> norm_int_saddle <- sapply(l.pts.estim,f_integrale_saddle,
|
||||
+ f=dsaddleapproxGAL,lower=-Inf,upper=Inf)
|
||||
\end{Sinput}
|
||||
\end{Schunk}
|
||||
|
||||
Séquence de points pour les graphiques
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> x_sRET <- seq(min(sRET)-sd(sRET),max(sRET)+sd(sRET),length.out=50)
|
||||
\end{Sinput}
|
||||
\end{Schunk}
|
||||
|
||||
Graphique de la fonction de densité
|
||||
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> colors2=c("black","red","green","blue","grey")
|
||||
> for (i in 1:dim(pts.estim)[2])
|
||||
+ {
|
||||
+ file=paste(strData,"-densite-", i, ".pdf", sep="")
|
||||
+ pdf(file=file, paper="special", width=6, height=6)
|
||||
+ plot(density(sRET),ylim=c(0,.7),type="l",
|
||||
+ main=paste("Densité de",strData, i),xlab=strData,
|
||||
+ ylab="f",lwd=2,lty=1)
|
||||
+ points(x_sRET,
|
||||
+ dGAL(x_sRET,pts.estim[,i]),
|
||||
+ type="b",ylim=c(0,4),col="red",pch=19,lwd=2,lty=2)
|
||||
+ points(x_sRET,
|
||||
+ dsaddleapproxGAL(x_sRET,pts.estim[,i])/norm_int_saddle[i],
|
||||
+ type="b",ylim=c(0,4),col="green",pch=20,lwd=2,lty=3)
|
||||
+
|
||||
+ lines(x_sRET,dnorm(x_sRET),type="b",col="blue",
|
||||
+ pch=21,lwd=2,lty=4)
|
||||
+ points(seq(-2,4,length.out=1000)[seq(40,1000,by=40)],
|
||||
+ cftodensity.fft(cfGAL,1000,-2,4,pts.estim[,i])$dens[seq(40,1000,by=40)],
|
||||
+ type="b",col="grey",pch=23,lty=6)
|
||||
+ legend(quantile(sRET,0.9),0.7, c("emp","est.GAL","pt.selle","appx.nrm","fft"),
|
||||
+ cex=0.8, col=colors2, pch=c(NA,19:23), lty=1:6, title="Courbes")
|
||||
+ dev.off()
|
||||
+ cat("\\includegraphics[height=4in, width=4in]{"
|
||||
+ ,file, "}\n", sep="")
|
||||
+ }
|
||||
\end{Sinput}
|
||||
\includegraphics[height=4in, width=4in]{Buckle95-densite-1.pdf}
|
||||
\includegraphics[height=4in, width=4in]{Buckle95-densite-2.pdf}
|
||||
\includegraphics[height=4in, width=4in]{Buckle95-densite-3.pdf}
|
||||
\includegraphics[height=4in, width=4in]{Buckle95-densite-4.pdf}
|
||||
\includegraphics[height=4in, width=4in]{Buckle95-densite-5.pdf}
|
||||
\includegraphics[height=4in, width=4in]{Buckle95-densite-6.pdf}
|
||||
\includegraphics[height=4in, width=4in]{Buckle95-densite-7.pdf}
|
||||
\includegraphics[height=4in, width=4in]{Buckle95-densite-8.pdf}\end{Schunk}
|
||||
|
||||
\subsection{Tests avec contraintes}
|
||||
|
||||
Test de Wald
|
||||
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> R <- matrix(c(0,0,1,0,
|
||||
+ 0,0,0,1),ncol=4)
|
||||
> r <- matrix(c(0,0),ncol=1)
|
||||
> V <- lapply(l.pts.estim,covariance.GMM,meanvariance.gmm.vector,
|
||||
+ sRET,meanQEE,varianceQEE)
|
||||
> D <- lapply(l.pts.estim,mean.variance.GMM.gradient.GAL,sRET)
|
||||
> xtable(mapply(Wald.Test,l.pts.estim,n,list(R),list(r),V,D),
|
||||
+ caption="Test de Wald", digits=2)
|
||||
\end{Sinput}
|
||||
\begin{Soutput}
|
||||
% latex table generated in R 3.0.3 by xtable 1.7-3 package
|
||||
% Sat Mar 29 12:42:33 2014
|
||||
\begin{table}[ht]
|
||||
\centering
|
||||
\begin{tabular}{rrrrrrrrr}
|
||||
\hline
|
||||
& pt.optim1 & pt.optim2 & pt.optim3 & pt.optim4 & pt.optim5 & pt.optim6 & pt.optim7 & pt.optim8 \\
|
||||
\hline
|
||||
wald.stat & 1861.21 & 1796.75 & 1690.26 & 1865.01 & 1814.81 & 1690.62 & 2111.08 & 2175.45 \\
|
||||
p.value & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\
|
||||
reject & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\caption{Test de Wald}
|
||||
\end{table}
|
||||
\end{Soutput}
|
||||
\end{Schunk}
|
||||
|
||||
\subsection{Vrais paramètres}
|
||||
|
||||
Comme nous avons estimé avec des données centrées et réduites, nous utilisons
|
||||
une propriété de la distribution GAL qui nous permet d'obtenir les paramètres
|
||||
des rendements non réduits.
