diff --git a/GAL-Buckle95.Rnw b/GAL-Buckle95.Rnw index abaa1e6..0309848 100644 --- a/GAL-Buckle95.Rnw +++ b/GAL-Buckle95.Rnw @@ -1,4 +1,5 @@ -\documentclass{report} +\documentclass[letter]{report} +\usepackage[margin=0.5in]{geometry} \usepackage{Sweave} \usepackage{graphicx} \usepackage[francais]{babel} @@ -29,7 +30,6 @@ library(MASS) library(xtable) library(multicore) library(moments) -library(TTR) library(FourierStuff) library(GeneralizedAsymmetricLaplace) library(GMMStuff) @@ -50,6 +50,8 @@ alpha.test <- 0.05 RETURNS <- head(read.csv("abbeyn.csv",sep="\t",header=TRUE)[,1],-1) #Taille de l'échantillon n <- length(RETURNS) +#Nom de l'échantillon +strData <- "Buckle95" @ \section{Test de normalité} @@ -166,7 +168,7 @@ optim7 <- optim.GMM(pt.depart, meanf=meanQEE,variancef=varianceQEE) pt.optim7 <- optim7$par cov.optim7 <- mean.variance.GMM.gradient.GAL(pt.optim7,sRET) %*% - covariance.GMM(meanvariance.gmm.vector,pt.optim7,sRET, + covariance.GMM(pt.optim7,meanvariance.gmm.vector,sRET, meanf=meanQEE,variancef=varianceQEE) %*% t(mean.variance.GMM.gradient.GAL(pt.optim7,sRET)) / n ## GMM itératif @@ -226,19 +228,19 @@ dist3 <- cbind(pGAL(xi,pt.optim1), \subsection{Graphiques} <>= - for (i in 1:8) - { - file<-paste("dist-GAL-",i,".pdf",sep="") - pdf(file=file,paper="special",width=6,height=6) - plot.ecdf(sRET,main=paste("Fonction de répartition ",i)) - lines(xi,dist1[,i],col="green") - lines(xi,dist2[,1],col="red") - lines(xi,dist3[,1],col="pink") - lines(xi,pnorm(xi),type="l",col="blue") - dev.off() - cat("\\includegraphics[height=2in,width=2in]{", - file,"}\n",sep="") - } +for (i in 1:8) +{ + file<-paste(strData,"-repart-",i,".pdf",sep="") + pdf(file=file,paper="special",width=6,height=6) + plot.ecdf(sRET,main=paste("Fonction de répartition ",i)) + lines(xi,dist1[,i],col="green") + lines(xi,dist2[,1],col="red") + lines(xi,dist3[,1],col="pink") + lines(xi,pnorm(xi),type="l",col="blue") + dev.off() + cat("\\includegraphics[height=4in,width=4in]{", + file,"}\n",sep="") +} @ \subsection{Statistiques} @@ -248,29 +250,169 @@ chisquare.test1 <- function(param,DATA.hist,FUN,method) { chisquare.test(DATA.hist,FUN,param,method=method) } -xtable(do.call(rbind,lapply(l.pts.estim,chisquare.test1,hist(sRET),cfGAL,"integral")),digits=6) +xtable(do.call(rbind,lapply(l.pts.estim,chisquare.test1,hist(sRET), + cfGAL,"integral")),digits=6) @ Test du $\chi^2$, Méthode avec point de selle <>= -xtable(do.call(rbind,lapply(l.pts.estim,chisquare.test1,hist(sRET),pGAL,"saddlepoint")),digits=6) +xtable(do.call(rbind,lapply(l.pts.estim,chisquare.test1,hist(sRET), + pGAL,"saddlepoint")),digits=6) @ Statistique de Kolmogorov-Smirnov <>= - ks.test1 <- function(param,x,y) ks.test(x,y,param) - xtable(do.call(rbind,mclapply(l.pts.estim,ks.test1,sRET,"pGAL")),digits=6) +ks.test1 <- function(param,x,y) ks.test(x,y,param) +xtable(do.call(rbind,mclapply(l.pts.estim,ks.test1,sRET,"pGAL")),digits=6) @ Statistique de distance minimale <>= - tvariate1 <- seq(-.1,.1,by=0.01) - 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) @ \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. + +<<>>= +f_integrale_saddle <- function(param,f,lower,upper) + integrate(f,lower,upper,param)$value +norm_int_saddle <- sapply(l.pts.estim,f_integrale_saddle, + f=dsaddleapproxGAL,lower=-Inf,upper=Inf) +@ + +Séquence de points pour les graphiques +<<>>= +x_sRET <- seq(min(sRET)-sd(sRET),max(sRET)+sd(sRET),length.out=50) +@ + +Graphique de la fonction de densité + +<>= +colors2=c("black","red","green","blue","grey") +for (i in 1:dim(pts.estim)[2]) +{ + file=paste(strData,"-densite-", i, ".pdf", sep="") + pdf(file=file, paper="special", width=6, height=6) + plot(density(sRET),ylim=c(0,.7),type="l", + main=paste("Densité de",strData, i),xlab=strData, + ylab="f",lwd=2,lty=1) + points(x_sRET, + dGAL(x_sRET,pts.estim[,i]), + type="b",ylim=c(0,4),col="red",pch=19,lwd=2,lty=2) + points(x_sRET, + dsaddleapproxGAL(x_sRET,pts.estim[,i])/norm_int_saddle[i], + type="b",ylim=c(0,4),col="green",pch=20,lwd=2,lty=3) + + lines(x_sRET,dnorm(x_sRET),type="b",col="blue", + pch=21,lwd=2,lty=4) + points(seq(-2,4,length.out=1000)[seq(40,1000,by=40)], + cftodensity.fft(cfGAL,1000,-2,4,pts.estim[,i])$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="") +} +@ + +\subsection{Tests avec contraintes} + +Test de Wald + +<<>>= +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) +@ + +\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. + +<<>>= +pts.estim.ns <- apply(pts.estim,2,scaleGAL,type="mu", + mean(RETURNS),sd(RETURNS)) +@ + +<>= + xtable(pts.estim.ns, + caption="Paramètres des données non centrées et réduites", + digits=4) +@ + +\section{Prix d'options} + +\subsection{Données de base} + +<<>>= +#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 +@ + +\subsection{Paramètres neutres au risque} + +<<>>= +pts.estim.ns.rn <- apply(pts.estim.ns,2,riskneutralparGAL,rfrate) +l.pts.estim.ns.rn <- as.list(data.frame(pts.estim.ns.rn)) +@ + +<>= +xtable(pts.estim.ns.rn,caption="Paramètres neutres au risque",digits=4) +@ + + +\subsection{Méthode de Epps} + +<<>>= + 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)) +@ + +<>= + xtable(prix_Epps,caption="Prix unitaire de l'option de vente, Méthode de Epps",digits=6) +@ + + + + + + + + + + + + diff --git a/GAL-Buckle95.pdf b/GAL-Buckle95.pdf index ff00ca9..742df5e 100644 Binary files a/GAL-Buckle95.pdf and b/GAL-Buckle95.pdf differ diff --git a/GAL-Buckle95.tex b/GAL-Buckle95.tex index 4d30be4..5bfbd98 100644 --- a/GAL-Buckle95.tex +++ b/GAL-Buckle95.tex @@ -1,4 +1,5 @@ -\documentclass{report} +\documentclass[letter]{report} +\usepackage[margin=0.5in]{geometry} \usepackage{Sweave} \usepackage{graphicx} \usepackage[francais]{babel} @@ -30,7 +31,6 @@ > library(xtable) > library(multicore) > library(moments) -> library(TTR) > library(FourierStuff) > library(GeneralizedAsymmetricLaplace) > library(GMMStuff) @@ -53,6 +53,8 @@ > RETURNS <- head(read.csv("abbeyn.csv",sep="\t",header=TRUE)[,1],-1) > #Taille de l'échantillon > n <- length(RETURNS) +> #Nom de l'échantillon +> strData <- "Buckle95" \end{Sinput} \end{Schunk} @@ -255,7 +257,7 @@ $Reject + meanf=meanQEE,variancef=varianceQEE) > pt.optim7 <- optim7$par > cov.optim7 <- mean.variance.GMM.gradient.GAL(pt.optim7,sRET) %*% -+ covariance.GMM(meanvariance.gmm.vector,pt.optim7,sRET, ++ covariance.GMM(pt.optim7,meanvariance.gmm.vector,sRET, + meanf=meanQEE,variancef=varianceQEE) %*% + t(mean.variance.GMM.gradient.GAL(pt.optim7,sRET)) / n > ## GMM itératif @@ -337,28 +339,28 @@ $Reject \begin{Schunk} \begin{Sinput} -> for (i in 1:8) -+ { -+ file<-paste("dist-GAL-",i,".pdf",sep="") -+ pdf(file=file,paper="special",width=6,height=6) -+ plot.ecdf(sRET,main=paste("Fonction de répartition ",i)) -+ lines(xi,dist1[,i],col="green") -+ lines(xi,dist2[,1],col="red") -+ lines(xi,dist3[,1],col="pink") -+ lines(xi,pnorm(xi),type="l",col="blue") -+ dev.off() -+ cat("\\includegraphics[height=2in,width=2in]{", -+ file,"}\n",sep="") -+ } +> for (i in 1:8) ++ { ++ file<-paste(strData,"-repart-",i,".pdf",sep="") ++ pdf(file=file,paper="special",width=6,height=6) ++ plot.ecdf(sRET,main=paste("Fonction de répartition ",i)) ++ lines(xi,dist1[,i],col="green") ++ lines(xi,dist2[,1],col="red") ++ lines(xi,dist3[,1],col="pink") ++ lines(xi,pnorm(xi),type="l",col="blue") ++ dev.off() ++ cat("\\includegraphics[height=4in,width=4in]{", ++ file,"}\n",sep="") ++ } \end{Sinput} -\includegraphics[height=2in,width=2in]{dist-GAL-1.pdf} -\includegraphics[height=2in,width=2in]{dist-GAL-2.pdf} -\includegraphics[height=2in,width=2in]{dist-GAL-3.pdf} -\includegraphics[height=2in,width=2in]{dist-GAL-4.pdf} -\includegraphics[height=2in,width=2in]{dist-GAL-5.pdf} -\includegraphics[height=2in,width=2in]{dist-GAL-6.pdf} -\includegraphics[height=2in,width=2in]{dist-GAL-7.pdf} -\includegraphics[height=2in,width=2in]{dist-GAL-8.pdf}\end{Schunk} +\includegraphics[height=4in,width=4in]{Buckle95-repart-1.pdf} +\includegraphics[height=4in,width=4in]{Buckle95-repart-2.pdf} +\includegraphics[height=4in,width=4in]{Buckle95-repart-3.pdf} +\includegraphics[height=4in,width=4in]{Buckle95-repart-4.pdf} +\includegraphics[height=4in,width=4in]{Buckle95-repart-5.pdf} +\includegraphics[height=4in,width=4in]{Buckle95-repart-6.pdf} +\includegraphics[height=4in,width=4in]{Buckle95-repart-7.pdf} +\includegraphics[height=4in,width=4in]{Buckle95-repart-8.pdf}\end{Schunk} \subsection{Statistiques} Test du $\chi^2$, Méthode avec intégration @@ -368,10 +370,11 @@ Test du $\chi^2$, Méthode avec intégration + { + chisquare.test(DATA.hist,FUN,param,method=method) + } -> xtable(do.call(rbind,lapply(l.pts.estim,chisquare.test1,hist(sRET),cfGAL,"integral")),digits=6) +> xtable(do.call(rbind,lapply(l.pts.estim,chisquare.test1,hist(sRET), ++ cfGAL,"integral")),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} @@ -393,10 +396,11 @@ pt.optim1 & 5.473824 & 6.000000 & 0.484626 \\ Test du $\chi^2$, Méthode avec point de selle \begin{Schunk} \begin{Sinput} -> xtable(do.call(rbind,lapply(l.pts.estim,chisquare.test1,hist(sRET),pGAL,"saddlepoint")),digits=6) +> xtable(do.call(rbind,lapply(l.pts.estim,chisquare.test1,hist(sRET), ++ pGAL,"saddlepoint")),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} @@ -418,11 +422,11 @@ pt.optim1 & 9.293574 & 6.000000 & 0.157728 \\ Statistique de Kolmogorov-Smirnov \begin{Schunk} \begin{Sinput} -> ks.test1 <- function(param,x,y) ks.test(x,y,param) -> xtable(do.call(rbind,mclapply(l.pts.estim,ks.test1,sRET,"pGAL")),digits=6) +> ks.test1 <- function(param,x,y) ks.test(x,y,param) +> xtable(do.call(rbind,mclapply(l.pts.estim,ks.test1,sRET,"pGAL")),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}{rrrrrr} @@ -445,11 +449,12 @@ Statistique de distance minimale \begin{Schunk} \begin{Sinput} -> tvariate1 <- seq(-.1,.1,by=0.01) -> 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} + + + + + + + + + + + + diff --git a/Rplots.pdf b/Rplots.pdf index 92bead9..4aad682 100644 --- a/Rplots.pdf +++ b/Rplots.pdf @@ -2,10 +2,10 @@ %ρ\r 1 0 obj << -/CreationDate (D:20140315113858) -/ModDate (D:20140315113858) +/CreationDate (D:20140329124233) +/ModDate (D:20140329124233) /Title (R Graphics Output) -/Producer (R 3.0.2) +/Producer (R 3.0.3) /Creator (R) >> endobj @@ -19,10 +19,10 @@ endobj %ρ\r 1 0 obj << -/CreationDate (D:20140315113858) -/ModDate (D:20140315113858) +/CreationDate (D:20140329124233) +/ModDate (D:20140329124233) /Title (R Graphics Output) -/Producer (R 3.0.2) +/Producer (R 3.0.3) /Creator (R) >> endobj @@ -36,10 +36,10 @@ endobj 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.iUM~Ǔ8Xij~Qx)<1/&ѭ\yϧ|)|ycy/8j}r<>>ۛکj{vsL|FO8o4ϝϟK3wzCS'r&J&|ނmTb.O6.