diff --git a/memoire/ABBEYN-callGAL-5.pdf b/graphiques/ABBEYN-callGAL-5.pdf similarity index 100% rename from memoire/ABBEYN-callGAL-5.pdf rename to graphiques/ABBEYN-callGAL-5.pdf diff --git a/memoire/ABBEYN-callGAL-7.pdf b/graphiques/ABBEYN-callGAL-7.pdf similarity index 100% rename from memoire/ABBEYN-callGAL-7.pdf rename to graphiques/ABBEYN-callGAL-7.pdf diff --git a/graphiques/ABBEYN-chronologie.pdf b/graphiques/ABBEYN-chronologie.pdf new file mode 100644 index 0000000..7d8209b Binary files /dev/null and b/graphiques/ABBEYN-chronologie.pdf differ diff --git a/memoire/ABBEYN-densiteGALmu-5.pdf b/graphiques/ABBEYN-densiteGALmu-5.pdf similarity index 100% rename from memoire/ABBEYN-densiteGALmu-5.pdf rename to graphiques/ABBEYN-densiteGALmu-5.pdf diff --git a/memoire/ABBEYN-densiteGALmu-7.pdf b/graphiques/ABBEYN-densiteGALmu-7.pdf similarity index 100% rename from memoire/ABBEYN-densiteGALmu-7.pdf rename to graphiques/ABBEYN-densiteGALmu-7.pdf diff --git a/graphiques/ABBEYN-histogramme.pdf b/graphiques/ABBEYN-histogramme.pdf new file mode 100644 index 0000000..7b21e11 Binary files /dev/null and b/graphiques/ABBEYN-histogramme.pdf differ diff --git a/graphiques/ABBEYN-qq.pdf b/graphiques/ABBEYN-qq.pdf new file mode 100644 index 0000000..c9a0b4b Binary files /dev/null and b/graphiques/ABBEYN-qq.pdf differ diff --git a/graphiques/dGAL-exemples.pdf b/graphiques/dGAL-exemples.pdf new file mode 100644 index 0000000..d55a2b6 Binary files /dev/null and b/graphiques/dGAL-exemples.pdf differ diff --git a/graphiques/dgal-exemples.r b/graphiques/dgal-exemples.r new file mode 100644 index 0000000..c75727a --- /dev/null +++ b/graphiques/dgal-exemples.r @@ -0,0 +1,25 @@ +## Exemples de courbes de densité +library(MASS) +source("fonctions.r") +dGAL1 <- function(x) dGALkappa(x,param=c(0,1,1,1)) +dGAL2 <- function(x) dGALkappa(x,param=c(0,1,2,1)) +dGAL3 <- function(x) dGALkappa(x,param=c(0,1,2,2)) +dGAL4 <- function(x) dGALkappa(x,param=c(0,1,.5,1)) +pdf("dGAL-exemples.pdf") +curve(dGAL1,from=-5,to=5,n=500,xlab="y",ylab="f(y)") +curve(dGAL2,from=-5,to=5,n=500,add=TRUE) +curve(dGAL3,from=-5,to=5,n=500,add=TRUE) +curve(dGAL4,from=-5,to=5,n=500,add=TRUE) +points(-2,dGAL1(-2),pch=21) +points(1,dGAL1(1),pch=21) +points(-2,dGAL2(-2),pch=22) +points(0.49,dGAL2(0.49),pch=22) +points(-2,dGAL3(-2),pch=15) +points(0.25,dGAL3(0.25),pch=15) +points(-2,dGAL4(-2),pch=16) +points(1.5,dGAL4(1.5),pch=16) +pchgraph <- c(21,22,15,16) +noms <- c("GAL(x; 0, 1, 1, 1)","GAL(x; 0, 1, 2, 1)","GAL(x; 0, 1, 2, 2)","GAL(x; 0, 1, 0.5, 1)") +legend(-5, 0.7, noms, cex=1.0, + pch=pchgraph, lty=1) +dev.off() diff --git a/graphiques/mitchell1.pdf b/graphiques/mitchell1.pdf new file mode 100644 index 0000000..44d237b Binary files /dev/null and b/graphiques/mitchell1.pdf differ diff --git a/graphiques/pointdeselleGMM.png b/graphiques/pointdeselleGMM.png new file mode 100644 index 0000000..c316eda Binary files /dev/null and b/graphiques/pointdeselleGMM.png differ diff 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width=4in]{../graphiques/ABBEYN-chronologie.pdf} \caption{Représentation en série chronologique de l'échantillon $R_1$} \label{fig:seriechronoR1} @@ -69,7 +69,7 @@ d'une courbe de densité à la figure \ref{fig:distributionR1}. \begin{figure}[!ht] \centering - \includegraphics[height=4in,width=4in]{../contenus/r/code/ABBEYN-histogramme.pdf} + \includegraphics[height=4in,width=4in]{../graphiques/ABBEYN-histogramme.pdf} \caption{Distribution de la variable aléatoire $R_1$} \label{fig:distributionR1} \end{figure} @@ -109,7 +109,7 @@ quantiles empiriques avec ceux de la loi normale présenté à la figure \begin{figure}[!ht] \centering \includegraphics[height=4in, - width=4in]{../contenus/r/code/ABBEYN-qq.pdf} + width=4in]{../graphiques/ABBEYN-qq.pdf} \caption{Graphique Quantile-Quantile} \label{fig:qqplotR1} \end{figure} @@ -395,7 +395,7 @@ On résout d'abord l'équation du point de selle $r=0.01$ à la figure \ref{fig:equationptselle0.01R1} : \begin{figure}[!ht] \centering - \includegraphics[scale=0.5]{../contenus/maxima/pointdeselleGMM.png} + \includegraphics[scale=0.5]{../graphiques/pointdeselleGMM.png} \caption{Équation du point de selle pour $r=0.01$} \label{fig:equationptselle0.01R1} \end{figure} @@ -513,7 +513,7 @@ la table \ref{tab:intapproxpointselleR1}. \begin{figure}[!ht] \centering \includegraphics[height=6in, - width=6in]{../contenus/r/code/ABBEYN-densiteGALmu-7.pdf} + width=6in]{../graphiques/ABBEYN-densiteGALmu-7.pdf} \caption{Densité de $R_1^{*}$ selon la méthode des moments généralisée} \label{fig:densite1R1} @@ -522,7 +522,7 @@ la table \ref{tab:intapproxpointselleR1}. \begin{figure}[!ht] \centering \includegraphics[height=6in, - width=6in]{../contenus/r/code/ABBEYN-densiteGALmu-5.pdf} + width=6in]{../graphiques/ABBEYN-densiteGALmu-5.pdf} \caption{Densité de $R_1^{*}$ selon la méthode de l'équation d'estimation optimale} \label{fig:densite3R1} @@ -681,7 +681,7 @@ d'ordre 1 est très précise dans ce contexte. \begin{figure}[!ht] \centering \includegraphics[height=6in, - width=6in]{../contenus/r/code/ABBEYN-callGAL-7.pdf} + width=6in]{../graphiques/ABBEYN-callGAL-7.pdf} \caption{Prix de l'option selon les paramètres estimés avec la méthode des moments généralisée} \label{fig:prix1R1-1} @@ -690,7 +690,7 @@ d'ordre 1 est très précise dans ce contexte. \begin{figure}[!ht] \centering \includegraphics[height=6in, - width=6in]{../contenus/r/code/ABBEYN-callGAL-5.pdf} + width=6in]{../graphiques/ABBEYN-callGAL-5.pdf} \caption{Prix de l'option selon les paramètres estimés avec la méthode de l'équation d'estimation optimale} \label{fig:prix1R1-3} diff --git a/memoire/conclusion.aux b/memoire/conclusion.aux new file mode 100644 index 0000000..3d38646 --- /dev/null +++ b/memoire/conclusion.aux @@ -0,0 +1,80 @@ +\relax +\providecommand\hyper@newdestlabel[2]{} +\@writefile{toc}{\contentsline {chapter}{Conclusion}{113}{section*.52}} +\@setckpt{conclusion}{ +\setcounter{page}{114} +\setcounter{equation}{0} +\setcounter{enumi}{4} 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Barndorff-Nielsen et Resnick(2001)]{barndorff2001levy} +T.E.~Mikosch O.E.E. Barndorff-Nielsen et S.I.E. Resnick. +\newblock \emph{L{\'e}vy Processes: Theory and Applications}. +\newblock Birkh{\"a}user, 2001. +\newblock ISBN 9780817641672. + +\bibitem[Praetz(1972)]{praetz1972distribution} +Peter~D Praetz. +\newblock The distribution of share price changes. +\newblock \emph{Journal Of Business}, pages 49--55, 1972. + +\bibitem[Press(1967)]{press1967compound} +S~James Press. +\newblock A compound events model for security prices. +\newblock \emph{Journal Of Business}, pages 317--335, 1967. + +\bibitem[Sato(1999)]{sato1999levy} +K.~Sato. +\newblock \emph{L{\'e}vy Processes And Infinitely Divisible Distributions}. +\newblock Cambridge Studies in Advanced Mathematics. 