|
||||
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> pts.estim.ns <- apply(pts.estim,2,scaleGAL,type="mu",
|
||||
+ mean(RETURNS),sd(RETURNS))
|
||||
\end{Sinput}
|
||||
\end{Schunk}
|
||||
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> xtable(pts.estim.ns,
|
||||
+ caption="Paramètres des données non centrées et réduites",
|
||||
+ digits=4)
|
||||
\end{Sinput}
|
||||
% latex table generated in R 3.0.3 by xtable 1.7-3 package
|
||||
% Sat Mar 29 12:42:33 2014
|
||||
\begin{table}[ht]
|
||||
\centering
|
||||
\begin{tabular}{rrrrrrrrr}
|
||||
\hline
|
||||
& pt.optim1 & pt.optim2 & pt.optim3 & pt.optim4 & pt.optim5 & pt.optim6 & pt.optim7 & pt.optim8 \\
|
||||
\hline
|
||||
1 & -0.0092 & -0.0080 & -0.0090 & -0.0092 & -0.0079 & -0.0091 & -0.0081 & -0.0081 \\
|
||||
2 & 0.0078 & 0.0083 & 0.0079 & 0.0078 & 0.0083 & 0.0079 & 0.0081 & 0.0081 \\
|
||||
3 & 0.0033 & 0.0031 & 0.0033 & 0.0033 & 0.0031 & 0.0033 & 0.0030 & 0.0030 \\
|
||||
4 & 2.0214 & 1.8783 & 1.9603 & 2.0220 & 1.8804 & 1.9616 & 1.9660 & 1.9727 \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\caption{Paramètres des données non centrées et réduites}
|
||||
\end{table}\end{Schunk}
|
||||
|
||||
\section{Prix d'options}
|
||||
|
||||
\subsection{Données de base}
|
||||
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> #Taux sans risque
|
||||
> rfrate <- .05/365
|
||||
> #Échéance
|
||||
> T <- 30
|
||||
> #Pas de discrétisation courbe des prix
|
||||
> pas <- 0.005
|
||||
> #Prix initial
|
||||
> stock0 <- 299
|
||||
> #Prix d'exercice dans le cours (put)
|
||||
> strike1 <- stock0*seq(0.98,1,pas)
|
||||
> #Prix d'exercice hors le cours (put)
|
||||
> strike2 <- stock0*seq(1+pas,1.02,pas)
|
||||
> #Prix d'exercice combinés
|
||||
> strike <- c(strike1,strike2)
|
||||
> #Damping parameter
|
||||
> alpha <- 3
|
||||
\end{Sinput}
|
||||
\end{Schunk}
|
||||
|
||||
\subsection{Paramètres neutres au risque}
|
||||
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> pts.estim.ns.rn <- apply(pts.estim.ns,2,riskneutralparGAL,rfrate)
|
||||
> l.pts.estim.ns.rn <- as.list(data.frame(pts.estim.ns.rn))
|
||||
\end{Sinput}
|
||||
\end{Schunk}
|
||||
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> xtable(pts.estim.ns.rn,caption="Paramètres neutres au risque",digits=4)
|
||||
\end{Sinput}
|
||||
% latex table generated in R 3.0.3 by xtable 1.7-3 package
|
||||
% Sat Mar 29 12:42:33 2014
|
||||
\begin{table}[ht]
|
||||
\centering
|
||||
\begin{tabular}{rrrrrrrrr}
|
||||
\hline
|
||||
& pt.optim1 & pt.optim2 & pt.optim3 & pt.optim4 & pt.optim5 & pt.optim6 & pt.optim7 & pt.optim8 \\
|
||||
\hline
|
||||
1 & -0.0066 & -0.0057 & -0.0065 & -0.0066 & -0.0057 & -0.0065 & -0.0058 & -0.0058 \\
|
||||
2 & 0.0078 & 0.0083 & 0.0079 & 0.0078 & 0.0083 & 0.0079 & 0.0081 & 0.0081 \\
|
||||
3 & 0.0033 & 0.0031 & 0.0033 & 0.0033 & 0.0031 & 0.0033 & 0.0030 & 0.0030 \\
|
||||
4 & 2.0214 & 1.8783 & 1.9603 & 2.0220 & 1.8804 & 1.9616 & 1.9660 & 1.9727 \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\caption{Paramètres neutres au risque}