|8oR$lM{9q?2r0or,w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|7:endstream endobj 9 0 obj << /Type /Page /Parent 3 0 R /Contents 10 0 R /Resources 4 0 R >> @@ -1099,10 +885,10 @@ endobj %ρ\r 1 0 obj << -/CreationDate (D:20140315113858) -/ModDate (D:20140315113858) +/CreationDate (D:20140329124233) +/ModDate (D:20140329124233) /Title (R Graphics Output) -/Producer (R 3.0.2) +/Producer (R 3.0.3) /Creator (R) >> endobj @@ -1114,12 +900,10 @@ endobj endobj 8 0 obj << -/Length 1122 /Filter /FlateDecode +/Length 1079 /Filter /FlateDecode >> stream -xoDsC][5J q@!ED$UǻMV]9׿3{4O -C -{q{qĦix}{~QzRK0_:7%1n Wwo{?߅WW_ݫ\y,?P6:CaOozmKpϛ뿏ԘҚ2ı?KsORy>f[&.5 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+927,10 @@ endobj endobj 8 0 obj << -/Length 1122 /Filter /FlateDecode +/Length 1079 /Filter /FlateDecode >> stream -xoDsC][5J q@!ED$UǻMV]9׿3{4O -C -{q{qĦix}{~QzRK0_:7%1n Wwo{?߅WW_ݫ\y,?P6:CaOozmKpϛ뿏ԘҚ2ı?KsORy>f[&.5 BV|c|Fso۶ޱu1om,צ9mzxӵmcLێae3폹x85Mm//46155///{7OPMPG7g{S;[mnӝs?'}͘sהbivsX/{h>qDC~=܄q[Je?ަQ%mZCit/G6X9]mX9]O=5w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|Ͼ1_I0endstream +xoDsC][5J q@!ED$UǻMV]aأyRxR voߋǷ߼׏&6M2ջj\2׹)vcm _}}.߾:\^]``:)֩bc}}l3؅\8t_}dy//?˗Ow6Є_v)~t]_OؗXk p$yNScNRnƔ|.855/uxʗr1ۺn.7vկnmt'k63>~ۜض]47gMyKmci7g,6Mi{ƛmgvM .iUM~Ǔ8Xij~Qx)<1/&ѭ\yϧ|)|ycy/8j}r<>>ۛکj{vsL|FO8o4ϝϟK3wzCS'r&J&|ނmTb.O6.|8oR$lM{9q?2r0or,w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|7:endstream endobj 9 0 obj << /Type /Page /Parent 3 0 R /Contents 10 0 R /Resources 4 0 R >> @@ -1157,10 +939,10 @@ endobj %ρ\r 1 0 obj << -/CreationDate (D:20140315113858) -/ModDate (D:20140315113858) +/CreationDate (D:20140329124233) +/ModDate (D:20140329124233) /Title (R Graphics Output) -/Producer (R 3.0.2) +/Producer (R 3.0.3) /Creator (R) >> endobj @@ -1172,12 +954,10 @@ endobj endobj 8 0 obj << -/Length 1122 /Filter /FlateDecode +/Length 1079 /Filter /FlateDecode >> stream -xoDsC][5J q@!ED$UǻMV]9׿3{4O -C -{q{qĦix}{~QzRK0_:7%1n Wwo{?߅WW_ݫ\y,?P6:CaOozmKpϛ뿏ԘҚ2ı?KsORy>f[&.5 BV|c|Fso۶ޱu1om,צ9mzxӵmcLێae3폹x85Mm//46155///{7OPMPG7g{S;[mnӝs?'}͘sהbivsX/{h>qDC~=܄q[Je?ަQ%mZCit/G6X9]mX9]O=5w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|Ͼ1_I0endstream +xoDsC][5J q@!ED$UǻMV]aأyRxR voߋǷ߼׏&6M2ջj\2׹)vcm _}}.߾:\^]``:)֩bc}}l3؅\8t_}dy//?˗Ow6Є_v)~t]_OؗXk p$yNScNRnƔ|.855/uxʗr1ۺn.7vկnmt'k63>~ۜض]47gMyKmci7g,6Mi{ƛmgvM .iUM~Ǔ8Xij~Qx)<1/&ѭ\yϧ|)|ycy/8j}r<>>ۛکj{vsL|FO8o4ϝϟK3wzCS'r&J&|ނmTb.O6.|8oR$lM{9q?2r0or,w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|7:endstream endobj 9 0 obj << /Type /Page /Parent 3 0 R /Contents 10 0 R /Resources 4 0 R >> @@ -1186,10 +966,10 @@ endobj %ρ\r 1 0 obj << -/CreationDate (D:20140315113858) -/ModDate (D:20140315113858) +/CreationDate (D:20140329124233) +/ModDate (D:20140329124233) /Title (R Graphics Output) -/Producer (R 3.0.2) +/Producer (R 3.0.3) /Creator (R) >> endobj @@ -1201,12 +981,10 @@ endobj endobj 8 0 obj << -/Length 1122 /Filter /FlateDecode +/Length 1079 /Filter /FlateDecode >> stream -xoDsC][5J q@!ED$UǻMV]9׿3{4O -C -{q{qĦix}{~QzRK0_:7%1n Wwo{?߅WW_ݫ\y,?P6:CaOozmKpϛ뿏ԘҚ2ı?KsORy>f[&.5 BV|c|Fso۶ޱu1om,צ9mzxӵmcLێae3폹x85Mm//46155///{7OPMPG7g{S;[mnӝs?'}͘sהbivsX/{h>qDC~=܄q[Je?ަQ%mZCit/G6X9]mX9]O=5w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|Ͼ1_I0endstream +xoDsC][5J q@!ED$UǻMV]aأyRxR voߋǷ߼׏&6M2ջj\2׹)vcm _}}.߾:\^]``:)֩bc}}l3؅\8t_}dy//?˗Ow6Є_v)~t]_OؗXk p$yNScNRnƔ|.855/uxʗr1ۺn.7vկnmt'k63>~ۜض]47gMyKmci7g,6Mi{ƛmgvM .iUM~Ǔ8Xij~Qx)<1/&ѭ\yϧ|)|ycy/8j}r<>>ۛکj{vsL|FO8o4ϝϟK3wzCS'r&J&|ނmTb.O6.