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+\newblock From characteristic function to distribution function: A simple + framework for the theory. +\newblock \emph{Econometric Theory}, 7\penalty0 (04):\penalty0 519--529, 1991. + +\bibitem[Spiegel et Liu(1999)]{spiegel1999schaum} +Murray~R Spiegel et John Liu. +\newblock \emph{Schaum's Mathematical Handbook Of Formulas And Tables}, volume + 1000. +\newblock McGraw-Hill, 1999. + +\bibitem[Stuart et Ord(1987)]{stuart1987kendall} +Alan Stuart et J~Keith Ord. +\newblock \emph{Kendall{\rq}s Advanced Theory Of Statistics, Vol. 1}. +\newblock Oxford University Press, New York, 1987. + +\bibitem[Teschl(2004)]{teschl2004topics} +Gerald Teschl. +\newblock Topics in real and functional analysis. +\newblock 2004. + +\bibitem[Walter(1995)]{walterlevy} +Christian Walter. +\newblock "levy-stability under addition and fractal structure of markets: + Implications for the actuaries and emphasized examination of matif national + contract". +\newblock In \emph{Proceedings of the 5th AFIR colloquium}, 1995. + +\bibitem[Wendel(1961)]{wendel1961non} +JG~Wendel. +\newblock The non-absolute convergence of gil-pelaez' inversion integral. +\newblock \emph{The Annals of Mathematical Statistics}, 32\penalty0 + (1):\penalty0 338--339, 1961. + +\bibitem[Wolfowitz(1957)]{wolfowitz1957minimum} +Jacob Wolfowitz. +\newblock The minimum distance method. +\newblock \emph{The Annals Of Mathematical Statistics}, pages 75--88, 1957. + +\bibitem[Wooldridge(2001)]{wooldridge2001econometric} +Jeffrey~M Wooldridge. +\newblock \emph{Econometric Analysis Of Cross Section And Panel Data}. +\newblock MIT press, 2001. + +\end{thebibliography} diff --git a/memoire/gabarit-maitrise.blg b/memoire/gabarit-maitrise.blg new file mode 100644 index 0000000..bd296be --- /dev/null +++ b/memoire/gabarit-maitrise.blg @@ -0,0 +1,66 @@ +This is BibTeX, Version 0.99d (TeX Live 2013/Debian) +Capacity: max_strings=35307, hash_size=35307, hash_prime=30011 +The top-level auxiliary file: gabarit-maitrise.aux +The 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d'ordre de l'\IeC {\'e}chantillon $R_1$\relax }}{97}{table.caption.29} +\contentsline {table}{\numberline {9.2}{\ignorespaces Valeurs relatives aux premiers moments de l'\IeC {\'e}chantillon $R_1$\relax }}{98}{table.caption.30} +\contentsline {table}{\numberline {9.3}{\ignorespaces Test de normalit\IeC {\'e} d'Epps-Pulley pour $R_1$\relax }}{98}{table.caption.32} +\contentsline {table}{\numberline {9.4}{\ignorespaces Param\IeC {\`e}tres $\theta _1$ de la premi\IeC {\`e}re optimisation\relax }}{100}{table.caption.34} +\contentsline {table}{\numberline {9.5}{\ignorespaces Param\IeC {\`e}tres $\theta _1$ de la premi\IeC {\`e}re optimisation\relax }}{102}{table.caption.35} +\contentsline {table}{\numberline {9.6}{\ignorespaces Param\IeC {\`e}tres des donn\IeC {\'e}es $R_1$\relax }}{103}{table.caption.36} +\contentsline {table}{\numberline {9.7}{\ignorespaces Approximation de la densit\IeC {\'e} de $R_1$\relax }}{104}{table.caption.38} +\contentsline {table}{\numberline {9.8}{\ignorespaces 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{9.15}{\ignorespaces Param\IeC {\`e}tres neutres au risque\relax }}{109}{table.caption.48} +\addvspace {10pt} +\addvspace {10pt} +\addvspace {10pt} +\contentsline {table}{\numberline {C.1}{\ignorespaces Prix du titre Abbey National (penny sterling) du 31 juillet au 8 octobre 1991\relax }}{129}{table.caption.60} diff --git a/memoire/gabarit-maitrise.out b/memoire/gabarit-maitrise.out new file mode 100644 index 0000000..fd914bf --- /dev/null +++ b/memoire/gabarit-maitrise.out @@ -0,0 +1,135 @@ +\BOOKMARK [0][-]{section*.2}{R\351sum\351}{}% 1 +\BOOKMARK [0][-]{section*.4}{Abstract}{}% 2 +\BOOKMARK [0][-]{section*.5}{Table des mati\350res}{}% 3 +\BOOKMARK [0][-]{section*.6}{Liste des tableaux}{}% 4 +\BOOKMARK [0][-]{section*.7}{Liste des figures}{}% 5 +\BOOKMARK [0][-]{section*.9}{Remerciements}{}% 6 +\BOOKMARK [0][-]{section*.11}{Introduction}{}% 7 +\BOOKMARK [0][-]{chapter.1}{Les mod\350les de rendements financiers}{}% 8 +\BOOKMARK [1][-]{section.1.1}{L'utilisation de mod\350les en finance}{chapter.1}% 9 +\BOOKMARK [2][-]{subsection.1.1.1}{Diff\351rents types de mod\350les}{section.1.1}% 10 +\BOOKMARK [2][-]{subsection.1.1.2}{Le risque de mod\351lisation}{section.1.1}% 11 +\BOOKMARK [1][-]{section.1.2}{Les rendements financiers}{chapter.1}% 12 +\BOOKMARK [2][-]{subsection.1.2.1}{D\351finitions et notations}{section.1.2}% 13 +\BOOKMARK [2][-]{subsection.1.2.2}{Rendements cumul\351s}{section.1.2}% 14 +\BOOKMARK [2][-]{subsection.1.2.3}{Donn\351es disponibles}{section.1.2}% 15 +\BOOKMARK [1][-]{section.1.3}{Les premiers mod\350les}{chapter.1}% 16 +\BOOKMARK [2][-]{subsection.1.3.1}{Le mod\350le de Bachelier}{section.1.3}% 17 +\BOOKMARK [2][-]{subsection.1.3.2}{Proposition de Mandelbrot}{section.1.3}% 18 +\BOOKMARK [2][-]{subsection.1.3.3}{Le mod\350le de Press}{section.1.3}% 19 +\BOOKMARK [2][-]{subsection.1.3.4}{Le mod\350le de Praetz}{section.1.3}% 20 +\BOOKMARK [1][-]{section.1.4}{Conditions essentielles de Madan et Seneta}{chapter.1}% 21 +\BOOKMARK [0][-]{chapter.2}{La distribution de Laplace asym\351trique g\351n\351ralis\351e}{}% 22 +\BOOKMARK [1][-]{section.2.1}{Le processus de Laplace}{chapter.2}% 23 +\BOOKMARK [2][-]{subsection.2.1.1}{Le processus gamma}{section.2.1}% 24 +\BOOKMARK [2][-]{subsection.2.1.2}{Le processus de Wiener}{section.2.1}% 25 +\BOOKMARK [2][-]{subsection.2.1.3}{Le processus de Laplace est un processus subordonn\351}{section.2.1}% 26 +\BOOKMARK [1][-]{section.2.2}{Distribution de Laplace asym\351trique g\351n\351ralis\351e}{chapter.2}% 27 +\BOOKMARK [2][-]{subsection.2.2.1}{Fonction caract\351ristique}{section.2.2}% 28 +\BOOKMARK [2][-]{subsection.2.2.2}{Invariance d'\351chelle}{section.2.2}% 29 +\BOOKMARK [2][-]{subsection.2.2.3}{Fonctions g\351n\351ratrices}{section.2.2}% 30 +\BOOKMARK [2][-]{subsection.2.2.4}{Moments et r\364le des param\350tres}{section.2.2}% 31 +\BOOKMARK [2][-]{subsection.2.2.5}{Changement d'\351chelle et de localisation}{section.2.2}% 32 +\BOOKMARK [2][-]{subsection.2.2.6}{Repr\351sentation alternative et simulation}{section.2.2}% 33 +\BOOKMARK [2][-]{subsection.2.2.7}{Fonction de Bessel et densit\351}{section.2.2}% 34 +\BOOKMARK [1][-]{section.2.3}{Cas particuliers}{chapter.2}% 35 +\BOOKMARK [2][-]{subsection.2.3.1}{Distribution de Laplace asym\351trique}{section.2.3}% 36 +\BOOKMARK [1][-]{section.2.4}{Relation avec le mod\350le de madan1990variance}{chapter.2}% 37 +\BOOKMARK [0][-]{chapter.3}{Approximation de la densit\351 et de la fonction de r\351partition}{}% 38 +\BOOKMARK [1][-]{section.3.1}{L'approximation de Laplace}{chapter.3}% 39 +\BOOKMARK [1][-]{section.3.2}{L'approximation de Temme}{chapter.3}% 40 +\BOOKMARK [1][-]{section.3.3}{La m\351thode du point de selle}{chapter.3}% 41 +\BOOKMARK [2][-]{subsection.3.3.1}{Approximation de la densit\351}{section.3.3}% 42 +\BOOKMARK [2][-]{subsection.3.3.2}{Unicit\351 du