|
||||
\end{table}\end{Schunk}
|
||||
|
||||
|
||||
\subsection{Méthode de Epps}
|
||||
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> f_putEpps <- function(param,strikeprice,char.fn,eval.time,expiry.time,rate)
|
||||
+ putEpps(strikeprice,char.fn,eval.time,expiry.time,rate,param=param)
|
||||
> prix_Epps <- as.data.frame(sapply(l.pts.estim.ns.rn,f_putEpps,strike/stock0,cfLM,0,T,rfrate))
|
||||
\end{Sinput}
|
||||
\end{Schunk}
|
||||
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> xtable(prix_Epps,caption="Prix unitaire de l'option de vente, Méthode de Epps",digits=6)
|
||||
\end{Sinput}
|
||||
% latex table generated in R 3.0.3 by xtable 1.7-3 package
|
||||
% Sat Mar 29 12:42:33 2014
|
||||
\begin{table}[ht]
|
||||
\centering
|
||||
\begin{tabular}{rrrrrrrrr}
|
||||
\hline
|
||||
& pt.optim1 & pt.optim2 & pt.optim3 & pt.optim4 & pt.optim5 & pt.optim6 & pt.optim7 & pt.optim8 \\
|
||||
\hline
|
||||
1 & 0.015415 & 0.015785 & 0.015431 & 0.015417 & 0.015794 & 0.015427 & 0.015792 & 0.015819 \\
|
||||
2 & 0.017360 & 0.017737 & 0.017377 & 0.017362 & 0.017746 & 0.017372 & 0.017742 & 0.017770 \\
|
||||
3 & 0.019456 & 0.019838 & 0.019474 & 0.019458 & 0.019847 & 0.019469 & 0.019843 & 0.019871 \\
|
||||
4 & 0.021705 & 0.022090 & 0.021724 & 0.021707 & 0.022099 & 0.021719 & 0.022093 & 0.022122 \\
|
||||
5 & 0.024107 & 0.024492 & 0.024126 & 0.024109 & 0.024501 & 0.024121 & 0.024495 & 0.024523 \\
|
||||
6 & 0.026661 & 0.027044 & 0.026681 & 0.026663 & 0.027053 & 0.026676 & 0.027046 & 0.027074 \\
|
||||
7 & 0.029365 & 0.029745 & 0.029385 & 0.029367 & 0.029753 & 0.029381 & 0.029745 & 0.029773 \\
|
||||
8 & 0.032217 & 0.032591 & 0.032238 & 0.032219 & 0.032600 & 0.032233 & 0.032591 & 0.032617 \\
|
||||
9 & 0.035214 & 0.035580 & 0.035235 & 0.035216 & 0.035589 & 0.035231 & 0.035579 & 0.035605 \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\caption{Prix unitaire de l'option de vente, Méthode de Epps}
|
||||
\end{table}\end{Schunk}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
1955
Rplots.pdf
1955
Rplots.pdf
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dist-GAL-1.pdf
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dist-GAL-1.pdf
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dist-GAL-2.pdf
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dist-GAL-2.pdf
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dist-GAL-3.pdf
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dist-GAL-3.pdf
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BIN
dist-GAL-4.pdf
BIN
dist-GAL-4.pdf
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dist-GAL-5.pdf
BIN
dist-GAL-5.pdf
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BIN
dist-GAL-6.pdf
BIN
dist-GAL-6.pdf
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dist-GAL-7.pdf
BIN
dist-GAL-7.pdf
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BIN
dist-GAL-8.pdf
BIN
dist-GAL-8.pdf
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Loading…
Add table
Reference in a new issue