|8oR$lM{9q?2r0or,w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|7:endstream endobj 9 0 obj << /Type /Page /Parent 3 0 R /Contents 10 0 R /Resources 4 0 R >> @@ -1215,10 +993,10 @@ endobj %ρ\r 1 0 obj << -/CreationDate (D:20140315113858) -/ModDate (D:20140315113858) +/CreationDate (D:20140329124233) +/ModDate (D:20140329124233) /Title (R Graphics Output) -/Producer (R 3.0.2) +/Producer (R 3.0.3) /Creator (R) >> endobj @@ -1230,12 +1008,10 @@ endobj endobj 8 0 obj << -/Length 1122 /Filter /FlateDecode +/Length 1079 /Filter /FlateDecode >> stream -xoDsC][5J q@!ED$UǻMV]9׿3{4O -C -{q{qĦix}{~QzRK0_:7%1n Wwo{?߅WW_ݫ\y,?P6:CaOozmKpϛ뿏ԘҚ2ı?KsORy>f[&.5 BV|c|Fso۶ޱu1om,צ9mzxӵmcLێae3폹x85Mm//46155///{7OPMPG7g{S;[mnӝs?'}͘sהbivsX/{h>qDC~=܄q[Je?ަQ%mZCit/G6X9]mX9]O=5w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|Ͼ1_I0endstream +xoDsC][5J q@!ED$UǻMV]aأyRxR voߋǷ߼׏&6M2ջj\2׹)vcm _}}.߾:\^]``:)֩bc}}l3؅\8t_}dy//?˗Ow6Є_v)~t]_OؗXk p$yNScNRnƔ|.855/uxʗr1ۺn.7vկnmt'k63>~ۜض]47gMyKmci7g,6Mi{ƛmgvM .iUM~Ǔ8Xij~Qx)<1/&ѭ\yϧ|)|ycy/8j}r<>>ۛکj{vsL|FO8o4ϝϟK3wzCS'r&J&|ނmTb.O6.|8oR$lM{9q?2r0or,w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|7:endstream endobj 9 0 obj << /Type /Page /Parent 3 0 R /Contents 10 0 R /Resources 4 0 R >> @@ -1244,10 +1020,10 @@ endobj %ρ\r 1 0 obj << -/CreationDate (D:20140315113858) -/ModDate (D:20140315113858) +/CreationDate (D:20140329124233) +/ModDate (D:20140329124233) /Title (R Graphics Output) -/Producer (R 3.0.2) +/Producer (R 3.0.3) /Creator (R) >> endobj @@ -1259,12 +1035,10 @@ endobj endobj 8 0 obj << -/Length 1122 /Filter /FlateDecode +/Length 1079 /Filter /FlateDecode >> stream -xoDsC][5J q@!ED$UǻMV]9׿3{4O -C -{q{qĦix}{~QzRK0_:7%1n Wwo{?߅WW_ݫ\y,?P6:CaOozmKpϛ뿏ԘҚ2ı?KsORy>f[&.5 BV|c|Fso۶ޱu1om,צ9mzxӵmcLێae3폹x85Mm//46155///{7OPMPG7g{S;[mnӝs?'}͘sהbivsX/{h>qDC~=܄q[Je?ަQ%mZCit/G6X9]mX9]O=5w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|Ͼ1_I0endstream +xoDsC][5J q@!ED$UǻMV]aأyRxR voߋǷ߼׏&6M2ջj\2׹)vcm _}}.߾:\^]``:)֩bc}}l3؅\8t_}dy//?˗Ow6Є_v)~t]_OؗXk p$yNScNRnƔ|.855/uxʗr1ۺn.7vկnmt'k63>~ۜض]47gMyKmci7g,6Mi{ƛmgvM .iUM~Ǔ8Xij~Qx)<1/&ѭ\yϧ|)|ycy/8j}r<>>ۛکj{vsL|FO8o4ϝϟK3wzCS'r&J&|ނmTb.O6.|8oR$lM{9q?2r0or,w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|7:endstream endobj 9 0 obj << /Type /Page /Parent 3 0 R /Contents 10 0 R /Resources 4 0 R >> @@ -1273,10 +1047,10 @@ endobj %ρ\r 1 0 obj << -/CreationDate (D:20140315113858) -/ModDate (D:20140315113858) +/CreationDate (D:20140329124233) +/ModDate (D:20140329124233) /Title (R Graphics Output) -/Producer (R 3.0.2) +/Producer (R 3.0.3) /Creator (R) >> endobj @@ -1288,12 +1062,10 @@ endobj endobj 8 0 obj << -/Length 1122 /Filter /FlateDecode +/Length 1079 /Filter /FlateDecode >> stream -xoDsC][5J q@!ED$UǻMV]9׿3{4O -C -{q{qĦix}{~QzRK0_:7%1n Wwo{?߅WW_ݫ\y,?P6:CaOozmKpϛ뿏ԘҚ2ı?KsORy>f[&.5 BV|c|Fso۶ޱu1om,צ9mzxӵmcLێae3폹x85Mm//46155///{7OPMPG7g{S;[mnӝs?'}͘sהbivsX/{h>qDC~=܄q[Je?ަQ%mZCit/G6X9]mX9]O=5w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|Ͼ1_I0endstream +xoDsC][5J q@!ED$UǻMV]aأyRxR voߋǷ߼׏&6M2ջj\2׹)vcm _}}.߾:\^]``:)֩bc}}l3؅\8t_}dy//?˗Ow6Є_v)~t]_OؗXk p$yNScNRnƔ|.855/uxʗr1ۺn.7vկnmt'k63>~ۜض]47gMyKmci7g,6Mi{ƛmgvM .iUM~Ǔ8Xij~Qx)<1/&ѭ\yϧ|)|ycy/8j}r<>>ۛکj{vsL|FO8o4ϝϟK3wzCS'r&J&|ނmTb.O6.|8oR$lM{9q?2r0or,w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|7:endstream endobj 9 0 obj << /Type /Page /Parent 3 0 R /Contents 10 0 R /Resources 4 0 R >> @@ -1302,10 +1074,10 @@ endobj %ρ\r 1 0 obj << -/CreationDate (D:20140315113858) -/ModDate (D:20140315113858) +/CreationDate (D:20140329124233) +/ModDate (D:20140329124233) /Title (R Graphics Output) -/Producer (R 3.0.2) +/Producer (R 3.0.3) /Creator (R) >> endobj @@ -1317,12 +1089,10 @@ endobj endobj 8 0 obj << -/Length 1122 /Filter /FlateDecode +/Length 1079 /Filter /FlateDecode >> stream -xoDsC][5J q@!ED$UǻMV]9׿3{4O -C -{q{qĦix}{~QzRK0_:7%1n Wwo{?