point de selle}{section.3.3}% 43 +\BOOKMARK [2][-]{subsection.3.3.3}{Approximation de la fonction de r\351partition}{section.3.3}% 44 +\BOOKMARK [2][-]{subsection.3.3.4}{Quelques propri\351t\351s des approximations}{section.3.3}% 45 +\BOOKMARK [1][-]{section.3.4}{Application de la m\351thode du point de selle}{chapter.3}% 46 +\BOOKMARK [2][-]{subsection.3.4.1}{Approximation de la densit\351}{section.3.4}% 47 +\BOOKMARK [2][-]{subsection.3.4.2}{Approximation de la fonction de r\351partition}{section.3.4}% 48 +\BOOKMARK [0][-]{chapter.4}{M\351thode des moments g\351n\351ralis\351e}{}% 49 +\BOOKMARK [1][-]{section.4.1}{Introduction}{chapter.4}% 50 +\BOOKMARK [2][-]{subsection.4.1.1}{M\351thode classique des moments}{section.4.1}% 51 +\BOOKMARK [1][-]{section.4.2}{M\351thode des moments g\351n\351ralis\351e}{chapter.4}% 52 +\BOOKMARK [2][-]{subsection.4.2.1}{D\351finition}{section.4.2}% 53 +\BOOKMARK [2][-]{subsection.4.2.2}{Convergence}{section.4.2}% 54 +\BOOKMARK [2][-]{subsection.4.2.3}{Matrice de pond\351ration optimale}{section.4.2}% 55 +\BOOKMARK [2][-]{subsection.4.2.4}{M\351thode des moments g\351n\351ralis\351e it\351rative}{section.4.2}% 56 +\BOOKMARK [2][-]{subsection.4.2.5}{Distribution asymptotique des estimateurs}{section.4.2}% 57 +\BOOKMARK [1][-]{section.4.3}{Estimation sous contraintes}{chapter.4}% 58 +\BOOKMARK [2][-]{subsection.4.3.1}{Distribution asymptotique des estimateurs contraints}{section.4.3}% 59 +\BOOKMARK [1][-]{section.4.4}{Tests d'hypoth\350ses param\351triques}{chapter.4}% 60 +\BOOKMARK [2][-]{subsection.4.4.1}{Test de Wald}{section.4.4}% 61 +\BOOKMARK [2][-]{subsection.4.4.2}{Test du multiplicateur de Lagrange}{section.4.4}% 62 +\BOOKMARK [2][-]{subsection.4.4.3}{Test bas\351 sur la statistique de m\351trique de distance}{section.4.4}% 63 +\BOOKMARK [2][-]{subsection.4.4.4}{En r\351sum\351}{section.4.4}% 64 +\BOOKMARK [0][-]{chapter.5}{M\351thode de l'\351quation d'estimation optimale}{}% 65 +\BOOKMARK [1][-]{section.5.1}{\311quation d'estimation optimale}{chapter.5}% 66 +\BOOKMARK [1][-]{section.5.2}{\311quation d'estimation optimale modifi\351e}{chapter.5}% 67 +\BOOKMARK [0][-]{chapter.6}{Estimation des param\350tres de la distribution de Laplace asym\351trique g\351n\351ralis\351e}{}% 68 +\BOOKMARK [1][-]{section.6.1}{Vecteur de param\350tres initiaux}{chapter.6}% 69 +\BOOKMARK [1][-]{section.6.2}{M\351thode des moments g\351n\351ralis\351e}{chapter.6}% 70 +\BOOKMARK [2][-]{subsection.6.2.1}{Matrice de pond\351ration optimale}{section.6.2}% 71 +\BOOKMARK [2][-]{subsection.6.2.2}{Variance-covariance des param\350tres}{section.6.2}% 72 +\BOOKMARK [2][-]{subsection.6.2.3}{Contraintes lin\351aires}{section.6.2}% 73 +\BOOKMARK [1][-]{section.6.3}{M\351thode de l'\351quation d'estimation optimale}{chapter.6}% 74 +\BOOKMARK [0][-]{chapter.7}{Tests statistiques}{}% 75 +\BOOKMARK [1][-]{section.7.1}{Test de normalit\351}{chapter.7}% 76 +\BOOKMARK [2][-]{subsection.7.1.1}{Test de Shapiro-Wilk}{section.7.1}% 77 +\BOOKMARK [2][-]{subsection.7.1.2}{Test d\220Epps-Pulley}{section.7.1}% 78 +\BOOKMARK [1][-]{section.7.2}{Tests d'ad\351quation}{chapter.7}% 79 +\BOOKMARK [2][-]{subsection.7.2.1}{Test 2 de Pearson}{section.7.2}% 80 +\BOOKMARK [2][-]{subsection.7.2.2}{Test de Kolmogorov-Smirnov}{section.7.2}% 81 +\BOOKMARK [2][-]{subsection.7.2.3}{Test de distance minimale bas\351 sur la fonction g\351n\351ratrice des moments}{section.7.2}% 82 +\BOOKMARK [0][-]{chapter.8}{\311valuation d'options}{}% 83 +\BOOKMARK [1][-]{section.8.1}{D\351finitions}{chapter.8}% 84 +\BOOKMARK [2][-]{subsection.8.1.1}{\311quation martingale}{section.8.1}% 85 +\BOOKMARK [2][-]{subsection.8.1.2}{Param\350tres neutres au risque}{section.8.1}% 86 +\BOOKMARK [1][-]{section.8.2}{Aper\347u du mod\350le de Black-Scholes}{chapter.8}% 87 +\BOOKMARK [1][-]{section.8.3}{M\351thodes d'\351valuation pour options europ\351ennes}{chapter.8}% 88 +\BOOKMARK [2][-]{subsection.8.3.1}{M\351thode de Heston}{section.8.3}% 89 +\BOOKMARK [2][-]{subsection.8.3.2}{M\351thode de Carr et Madan}{section.8.3}% 90 +\BOOKMARK [2][-]{subsection.8.3.3}{Prix d'exercice hors du cours}{section.8.3}% 91 +\BOOKMARK [2][-]{subsection.8.3.4}{Critique de la m\351thode de Carr-Madan}{section.8.3}% 92 +\BOOKMARK [2][-]{subsection.8.3.5}{M\351thode d\220Epps}{section.8.3}% 93 +\BOOKMARK [1][-]{section.8.4}{Particularit\351s}{chapter.8}% 94 +\BOOKMARK [2][-]{subsection.8.4.1}{Option sur actions avec dividendes}{section.8.4}% 95 +\BOOKMARK [2][-]{subsection.8.4.2}{Options sur contrats \340 terme et taux de change}{section.8.4}% 96 +\BOOKMARK [0][-]{chapter.9}{Exemple d'application}{}% 97 +\BOOKMARK [1][-]{section.9.1}{Description des donn\351es}{chapter.9}% 98 +\BOOKMARK [1][-]{section.9.2}{Estimation}{chapter.9}% 99 +\BOOKMARK [1][-]{section.9.3}{Approximation}{chapter.9}% 100 +\BOOKMARK [1][-]{section.9.4}{Graphiques}{chapter.9}% 101 +\BOOKMARK [1][-]{section.9.5}{Tests statistiques}{chapter.9}% 102 +\BOOKMARK [1][-]{section.9.6}{\311valuation d'options}{chapter.9}% 103 +\BOOKMARK [0][-]{section*.52}{Conclusion}{}% 104 +\BOOKMARK [0][-]{appendix.A}{\311l\351ments de th\351orie des probabilit\351s}{}% 105 +\BOOKMARK [1][-]{section.A.1}{D\351finitions de base}{appendix.A}% 106 +\BOOKMARK [1][-]{section.A.2}{Transform\351es d'une variable al\351atoire}{appendix.A}% 107 +\BOOKMARK [2][-]{subsection.A.2.1}{La fonction caract\351ristique}{section.A.2}% 108 +\BOOKMARK [3][-]{section*.53}{Transform\351e de Fourier}{subsection.A.2.1}% 109 +\BOOKMARK [3][-]{section*.54}{D\351finition}{subsection.A.2.1}% 110 +\BOOKMARK [3][-]{section*.55}{Les moments}{subsection.A.2.1}% 111 +\BOOKMARK [2][-]{subsection.A.2.2}{Inversion de la fonction caract\351ristique}{section.A.2}% 112 +\BOOKMARK [3][-]{section*.56}{La densit\351}{subsection.A.2.2}% 113 +\BOOKMARK [3][-]{section*.57}{La fonction de r\351partition}{subsection.A.2.2}% 114 +\BOOKMARK [2][-]{subsection.A.2.3}{La fonction g\351n\351ratrice des moments}{section.A.2}% 115 +\BOOKMARK [2][-]{subsection.A.2.4}{La fonction g\351n\351ratrice des cumulants}{section.A.2}% 116 +\BOOKMARK [2][-]{subsection.A.2.5}{La transform\351e d'Esscher}{section.A.2}% 117 +\BOOKMARK [1][-]{section.A.3}{La transform\351e de Fourier rapide}{appendix.A}% 118 +\BOOKMARK [1][-]{section.A.4}{Processus de L\351vy}{appendix.A}% 119 +\BOOKMARK [2][-]{subsection.A.4.1}{D\351finition et propri\351t\351s}{section.A.4}% 120 +\BOOKMARK [3][-]{section*.58}{Repr\351sentation de L\351vy-Khintchine}{subsection.A.4.1}% 121 +\BOOKMARK [3][-]{section*.59}{Repr\351sentation de L\351vy-It\364}{subsection.A.4.1}% 122 +\BOOKMARK [2][-]{subsection.A.4.2}{Processus subordonn\351}{section.A.4}% 123 +\BOOKMARK [1][-]{section.A.5}{Th\351or\350mes d'int\351gration}{appendix.A}% 124 +\BOOKMARK [2][-]{subsection.A.5.1}{Th\351or\350me de convergence domin\351e de Lebesgue}{section.A.5}% 125 +\BOOKMARK [2][-]{subsection.A.5.2}{Th\351or\350me de