߅WW_ݫ\y,?P6:CaOozmKpϛ뿏ԘҚ2ı?KsORy>f[&.5 BV|c|Fso۶ޱu1om,צ9mzxӵmcLێae3폹x85Mm//46155///{7OPMPG7g{S;[mnӝs?'}͘sהbivsX/{h>qDC~=܄q[Je?ަQ%mZCit/G6X9]mX9]O=5w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|Ͼ1_I0endstream +xoDsC][5J q@!ED$UǻMV]aأyRxR voߋǷ߼׏&6M2ջj\2׹)vcm _}}.߾:\^]``:)֩bc}}l3؅\8t_}dy//?˗Ow6Є_v)~t]_OؗXk p$yNScNRnƔ|.855/uxʗr1ۺn.7vկnmt'k63>~ۜض]47gMyKmci7g,6Mi{ƛmgvM .iUM~Ǔ8Xij~Qx)<1/&ѭ\yϧ|)|ycy/8j}r<>>ۛکj{vsL|FO8o4ϝϟK3wzCS'r&J&|ނmTb.O6.|8oR$lM{9q?2r0or,w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|7:endstream endobj 9 0 obj << /Type /Page /Parent 3 0 R /Contents 10 0 R /Resources 4 0 R >> @@ -1331,10 +1101,10 @@ endobj %ρ\r 1 0 obj << -/CreationDate (D:20140315113858) -/ModDate (D:20140315113858) +/CreationDate (D:20140329124233) +/ModDate (D:20140329124233) /Title (R Graphics Output) -/Producer (R 3.0.2) +/Producer (R 3.0.3) /Creator (R) >> endobj @@ -1346,12 +1116,10 @@ endobj endobj 8 0 obj << -/Length 1122 /Filter /FlateDecode +/Length 1079 /Filter /FlateDecode >> stream -xoDsC][5J q@!ED$UǻMV]9׿3{4O -C -{q{qĦix}{~QzRK0_:7%1n Wwo{?߅WW_ݫ\y,?P6:CaOozmKpϛ뿏ԘҚ2ı?KsORy>f[&.5 BV|c|Fso۶ޱu1om,צ9mzxӵmcLێae3폹x85Mm//46155///{7OPMPG7g{S;[mnӝs?'}͘sהbivsX/{h>qDC~=܄q[Je?ަQ%mZCit/G6X9]mX9]O=5w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|Ͼ1_I0endstream +xoDsC][5J q@!ED$UǻMV]aأyRxR voߋǷ߼׏&6M2ջj\2׹)vcm _}}.߾:\^]``:)֩bc}}l3؅\8t_}dy//?˗Ow6Є_v)~t]_OؗXk p$yNScNRnƔ|.855/uxʗr1ۺn.7vկnmt'k63>~ۜض]47gMyKmci7g,6Mi{ƛmgvM .iUM~Ǔ8Xij~Qx)<1/&ѭ\yϧ|)|ycy/8j}r<>>ۛکj{vsL|FO8o4ϝϟK3wzCS'r&J&|ނmTb.O6.|8oR$lM{9q?2r0or,w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|7:endstream endobj 9 0 obj << /Type /Page /Parent 3 0 R /Contents 10 0 R /Resources 4 0 R >> @@ -1360,10 +1128,10 @@ endobj %ρ\r 1 0 obj << -/CreationDate (D:20140315113858) -/ModDate (D:20140315113858) +/CreationDate (D:20140329124233) +/ModDate (D:20140329124233) /Title (R Graphics Output) -/Producer (R 3.0.2) +/Producer (R 3.0.3) /Creator (R) >> endobj @@ -1375,12 +1143,10 @@ endobj endobj 8 0 obj << -/Length 1122 /Filter /FlateDecode +/Length 1079 /Filter /FlateDecode >> stream -xoDsC][5J q@!ED$UǻMV]9׿3{4O -C -{q{qĦix}{~QzRK0_:7%1n Wwo{?߅WW_ݫ\y,?P6:CaOozmKpϛ뿏ԘҚ2ı?KsORy>f[&.5 BV|c|Fso۶ޱu1om,צ9mzxӵmcLێae3폹x85Mm//46155///{7OPMPG7g{S;[mnӝs?'}͘sהbivsX/{h>qDC~=܄q[Je?ަQ%mZCit/G6X9]mX9]O=5w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|Ͼ1_I0endstream +xoDsC][5J q@!ED$UǻMV]aأyRxR voߋǷ߼׏&6M2ջj\2׹)vcm _}}.߾:\^]``:)֩bc}}l3؅\8t_}dy//?˗Ow6Є_v)~t]_OؗXk p$yNScNRnƔ|.855/uxʗr1ۺn.7vկnmt'k63>~ۜض]47gMyKmci7g,6Mi{ƛmgvM .iUM~Ǔ8Xij~Qx)<1/&ѭ\yϧ|)|ycy/8j}r<>>ۛکj{vsL|FO8o4ϝϟK3wzCS'r&J&|ނmTb.O6.|8oR$lM{9q?2r0or,w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|7:endstream endobj 9 0 obj << /Type /Page /Parent 3 0 R /Contents 10 0 R /Resources 4 0 R >> @@ -1389,10 +1155,10 @@ endobj %ρ\r 1 0 obj << -/CreationDate (D:20140315113858) -/ModDate (D:20140315113858) +/CreationDate (D:20140329124233) +/ModDate (D:20140329124233) /Title (R Graphics Output) -/Producer (R 3.0.2) +/Producer (R 3.0.3) /Creator (R) >> endobj @@ -1404,23 +1170,1290 @@ endobj endobj 8 0 obj << -/Length 1122 /Filter /FlateDecode +/Length 1079 /Filter /FlateDecode >> stream -xoDsC][5J q@!ED$UǻMV]9׿3{4O -C -{q{qĦix}{~QzRK0_:7%1n Wwo{?߅WW_ݫ\y,?P6:CaOozmKpϛ뿏ԘҚ2ı?KsORy>f[&.5 BV|c|Fso۶ޱu1om,צ9mzxӵmcLێae3폹x85Mm//46155///{7OPMPG7g{S;[mnӝs?'}͘sהbivsX/{h>qDC~=܄q[Je?ަQ%mZCit/G6X9]mX9]O=5w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|Ͼ1_I0endstream +xoDsC][5J q@!ED$UǻMV]aأyRxR voߋǷ߼׏&6M2ջj\2׹)vcm _}}.߾:\^]``:)֩bc}}l3؅\8t_}dy//?˗Ow6Є_v)~t]_OؗXk p$yNScNRnƔ|.855/uxʗr1ۺn.7vկnmt'k63>~ۜض]47gMyKmci7g,6Mi{ƛmgvM .iUM~Ǔ8Xij~Qx)<1/&ѭ\yϧ|)|ycy/8j}r<>>ۛکj{vsL|FO8o4ϝϟK3wzCS'r&J&|ނmTb.O6.|8oR$lM{9q?2r0or,w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|7:endstream +endobj +9 0 obj +<< /Type /Page /Parent 3 0 R /Contents 10 0 R /Resources 4 0 R >> +endobj +%PDF-1.4 +%ρ\r +1 0 obj +<< +/CreationDate (D:20140329124233) +/ModDate (D:20140329124233) +/Title (R Graphics Output) +/Producer (R 3.0.3) +/Creator (R) +>> +endobj +2 0 obj +<< /Type /Catalog /Pages 3 0 R >> +endobj +7 0 obj +<< /Type /Page /Parent 3 0 R /Contents 8 0 R /Resources 4 0 R >> +endobj +8 0 obj +<< +/Length 1079 /Filter /FlateDecode +>> +stream +xoDsC][5J q@!ED$UǻMV]aأyRxR voߋǷ߼׏&6M2ջj\2׹)vcm _}}.߾:\^]``:)֩bc}}l3؅\8t_}dy//?˗Ow6Є_v)~t]_OؗXk p$yNScNRnƔ|.855/uxʗr1ۺn.7vկnmt'k63>~ۜض]47gMyKmci7g,6Mi{ƛmgvM .iUM~Ǔ8Xij~Qx)<1/&ѭ\yϧ|)|ycy/8j}r<>>ۛکj{vsL|FO8o4ϝϟK3wzCS'r&J&|ނmTb.O6.|8oR$lM{9q?2r0or,w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|7:endstream +endobj +9 0 obj +<< /Type /Page /Parent 3 0 R /Contents 10 0 R /Resources 4 0 R >> +endobj +%PDF-1.4 +%ρ\r +1 0 obj +<< +/CreationDate (D:20140329124233) +/ModDate (D:20140329124233) +/Title (R Graphics Output) +/Producer (R 3.0.3) +/Creator (R) +>> +endobj +2 0 obj +<< /Type /Catalog /Pages 3 0 R >> +endobj +7 0 obj +<< /Type /Page /Parent 3 0 R /Contents 8 0 R /Resources 4 0 R >> +endobj +8 0 obj +<< +/Length 1079 /Filter /FlateDecode +>> +stream +xoDsC][5J q@!ED$UǻMV]aأyRxR voߋǷ߼׏&6M2ջj\2׹)vcm _}}.߾:\^]``:)֩bc}}l3؅\8t_}dy//?˗Ow6Є_v)~t]_OؗXk p$yNScNRnƔ|.855/uxʗr1ۺn.7vկnmt'k63>~ۜض]47gMyKmci7g,6Mi{ƛmgvM .iUM~Ǔ8Xij~Qx)<1/&ѭ\yϧ|)|ycy/8j}r<>>ۛکj{vsL|FO8o4ϝϟK3wzCS'r&J&|ނmTb.O6.|8oR$lM{9q?2r0or,w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|7:endstream +endobj +9 0 obj +<< /Type /Page /Parent 3 0 R /Contents 10 0 R /Resources 4 0 R >> +endobj +%PDF-1.4 +%ρ\r +1 0 obj +<< +/CreationDate (D:20140329124233) +/ModDate (D:20140329124233) +/Title (R Graphics Output) +/Producer (R 3.0.3) +/Creator (R) +>> +endobj +2 0 obj +<< /Type /Catalog /Pages 3 0 R >> +endobj +7 0 obj +<< /Type /Page /Parent 3 0 R /Contents 8 0 R /Resources 4 0 R >> +endobj +8 0 obj +<< +/Length 1079 /Filter /FlateDecode +>> +stream +xoDsC][5J q@!ED$UǻMV]aأyRxR voߋǷ߼׏&6M2ջj\2׹)vcm _}}.߾:\^]``:)֩bc}}l3؅\8t_}dy//?˗Ow6Є_v)~t]_OؗXk p$yNScNRnƔ|.855/uxʗr1ۺn.7vկnmt'k63>~ۜض]47gMyKmci7g,6Mi{ƛmgvM .iUM~Ǔ8Xij~Qx)<1/&ѭ\yϧ|)|ycy/8j}r<>>ۛکj{vsL|FO8o4ϝϟK3wzCS'r&J&|ނmTb.O6.|8oR$lM{9q?2r0or,w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|7:endstream +endobj +9 0 obj +<< /Type /Page /Parent 3 0 R /Contents 10 0 R /Resources 4 0 R >> +endobj +%PDF-1.4 +%ρ\r +1 0 obj +<< +/CreationDate (D:20140329124233) +/ModDate (D:20140329124233) +/Title (R Graphics Output) +/Producer (R 3.0.3) +/Creator (R) +>> +endobj +2 0 obj +<< /Type /Catalog /Pages 3 0 R >> +endobj +7 0 obj +<< /Type /Page /Parent 3 0 R /Contents 8 0 R /Resources 4 0 R >> +endobj +8 0 obj +<< +/Length 1079 /Filter /FlateDecode +>> +stream +xoDsC][5J q@!ED$UǻMV]aأyRxR voߋǷ߼׏&6M2ջj\2׹)vcm _}}.߾:\^]``:)֩bc}}l3؅\8t_}dy//?˗Ow6Є_v)~t]_OؗXk p$yNScNRnƔ|.855/uxʗr1ۺn.7vկnmt'k63>~ۜض]47gMyKmci7g,6Mi{ƛmgvM .iUM~Ǔ8Xij~Qx)<1/&ѭ\yϧ|)|ycy/8j}r<>>ۛکj{vsL|FO8o4ϝϟK3wzCS'r&J&|ނmTb.O6.|8oR$lM{9q?2r0or,w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|7:endstream +endobj +9 0 obj +<< /Type /Page /Parent 3 0 R /Contents 10 0 R /Resources 4 0 R >> +endobj +%PDF-1.4 +%ρ\r +1 0 obj +<< +/CreationDate (D:20140329124233) +/ModDate (D:20140329124233) +/Title (R Graphics Output) +/Producer (R 3.0.3) +/Creator (R) +>> +endobj +2 0 obj +<< /Type /Catalog /Pages 3 0 R >> +endobj +7 0 obj +<< /Type /Page /Parent 3 0 R /Contents 8 0 R /Resources 4 0 R >> +endobj +8 0 obj +<< +/Length 1079 /Filter /FlateDecode +>> +stream +xoDsC][5J q@!ED$UǻMV]aأyRxR voߋǷ߼׏&6M2ջj\2׹)vcm _}}.߾:\^]``:)֩bc}}l3؅\8t_}dy//?˗Ow6Є_v)~t]_OؗXk p$yNScNRnƔ|.855/uxʗr1ۺn.7vկnmt'k63>~ۜض]47gMyKmci7g,6Mi{ƛmgvM .iUM~Ǔ8Xij~Qx)<1/&ѭ\yϧ|)|ycy/8j}r<>>ۛکj{vsL|FO8o4ϝϟK3wzCS'r&J&|ނmTb.O6.|8oR$lM{9q?2r0or,w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|7:endstream +endobj +9 0 obj +<< /Type /Page /Parent 3 0 R /Contents 10 0 R /Resources 4 0 R >> +endobj +%PDF-1.4 +%ρ\r +1 0 obj +<< +/CreationDate (D:20140329124233) +/ModDate (D:20140329124233) +/Title (R Graphics Output) +/Producer (R 3.0.3) +/Creator (R) +>> +endobj +2 0 obj +<< /Type /Catalog /Pages 3 0 R >> +endobj +7 0 obj +<< /Type /Page /Parent 3 0 R /Contents 8 0 R /Resources 4 0 R >> +endobj +8 0 obj +<< +/Length 1079 /Filter /FlateDecode +>> +stream +xoDsC][5J q@!ED$UǻMV]aأyRxR voߋǷ߼׏&6M2ջj\2׹)vcm _}}.߾:\^]``:)֩bc}}l3؅\8t_}dy//?˗Ow6Є_v)~t]_OؗXk p$yNScNRnƔ|.855/uxʗr1ۺn.7vկnmt'k63>~ۜض]47gMyKmci7g,6Mi{ƛmgvM .iUM~Ǔ8Xij~Qx)<1/&ѭ\yϧ|)|ycy/8j}r<>>ۛکj{vsL|FO8o4ϝϟK3wzCS'r&J&|ނmTb.O6.|8oR$lM{9q?2r0or,w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|7:endstream +endobj +9 0 obj +<< /Type /Page /Parent 3 0 R /Contents 10 0 R /Resources 4 0 R >> +endobj +%PDF-1.4 +%ρ\r +1 0 obj +<< +/CreationDate (D:20140329124233) +/ModDate (D:20140329124233) +/Title (R Graphics Output) +/Producer (R 3.0.3) +/Creator (R) +>> +endobj +2 0 obj +<< /Type /Catalog /Pages 3 0 R >> +endobj +7 0 obj +<< /Type /Page /Parent 3 0 R /Contents 8 0 R /Resources 4 0 R >> +endobj +8 0 obj +<< +/Length 1079 /Filter /FlateDecode +>> +stream +xoDsC][5J q@!ED$UǻMV]aأyRxR voߋǷ߼׏&6M2ջj\2׹)vcm _}}.߾:\^]``:)֩bc}}l3؅\8t_}dy//?˗Ow6Є_v)~t]_OؗXk p$yNScNRnƔ|.855/uxʗr1ۺn.7vկnmt'k63>~ۜض]47gMyKmci7g,6Mi{ƛmgvM .iUM~Ǔ8Xij~Qx)<1/&ѭ\yϧ|)|ycy/8j}r<>>ۛکj{vsL|FO8o4ϝϟK3wzCS'r&J&|ނmTb.O6.|8oR$lM{9q?2r0or,w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|7:endstream +endobj +9 0 obj +<< /Type /Page /Parent 3 0 R /Contents 10 0 R /Resources 4 0 R >> +endobj +%PDF-1.4 +%ρ\r +1 0 obj +<< +/CreationDate (D:20140329124233) +/ModDate (D:20140329124233) +/Title (R Graphics Output) +/Producer (R 3.0.3) +/Creator (R) +>> +endobj +2 0 obj +<< /Type /Catalog /Pages 3 0 R >> +endobj +7 0 obj +<< /Type /Page /Parent 3 0 R /Contents 8 0 R /Resources 4 0 R >> +endobj +8 0 obj +<< +/Length 1079 /Filter /FlateDecode +>> +stream +xoDsC][5J q@!ED$UǻMV]aأyRxR voߋǷ߼׏&6M2ջj\2׹)vcm _}}.߾:\^]``:)֩bc}}l3؅\8t_}dy//?˗Ow6Є_v)~t]_OؗXk p$yNScNRnƔ|.855/uxʗr1ۺn.7vկnmt'k63>~ۜض]47gMyKmci7g,6Mi{ƛmgvM .iUM~Ǔ8Xij~Qx)<1/&ѭ\yϧ|)|ycy/8j}r<>>ۛکj{vsL|FO8o4ϝϟK3wzCS'r&J&|ނmTb.O6.|8oR$lM{9q?2r0or,w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|;w|7:endstream +endobj +9 0 obj +<< /Type /Page /Parent 3 0 R /Contents 10 0 R /Resources 4 0 R >> +endobj +%PDF-1.4 +%ρ\r +1 0 obj +<< +/CreationDate (D:20140329124233) +/ModDate (D:20140329124233) +/Title (R Graphics Output) +/Producer (R 3.0.3) +/Creator (R) +>> +endobj +2 0 obj +<< /Type /Catalog /Pages 3 0 R >> +endobj +7 0 obj +<< /Type /Page /Parent 3 0 R /Contents 8 0 R /Resources 4 0 R >> +endobj +8 0 obj +<< +/Length 1079 /Filter /FlateDecode +>> +stream +xoDsC][5J q@!ED$UǻMV]aأyRxR voߋǷ߼׏&6M2ջj\2׹)vcm _}}.߾:\^]``:)֩bc}}l3؅\8t_}dy//?˗Ow6Є_v)~t]_OؗXk p$yNScNRnƔ|.855/uxʗr1ۺn.7vկnmt'k63>~ۜض]47gMyKmci7g,6Mi{ƛmgvM 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