Fubini}{section.A.5}% 126 +\BOOKMARK [0][-]{appendix.B}{\311l\351ments de statistique math\351matique}{}% 127 +\BOOKMARK [1][-]{section.B.1}{Loi faible des grands nombres}{appendix.B}% 128 +\BOOKMARK [1][-]{section.B.2}{Th\351or\350me central limite}{appendix.B}% 129 +\BOOKMARK [2][-]{subsection.B.2.1}{Cas univari\351}{section.B.2}% 130 +\BOOKMARK [2][-]{subsection.B.2.2}{Cas multivari\351}{section.B.2}% 131 +\BOOKMARK [1][-]{section.B.3}{M\351thode delta multivari\351e}{appendix.B}% 132 +\BOOKMARK [0][-]{appendix.C}{Donn\351es}{}% 133 +\BOOKMARK [0][-]{section*.62}{Bibliographie}{}% 134 +\BOOKMARK [0][-]{section*.64}{Contrat de partage}{}% 135 diff --git a/memoire/gabarit-maitrise.pdf b/memoire/gabarit-maitrise.pdf index ca21342..1167e9f 100644 Binary files a/memoire/gabarit-maitrise.pdf and b/memoire/gabarit-maitrise.pdf differ diff --git a/memoire/gabarit-maitrise.toc b/memoire/gabarit-maitrise.toc new file mode 100644 index 0000000..68e7b42 --- /dev/null +++ b/memoire/gabarit-maitrise.toc @@ -0,0 +1,137 @@ +\select@language {french} +\select@language {french} +\contentsline {chapter}{R\IeC {\'e}sum\IeC {\'e}}{iii}{section*.2} +\contentsline {chapter}{Abstract}{v}{section*.4} +\contentsline {chapter}{Table des mati{\`e}res}{vii}{section*.5} +\contentsline {chapter}{Liste des tableaux}{xi}{section*.6} +\contentsline {chapter}{Liste des figures}{xiii}{section*.7} +\contentsline {chapter}{Remerciements}{xvii}{section*.9} +\contentsline {chapter}{Introduction}{1}{section*.11} +\contentsline {chapter}{\chapternumberline {1}Les mod\IeC {\`e}les de rendements financiers}{3}{chapter.1} +\contentsline {section}{\numberline {1.1}L'utilisation de mod\IeC {\`e}les en finance}{3}{section.1.1} +\contentsline {subsection}{\numberline {1.1.1}Diff\IeC {\'e}rents types de mod\IeC {\`e}les}{3}{subsection.1.1.1} +\contentsline {subsection}{\numberline {1.1.2}Le risque de mod\IeC {\'e}lisation}{4}{subsection.1.1.2} +\contentsline {section}{\numberline {1.2}Les rendements financiers}{5}{section.1.2} +\contentsline {subsection}{\numberline {1.2.1}D\IeC {\'e}finitions et notations}{5}{subsection.1.2.1} +\contentsline {subsection}{\numberline {1.2.2}Rendements cumul\IeC {\'e}s}{7}{subsection.1.2.2} +\contentsline {subsection}{\numberline {1.2.3}Donn\IeC {\'e}es disponibles}{8}{subsection.1.2.3} +\contentsline {section}{\numberline {1.3}Les premiers mod\IeC {\`e}les}{8}{section.1.3} +\contentsline {subsection}{\numberline {1.3.1}Le mod\IeC {\`e}le de Bachelier}{8}{subsection.1.3.1} +\contentsline {subsection}{\numberline {1.3.2}Proposition de Mandelbrot}{11}{subsection.1.3.2} +\contentsline {subsection}{\numberline {1.3.3}Le mod\IeC {\`e}le de Press}{12}{subsection.1.3.3} +\contentsline {subsection}{\numberline {1.3.4}Le mod\IeC {\`e}le de Praetz}{15}{subsection.1.3.4} +\contentsline {section}{\numberline {1.4}Conditions essentielles de Madan et Seneta}{16}{section.1.4} +\contentsline {chapter}{\chapternumberline {2}La distribution de Laplace asym\IeC {\'e}trique g\IeC {\'e}n\IeC {\'e}ralis\IeC {\'e}e}{19}{chapter.2} +\contentsline {section}{\numberline {2.1}Le processus de Laplace}{19}{section.2.1} +\contentsline {subsection}{\numberline {2.1.1}Le processus gamma}{20}{subsection.2.1.1} +\contentsline {subsection}{\numberline {2.1.2}Le processus de Wiener}{21}{subsection.2.1.2} +\contentsline {subsection}{\numberline {2.1.3}Le processus de Laplace est un processus subordonn\IeC {\'e}}{22}{subsection.2.1.3} +\contentsline {section}{\numberline {2.2}Distribution de Laplace asym\IeC {\'e}trique g\IeC {\'e}n\IeC {\'e}ralis\IeC {\'e}e}{25}{section.2.2} +\contentsline {subsection}{\numberline {2.2.1}Fonction caract\IeC {\'e}ristique}{25}{subsection.2.2.1} +\contentsline {subsection}{\numberline {2.2.2}Invariance d'\IeC {\'e}chelle}{26}{subsection.2.2.2} +\contentsline {subsection}{\numberline {2.2.3}Fonctions g\IeC {\'e}n\IeC {\'e}ratrices}{28}{subsection.2.2.3} +\contentsline {subsection}{\numberline {2.2.4}Moments et r\IeC {\^o}le des param\IeC {\`e}tres}{28}{subsection.2.2.4} +\contentsline {subsection}{\numberline {2.2.5}Changement d'\IeC {\'e}chelle et de localisation}{30}{subsection.2.2.5} +\contentsline {subsection}{\numberline {2.2.6}Repr\IeC {\'e}sentation alternative et simulation}{32}{subsection.2.2.6} +\contentsline {subsection}{\numberline {2.2.7}Fonction de Bessel et densit\IeC {\'e}}{33}{subsection.2.2.7} +\contentsline {section}{\numberline {2.3}Cas particuliers}{35}{section.2.3} +\contentsline {subsection}{\numberline {2.3.1}Distribution de Laplace asym\IeC {\'e}trique}{35}{subsection.2.3.1} +\contentsline {section}{\numberline {2.4}Relation avec le mod\IeC {\`e}le de \cite {madan1990variance}}{37}{section.2.4} +\contentsline {chapter}{\chapternumberline {3}Approximation de la densit\IeC {\'e} et de la fonction de r\IeC {\'e}partition}{39}{chapter.3} +\contentsline {section}{\numberline {3.1}L'approximation de Laplace}{39}{section.3.1} +\contentsline {section}{\numberline {3.2}L'approximation de Temme}{41}{section.3.2} +\contentsline {section}{\numberline {3.3}La m\IeC {\'e}thode du point de selle}{42}{section.3.3} +\contentsline {subsection}{\numberline {3.3.1}Approximation de la densit\IeC {\'e}}{42}{subsection.3.3.1} +\contentsline {subsection}{\numberline {3.3.2}Unicit\IeC {\'e} du point de selle}{44}{subsection.3.3.2} +\contentsline {subsection}{\numberline {3.3.3}Approximation de la fonction de r\IeC {\'e}partition}{44}{subsection.3.3.3} +\contentsline {subsection}{\numberline {3.3.4}Quelques propri\IeC {\'e}t\IeC {\'e}s des approximations}{45}{subsection.3.3.4} +\contentsline {section}{\numberline {3.4}Application de la m\IeC {\'e}thode du point de selle}{46}{section.3.4} +\contentsline {subsection}{\numberline {3.4.1}Approximation de la densit\IeC {\'e}}{46}{subsection.3.4.1} +\contentsline {subsection}{\numberline {3.4.2}Approximation de la fonction de r\IeC {\'e}partition}{47}{subsection.3.4.2} +\contentsline {chapter}{\chapternumberline {4}M\IeC {\'e}thode des moments g\IeC {\'e}n\IeC {\'e}ralis\IeC {\'e}e}{49}{chapter.4} +\contentsline {section}{\numberline {4.1}Introduction}{49}{section.4.1} +\contentsline {subsection}{\numberline {4.1.1}M\IeC {\'e}thode classique des moments}{50}{subsection.4.1.1} +\contentsline {section}{\numberline {4.2}M\IeC {\'e}thode des moments g\IeC {\'e}n\IeC {\'e}ralis\IeC {\'e}e}{50}{section.4.2} +\contentsline {subsection}{\numberline {4.2.1}D\IeC {\'e}finition}{51}{subsection.4.2.1} +\contentsline {subsection}{\numberline {4.2.2}Convergence}{52}{subsection.4.2.2} +\contentsline {subsection}{\numberline {4.2.3}Matrice de pond\IeC {\'e}ration optimale}{53}{subsection.4.2.3} +\contentsline {subsection}{\numberline {4.2.4}M\IeC {\'e}thode des moments g\IeC {\'e}n\IeC {\'e}ralis\IeC {\'e}e it\IeC {\'e}rative}{55}{subsection.4.2.4} +\contentsline {subsection}{\numberline {4.2.5}Distribution asymptotique des estimateurs}{55}{subsection.4.2.5} +\contentsline {section}{\numberline {4.3}Estimation sous contraintes}{58}{section.4.3} +\contentsline {subsection}{\numberline {4.3.1}Distribution asymptotique des estimateurs contraints}{59}{subsection.4.3.1} +\contentsline {section}{\numberline {4.4}Tests d'hypoth\IeC {\`e}ses param\IeC {\'e}triques}{61}{section.4.4} +\contentsline {subsection}{\numberline {4.4.1}Test de Wald}{61}{subsection.4.4.1} +\contentsline {subsection}{\numberline {4.4.2}Test du multiplicateur de Lagrange}{62}{subsection.4.4.2} +\contentsline {subsection}{\numberline {4.4.3}Test bas\IeC {\'e} sur la statistique de m\IeC {\'e}trique de distance}{63}{subsection.4.4.3} +\contentsline {subsection}{\numberline {4.4.4}En r\IeC {\'e}sum\IeC {\'e}}{63}{subsection.4.4.4} +\contentsline {chapter}{\chapternumberline {5}M\IeC {\'e}thode de l'\IeC {\'e}quation d'estimation optimale}{65}{chapter.5} +\contentsline {section}{\numberline {5.1}\IeC {\'E}quation d'estimation optimale}{67}{section.5.1} +\contentsline {section}{\numberline {5.2}\IeC {\'E}quation d'estimation optimale modifi\IeC {\'e}e}{70}{section.5.2} +\contentsline {chapter}{\chapternumberline {6}Estimation des param\IeC {\`e}tres de la distribution de Laplace asym\IeC {\'e}trique g\IeC {\'e}n\IeC {\'e}ralis\IeC {\'e}e}{73}{chapter.6} +\contentsline {section}{\numberline {6.1}Vecteur de param\IeC {\`e}tres initiaux}{73}{section.6.1} +\contentsline {section}{\numberline {6.2}M\IeC {\'e}thode des moments g\IeC {\'e}n\IeC {\'e}ralis\IeC {\'e}e}{74}{section.6.2} +\contentsline {subsection}{\numberline {6.2.1}Matrice de pond\IeC {\'e}ration optimale}{75}{subsection.6.2.1} +\contentsline {subsection}{\numberline {6.2.2}Variance-covariance des param\IeC {\`e}tres}{76}{subsection.6.2.2} +\contentsline {subsection}{\numberline {6.2.3}Contraintes lin\IeC {\'e}aires}{77}{subsection.6.2.3} +\contentsline {section}{\numberline {6.3}M\IeC {\'e}thode de l'\IeC {\'e}quation d'estimation optimale}{78}{section.6.3} +\contentsline {chapter}{\chapternumberline {7}Tests statistiques}{81}{chapter.7} +\contentsline {section}{\numberline {7.1}Test de normalit\IeC {\'e}}{81}{section.7.1} +\contentsline {subsection}{\numberline {7.1.1}Test de Shapiro-Wilk}{81}{subsection.7.1.1} +\contentsline {subsection}{\numberline {7.1.2}Test d\IeC {\textquoteright }Epps-Pulley}{82}{subsection.7.1.2} +\contentsline {section}{\numberline {7.2}Tests d'ad\IeC {\'e}quation}{82}{section.7.2} +\contentsline {subsection}{\numberline {7.2.1}Test $\chi ^2$ de Pearson}{83}{subsection.7.2.1} +\contentsline {subsection}{\numberline {7.2.2}Test de Kolmogorov-Smirnov}{84}{subsection.7.2.2} +\contentsline {subsection}{\numberline {7.2.3}Test de distance minimale bas\IeC {\'e} sur la fonction g\IeC {\'e}n\IeC {\'e}ratrice des moments}{85}{subsection.7.2.3} +\contentsline {chapter}{\chapternumberline {8}\IeC {\'E}valuation d'options}{87}{chapter.8} +\contentsline {section}{\numberline {8.1}D\IeC {\'e}finitions}{87}{section.8.1} +\contentsline {subsection}{\numberline {8.1.1}\IeC {\'E}quation martingale}{88}{subsection.8.1.1} +\contentsline {subsection}{\numberline {8.1.2}Param\IeC {\`e}tres neutres au risque}{89}{subsection.8.1.2} +\contentsline {section}{\numberline {8.2}Aper\IeC {\c c}u du mod\IeC {\`e}le de Black-Scholes}{90}{section.8.2} +\contentsline {section}{\numberline {8.3}M\IeC {\'e}thodes d'\IeC {\'e}valuation pour options europ\IeC {\'e}ennes}{90}{section.8.3} +\contentsline {subsection}{\numberline {8.3.1}M\IeC {\'e}thode de Heston}{91}{subsection.8.3.1} +\contentsline {subsection}{\numberline {8.3.2}M\IeC {\'e}thode de Carr et Madan}{91}{subsection.8.3.2} +\contentsline {subsection}{\numberline {8.3.3}Prix d'exercice hors du cours}{93}{subsection.8.3.3} +\contentsline {subsection}{\numberline {8.3.4}Critique de la m\IeC {\'e}thode de Carr-Madan}{93}{subsection.8.3.4} +\contentsline {subsection}{\numberline {8.3.5}M\IeC {\'e}thode d\IeC {\textquoteright }Epps}{93}{subsection.8.3.5} +\contentsline {section}{\numberline {8.4}Particularit\IeC {\'e}s}{95}{section.8.4} +\contentsline {subsection}{\numberline {8.4.1}Option sur actions avec dividendes}{95}{subsection.8.4.1} +\contentsline {subsection}{\numberline {8.4.2}Options sur contrats \IeC {\`a} terme et taux de change}{95}{subsection.8.4.2} +\contentsline {chapter}{\chapternumberline {9}Exemple d'application}{97}{chapter.9} +\contentsline {section}{\numberline {9.1}Description des donn\IeC {\'e}es}{97}{section.9.1} +\contentsline {section}{\numberline {9.2}Estimation}{99}{section.9.2} +\contentsline {section}{\numberline {9.3}Approximation}{104}{section.9.3} +\contentsline {section}{\numberline {9.4}Graphiques}{105}{section.9.4} +\contentsline {section}{\numberline {9.5}Tests statistiques}{108}{section.9.5} +\contentsline {section}{\numberline {9.6}\IeC {\'E}valuation d'options}{109}{section.9.6} +\contentsline {chapter}{Conclusion}{113}{section*.52} +\contentsline {appendix}{\chapternumberline {A}\IeC {\'E}l\IeC {\'e}ments de th\IeC {\'e}orie des probabilit\IeC {\'e}s}{115}{appendix.A} +\contentsline {section}{\numberline {A.1}D\IeC {\'e}finitions de base}{115}{section.A.1} +\contentsline {section}{\numberline {A.2}Transform\IeC {\'e}es d'une variable al\IeC {\'e}atoire}{116}{section.A.2} +\contentsline {subsection}{\numberline {A.2.1}La fonction caract\IeC {\'e}ristique}{116}{subsection.A.2.1} +\contentsline {subsubsection}{Transform\IeC {\'e}e de Fourier}{116}{section*.53} +\contentsline {subsubsection}{D\IeC {\'e}finition}{116}{section*.54} +\contentsline {subsubsection}{Les moments}{117}{section*.55} +\contentsline {subsection}{\numberline {A.2.2}Inversion de la fonction caract\IeC {\'e}ristique}{117}{subsection.A.2.2} +\contentsline {subsubsection}{La densit\IeC {\'e}}{117}{section*.56} +\contentsline {subsubsection}{La fonction de r\IeC {\'e}partition}{117}{section*.57} +\contentsline {subsection}{\numberline {A.2.3}La fonction g\IeC {\'e}n\IeC {\'e}ratrice des moments}{118}{subsection.A.2.3} +\contentsline {subsection}{\numberline {A.2.4}La fonction g\IeC {\'e}n\IeC {\'e}ratrice des cumulants}{119}{subsection.A.2.4} +\contentsline {subsection}{\numberline {A.2.5}La transform\IeC {\'e}e d'Esscher}{120}{subsection.A.2.5} +\contentsline {section}{\numberline {A.3}La transform\IeC {\'e}e de Fourier rapide}{120}{section.A.3} +\contentsline {section}{\numberline {A.4}Processus de L\IeC {\'e}vy}{121}{section.A.4} +\contentsline {subsection}{\numberline {A.4.1}D\IeC {\'e}finition et propri\IeC {\'e}t\IeC {\'e}s}{121}{subsection.A.4.1} +\contentsline {subsubsection}{Repr\IeC {\'e}sentation de L\IeC {\'e}vy-Khintchine}{122}{section*.58} +\contentsline {subsubsection}{Repr\IeC {\'e}sentation de L\IeC {\'e}vy-It\IeC {\^o}}{122}{section*.59} +\contentsline {subsection}{\numberline {A.4.2}Processus subordonn\IeC {\'e}}{123}{subsection.A.4.2} +\contentsline {section}{\numberline {A.5}Th\IeC {\'e}or\IeC {\`e}mes d'int\IeC {\'e}gration}{123}{section.A.5} +\contentsline {subsection}{\numberline {A.5.1}Th\IeC {\'e}or\IeC {\`e}me de convergence domin\IeC {\'e}e de Lebesgue}{124}{subsection.A.5.1} +\contentsline {subsection}{\numberline {A.5.2}Th\IeC {\'e}or\IeC {\`e}me de Fubini}{124}{subsection.A.5.2} +\contentsline {appendix}{\chapternumberline {B}\IeC {\'E}l\IeC {\'e}ments de statistique math\IeC {\'e}matique}{125}{appendix.B} +\contentsline {section}{\numberline {B.1}Loi faible des grands nombres}{125}{section.B.1} +\contentsline {section}{\numberline {B.2}Th\IeC {\'e}or\IeC {\`e}me central limite}{125}{section.B.2} +\contentsline {subsection}{\numberline {B.2.1}Cas univari\IeC {\'e}}{126}{subsection.B.2.1} +\contentsline {subsection}{\numberline {B.2.2}Cas multivari\IeC {\'e}}{126}{subsection.B.2.2} +\contentsline {section}{\numberline {B.3}M\IeC {\'e}thode delta multivari\IeC {\'e}e}{127}{section.B.3} +\contentsline {appendix}{\chapternumberline {C}Donn\IeC {\'e}es}{129}{appendix.C} +\contentsline {chapter}{Bibliographie}{131}{section*.62} +\contentsline {chapter}{Contrat de partage}{137}{section*.64} diff --git a/memoire/introduction.aux b/memoire/introduction.aux new file mode 100644 index 0000000..9835c49 --- /dev/null +++ b/memoire/introduction.aux @@ -0,0 +1,80 @@ +\relax 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A.}, - title = {A goodness-of-fit test of simple hypotheses based on - the empirical characteristic function}, - volume = 67, - number = 1, - pages = {238-240}, - year = 1980, - doi = {10.1093/biomet/67.1.238}, - abstract = {SUMMARY The empirical characteristic function φn(t) - and its asymptotic distribution are utilized to find - a chi-squared goodness-of-fit test for simple null - hypotheses. In addition the optimum number and - location of points t at which φn(t) has to be - evaluated is investigated for specified alternative - hypotheses.}, - URL = - {http://biomet.oxfordjournals.org/content/67/1/238.abstract}, - eprint = - {http://biomet.oxfordjournals.org/content/67/1/238.full.pdf+html}, - journal = {Biometrika} +@Article{KOUTROUVELIS01011980, + Author = "I. A. Koutrouvelis", + Doi = "10.1093/biomet/67.1.238", + Journal = "Biometrika", + Number = 1, + Pages = "238--240", + Title = "{A Goodness-Of-Fit Test Of Simple Hypotheses Based + On The Empirical Characteristic Function}", + Volume = 67, + Year = 1980 } @Manual{RpackageVarianceGamma, - title = {VarianceGamma: The Variance Gamma Distribution}, - author = {David Scott and Christine Yang Dong}, - year = 2012, - note = {R package version 0.3-1}, - url = {http://CRAN.R-project.org/package=VarianceGamma}, + Author = "David Scott and Christine Yang Dong", + Note = "R package version 0.3-1", + Title = "{Variancegamma: The Variance Gamma Distribution}", + Url = "http://CRAN.R-project.org/package=VarianceGamma", + Year = 2012 } @Manual{Rsoftware, - title = {R: A Language and Environment for Statistical - Computing}, - author = {{R Core Team}}, - organization = {R Foundation for Statistical Computing}, - address = {Vienna, Austria}, - year = 2012, - note = {{ISBN} 3-900051-07-0}, - url = {http://www.R-project.org/}, + Address = "Vienna, Austria", + Author = "{R Core Team}", + Isbn = "3-900051-07-0", + Organization = "R Foundation for Statistical Computing", + Title = "{R: A Language and Environment for Statistical + Computing}", + Url = "http://www.R-project.org", + Year = 2012 } -@ARTICLE{Singer:2009, - AUTHOR = {Singer, S. and Nelder, J. }, - TITLE = {Nelder-Mead algorithm}, - YEAR = 2009, - JOURNAL = {Scholarpedia}, - VOLUME = 4, - NUMBER = 7, - PAGES = 2928, - URL = {http://dx.doi.org/10.4249/scholarpedia.2928} +@Article{Singer:2009, + Author = "Sa\v{s}a Singer and John Nelder", + Doi = "10.4249/scholarpedia.2928", + Journal = "Scholarpedia", + Number = 7, + Pages = 2928, + Title = "{Nelder-Mead Algorithm}", + Volume = 4, + Year = 2009 } -@book{abramowitz1965handbook, - title = {Handbook of mathematical functions: with formulas, - graphs, and mathematical tables}, - author = {Abramowitz, Milton and Stegun, Irene A}, - volume = 55, - year = 1965, - publisher = {Dover publications} +@Book{abramowitz1965handbook, + Author = "Milton Abramowitz and Irene A. Stegun", + Publisher = "Dover Publications", + Title = "Handbook Of Mathematical Functions: With Formulas, + Graphs, And Mathematical Tables", + Volume = 55, + Year = 1965 } -@article{applebaum2004levy, - title = {L{\'e}vy processes: From probability to finance and - quantum groups}, - author = {Applebaum, David}, - journal = {Notices of the AMS}, - volume = 51, - number = 11, - pages = {1336--1347}, - year = 2004 +@Article{applebaum2004levy, + Author = "David Applebaum", + Journal = "Notices Of The American Mathematical Society", + Number = 11, + Pages = "1336--1347", + Title = "Lévy Processes: From Probability To Finance And + Quantum Groups", + Volume = 51, + Year = 2004 } -@book{bachelier1900theorie, - title = {Th{\'e}orie de la sp{\'e}culation}, - author = {Bachelier, Louis}, - year = 1900, - publisher = {Gauthier-Villars} +@Book{bachelier1900theorie, + Author = "Louis Bachelier", + Publisher = "Gauthier-Villars", + Title = "Th{\'e}orie De La Sp{\'e}culation", + Year = 1900 } -@book{barndorff2001levy, - title = {L{\'e}vy Processes: Theory and Applications}, - author = {Barndorff-Nielsen, O.E.E. and Mikosch, T.E. and - Resnick, S.I.E.}, - isbn = 9780817641672, - lccn = {lc00068064}, - url = {http://books.google.ca/books?id=ExpTdTauXMwC}, - year = 2001, - publisher = {Birkhäuser} +@Book{barndorff2001levy, + Author = "O.E.E. Barndorff-Nielsen, T.E. Mikosch and + S.I.E. Resnick", + Isbn = 9780817641672, + Publisher = "Birkh{\"a}user", + Title = "L{\'e}vy Processes: Theory and Applications", + Year = 2001 } -@article{berkson1980minimum, - title = {Minimum chi-square, not maximum likelihood!}, - author = {Berkson, Joseph}, - journal = {The Annals of Statistics}, - pages = {457--487}, - year = 1980, - publisher = {JSTOR} +@Article{berkson1980minimum, + Author = "Joseph Berkson", + Journal = "The Annals of Statistics", + Pages = "457--487", + Publisher = "JSTOR", + Title = "Minimum Chi-Square, Not Maximum Likelihood!", + Year = 1980 } -@book{bingham2004risk, - title = {Risk-neutral valuation: Pricing and hedging of - financial derivatives}, - author = {Bingham, Nicholas H and Kiesel, R{\"u}diger}, - year = 2004, - publisher = {Springer} +@Book{bingham2004risk, + Author = "Nicholas H. Bingham and R{\"u}diger Kiesel", + Publisher = "Springer", + Title = "Risk-Neutral Valuation: Pricing And Hedging Of + Financial Derivatives", + Year = 2004 } -@article{black1973pricing, - title = {The pricing of options and corporate liabilities}, - author = {Black, Fischer and Scholes, Myron}, - journal = {The journal of political economy}, - pages = {637--654}, - year = 1973, - publisher = {JSTOR} +@Article{black1973pricing, + Author = "Fischer Black and Myron Scholes", + Journal = "The Journal Of Political Economy", + Pages = "637--654", + Publisher = "JSTOR", + Title = "The Pricing Of Options And Corporate Liabilities", + Year = 1973 } -@article{black1976pricing, - title = {The pricing of commodity contracts}, - author = {Black, Fischer}, - journal = {Journal of financial economics}, - volume = 3, - number = 1, - pages = {167--179}, - year = 1976, - publisher = {Elsevier} +@Article{black1976pricing, + Author = "Fischer Black", + Journal = "Journal Of Financial Economics", + Number = 1, + Pages = "167--179", + Publisher = "Elsevier", + Title = "The Pricing Of Commodity Contracts", + Volume = 3, + Year = 1976 } -@article{buckle1995bayesian, - title = {Bayesian inference for stable distributions}, - author = {Buckle, DJ}, - journal = {Journal of the American Statistical Association}, - volume = 90, - number = 430, - pages = {605--613}, +@Article{buckle1995bayesian, + Author = "D. J. Buckle", + Journal = "Journal of the American Statistical Association", + Number = 430, + Pages = "605--613", + Publisher = "Taylor \& Francis Group", + Title = "Bayesian Inference For Stable Distributions", + Volume = 90, + Year = 1995 +} + +@Book{butler2007saddlepoint, + Author = "Ronald W. Butler", + Publisher = "Cambridge University Press", + Title = "Saddlepoint Approximations With Applications", + Volume = 22, + Year = 2007 +} + +@Article{carr1999option, + Author = "Peter Carr and Dilip Madan", + Journal = "Journal Of Computational Finance", + Number = 4, + Pages = "61--73", + Title = "Option Valuation Using The Fast Fourier Transform", + Volume = 2, + Year = 1999 +} + +@Article{crowder1986consistency, + Author = "Martin Crowder", + Journal = "Econometric Theory", + Pages = "305--330", + Publisher = "JSTOR", + Title = "On Consistency And Inconsistency Of Estimating + Equations", + Year = 1986 +} + +@Article{crowder1987linear, + Author = "Martin Crowder", + Journal = "Biometrika", + Number = 3, + Pages = "591--597", + Publisher = "Biometrika Trust", + Title = "On Linear And Quadratic Estimating Functions", + Volume = 74, + Year = 1987 +} + +@Article{daniels1954saddlepoint, + Author = "Henry E Daniels", + Journal = "The Annals of Mathematical Statistics", + Pages = "631--650", + Publisher = "JSTOR", + Title = "Saddlepoint Approximations In Statistics", + Year = 1954 +} + +@Article{daniels1987tail, + Author = "Henry E Daniels", + Journal = "International Statistical Review/Revue + Internationale de Statistique", + Pages = "37--48", + Publisher = "JSTOR", + Title = "Tail Probability Approximations", + Year = 1987 +} + +@Techreport{derman1996modelrisk, + Author = "Emanuel Derman", + Institution = "Goldman Sachs", + Title = "Model Risk", + Year = 1996 +} + +@Book{dodge2004statistique, + Author = "Yadolah Dodge", + Publisher = "Springer Verlag France", + Title = "Statistique: Dictionnaire Encyclop{\'e}dique", + Year = 2004 +} + +@Article{epps1983test, + Author = "Thomas W Epps and Lawrence B Pulley", + Journal = "Biometrika", + Number = 3, + Pages = "723--726", + Publisher = "Biometrika Trust", + Title = "A Test For Normality Based On The Empirical + Characteristic Function", + Volume = 70, + Year = 1983 +} + +@Book{epps2007pricing, + Author = "Thomas W Epps", + Publisher = "World Scientific Publishing Company Incorporated", + Title = "Pricing Derivative Securities", + Year = 2007 +} + +@Book{everitt2006cambridge, + Author = "Brian Everitt and Anders Skrondal", + Publisher = "Cambridge University Press Cambridge", + Title = "The Cambridge Dictionary Of Statistics", + Volume = 4, + Year = 2006 +} + +@Article{feuerverger1981efficiency, + Author = "Andrey Feuerverger and Philip McDunnough", + Journal = "Journal Of The Royal Statistical Society. Series B + (methodological)", + Pages = "20--27", + Publisher = "JSTOR", + Title = "On The Efficiency Of Empirical Characteristic + Function Procedures", + Year = 1981 +} + +@Article{fox1986large, + Author = "Robert Fox and Murad S Taqqu", + Journal = "The Annals of Statistics", + Number = 2, + Pages = "517--532", + Publisher = "Institute of Mathematical Statistics", + Title = "Large-Sample Properties Of Parameter Estimates For + Strongly Dependent Stationary Gaussian Time Series", + Volume = 14, + Year = 1986 +} + +@Article{gil1951note, + Author = "J Gil-Pelaez", + Journal = "Biometrika", + Number = "3-4", + Pages = "481--482", + Publisher = "Biometrika Trust", + Title = "Note On The Inversion Theorem", + Volume = 38, + Year = 1951 +} + +@Book{gourieroux1989statistique, + Author = "Christian Gourieroux and Alain Monfort", + Publisher = "Economica", + Title = "Statistique Et Mod{\`e}les {\'E}conom{\'e}triques: + Notions G{\'e}n{\'e}rales, Estimation, + Pr{\'e}vision, Algorithmes", + Volume = 1, + Year = 1989 +} + +@Book{hall2005generalized, + Author = "Alastair R Hall", + Publisher = "Oxford University Press Oxford", + Title = "Generalized Method Of Moments", + Year = 2005 +} + +@Book{hamilton1994time, + Author = "James Douglas Hamilton", + Publisher = "Cambridge University Press", + Title = "Time Series Analysis", + Volume = 2, + Year = 1994 +} + +@Article{hansen1982large, + Author = "Lars Peter Hansen", + Journal = "Econometrica: Journal Of The Econometric Society", + Pages = "1029--1054", + Publisher = "JSTOR", + Title = "Large Sample Properties Of Generalized Method Of + Moments Estimators", + Year = 1982 +} + +@Article{henze1990approximation, + Author = "N Henze", + Journal = "Metrika", + Number = 1, + Pages = "7--18", + Publisher = "Springer", + Title = "An Approximation To The Limit Distribution Of The + Epps-Pulley Test Statistic For Normality", + Volume = 37, + Year = 1990 +} + +@Article{heston1993closed, + Author = "Steven L Heston", + Journal = "Review Of Financial Studies", + Number = 2, + Pages = "327--343", + Publisher = "Soc Financial Studies", + Title = "A Closed-Form Solution For Options With Stochastic + Volatility With Applications To Bond And Currency + Options", + Volume = 6, + Year = 1993 +} + +@Article{hinkley1977estimation, + Author = "David V Hinkley and Nagesh S Revankar", + Journal = "Journal Of Econometrics", + Number = 1, + Pages = "1--11", + Publisher = "Elsevier", + Title = "Estimation Of The Pareto Law From Underreported + Data: A Further Analysis", + Volume = 5, + Year = 1977 +} + +@Book{hogg1978introduction, + Author = "R.V. Hogg and A.T. Craig", + Isbn = 9780029789902, + Publisher = "Macmillan", + Title = "Introduction To Mathematical Statistics", + Year = 1978 +} + +@Book{hull1999options, + Author = "John C Hull", + Publisher = "Pearson Education India", + Title = "Options, Futures, And Other Derivatives", + Year = 1999 +} + +@Article{itkin2005pricing, + Author = "Andrey Itkin", + Journal = "arXiv preprint physics/0503137", + Title = "Pricing Options With VG Model Using FFT", + Year = 2005 +} + +@Book{kotz2001laplace, + Author = "S. Kotz and T.J. Kozubowski and K. Podg{\'o}rski", + Isbn = 9780817641665, + Publisher = "Birkh{\"a}user", + Series = "Progress in Mathematics Series", + Title = "The Laplace Distribution And Generalizations: A + Revisit With Applications To Communications, + Exonomics, Engineering, And Finance", + Year = 2001 +} + +@Article{kozubowski1999class, + Author = "Tomasz J Kozubowski and Krzysztof Podg{\'o}rski", + Journal = "Actuarial Research Clearing House", + Pages = "113--134", + Publisher = "Citeseer", + Title = "A Class Of Asymmetric Distributions", + Volume = 1, + Year = 1999 +} + +@Article{kozubowski2001asymmetric, + Author = "Tomasz J Kozubowski and Krzysztof Podg{\'o}rski", + Journal = "Mathematical And Computer Modeling", + Number = 9, + Pages = "1003--1021", + Publisher = "Elsevier", + Title = "Asymmetric Laplace Laws And Modeling Financial Data", + Volume = 34, + Year = 2001 +} + +@Book{kyprianou2007introductory, + Author = "Andreas E Kyprianou", + Publisher = "Springer", + Title = "Introductory Lectures On Fluctuations Of L{\'e}Vy + Processes With Applications", + Year = 2007 +} + +@Article{lugannani1980saddle, + Author = "Robert Lugannani and Stephen Rice", + Journal = "Advances In Applied Probability", + Pages = "475--490", + Publisher = "JSTOR", + Title = "Saddle Point Approximation For The Distribution Of + The Sum Of Independent Random Variables", + Year = 1980 +} + +@Book{lukacs1960characteristic, + Author = "Eugene Lukacs", + Publisher = "Griffin London", + Title = "Characteristic Functions", + Volume = 4, + Year = 1960 +} + +@Article{luong1987minimum, + Author = "Andrew Luong and Mary E. Thompson", + Journal = "Canadian Journal of Statistics", + Number = 3, + Pages = "239--251", + Publisher = "Wiley Online Library", + Title = "Minimum-Distance Methods Based On Quadratic + Distances For Transforms", + Volume = 15, + Year = 1987 +} + +@Article{madan1990variance, + Author = "Dilip B Madan and Eugene Seneta", + Journal = "Journal Of Business", + Pages = "511--524", + Publisher = "JSTOR", + Title = "The Variance Gamma Model For Share Market Returns", + Year = 1990 +} + +@Article{madan1998variance, + Author = "Dilip B Madan, Peter P Carr and Eric C Chang", + Journal = "European Finance Review", + Number = 1, + Pages = "79--105", + Publisher = "Kluwer Academic Publishers", + Title = "The Variance Gamma Process And Option Pricing", + Volume = 2, + Year = 1998 +} + +@Article{mandelbrot1963variation, + Author = "Benoit Mandelbrot", + Journal = "Journal Of Business", + Pages = "394--419", + Publisher = "University of Chicago Press", + Title = "The Variation Of Certain Speculative Prices", + Year = 1963 +} + +@Article{merton1976option, + Author = "Robert C Merton", + Journal = "Journal Of Financial Economics", + Number = 1, + Pages = "125--144", + Publisher = "Elsevier", + Title = "Option Pricing When Underlying Stock Returns Are + Discontinuous", + Volume = 3, + Year = 1976 +} + +@Article{mitchell1916critique, + Author = "Wesley C Mitchell", + Journal = "The Journal Of Political Economy", + Pages = "625--693", + Publisher = "JSTOR", + Title = "A critique of index numbers of the prices of stocks", + Year = 1916 +} + +@Book{musiela2005martingale, + Author = "Marek Musiela and Marek Rutkowski", + Publisher = "Springer", + Title = "Martingale Methods In Financial Modelling", + Volume = 36, + Year = 2005 +} + +@Article{newey1987hypothesis, + Author = "Whitney K Newey and Kenneth D West", + Journal = "International Economic Review", + Number = 3, + Pages = "777--787", + Publisher = "JSTOR", + Title = "Hypothesis Testing With Efficient Method Of Moments + Estimation", + Volume = 28, + Year = 1987 +} + +@Article{newey1994large, + Author = "Whitney K Newey and Daniel McFadden", + Journal = "Handbook Of Econometrics", + Pages = "2111--2245", + Publisher = "Elsevier", + Title = "Large Sample Estimation And Hypothesis Testing", + Volume = 4, + Year = 1994 +} + +@Article{praetz1972distribution, + Author = "Peter D Praetz", + Journal = "Journal Of Business", + Pages = "49--55", + Publisher = "JSTOR", + Title = "The Distribution Of Share Price Changes", + Year = 1972 +} + +@Article{press1967compound, + Author = "S James Press", + Journal = "Journal Of Business", + Pages = "317--335", + Publisher = "JSTOR", + Title = "A Compound Events Model For Security Prices", + Year = 1967 +} + +@Article{randal2004non, + Author = "John A Randal and Peter J Thomson and Martin T + Lally", + Journal = "Quantitative Finance", + Number = 4, + Pages = "427--440", + Publisher = "Taylor \& Francis", + Title = "Non-Parametric Estimation Of Historical Volatility", + Volume = 4, + Year = 2004 +} + +@Book{sato1999levy, + Author = "K. Sato", + Isbn = 9780521553025, + Publisher = "Cambridge University Press", + Series = "Cambridge Studies in Advanced Mathematics", + Title = "L{\'e}vy Processes And Infinitely Divisible + Distributions", + Year = 1999 +} + +@Book{schoutens2003levy, + Author = "Wim Schoutens", + Publisher = "Wiley", + Title = "L{\'e}vy Processes In Finance", + Year = 2003 +} + +@Article{seneta2004fitting, + Author = "Eugene Seneta", + Journal = "Journal Of Applied Probability", + Pages = "177--187", + Publisher = "JSTOR", + Title = "Fitting The Variance-Gamma Model To Financial Data", + Year = 2004 +} + +@Article{shapiro1965analysis, + Author = "Samuel Sanford Shapiro and Martin B Wilk", + Journal = "Biometrika", + Number = "3/4", + Pages = "591--611", + Publisher = "JSTOR", + Title = "An Analysis Of Variance Test For Normality (complete + Samples)", + Volume = 52, + Year = 1965 +} + +@Article{shephard1991characteristic, + Author = "Neil G Shephard", + Journal = "Econometric Theory", + Number = 04, + Pages = "519--529", + Publisher = "Cambridge Univ Press", + Title = "From Characteristic Function To Distribution + Function: A Simple Framework For The Theory", + Volume = 7, + Year = 1991 +} + +@Book{spiegel1999schaum, + Author = "Murray R Spiegel and John Liu", + Publisher = "McGraw-Hill", + Title = "Schaum's Mathematical Handbook Of Formulas And + Tables", + Volume = 1000, + Year = 1999 +} + +@Book{stuart1987kendall, + Author = "Alan Stuart and J Keith Ord", + Publisher = "Oxford University Press, New York", + Title = "Kendall{\rq}s Advanced Theory Of Statistics, Vol. 1", + Year = 1987 +} + +@Phdthesis{torczon1989multi, + Author = "Virginia Joanne Torczon", + Title = "Multi-directional search: a direct search algorithm + for parallel machines", + Year = 1989 +} + +@Article{wang2003evaluating, + Author = "Jingbo Wang, Wai Wan Tsang and George Marsaglia", + Journal = "Journal of Statistical Software", + Number = 18, + Pages = "1--4", + Publisher = "American Statistical Association", + Title = "Evaluating Kolmogorov's Distribution", + Volume = 8, + Year = 2003 +} + +@Article{wendel1961non, + Author = "JG Wendel", + Journal = "The Annals of Mathematical Statistics", + Number = 1, + Pages = "338--339", + Publisher = "Institute of Mathematical Statistics", + Title = "The Non-Absolute Convergence Of Gil-Pelaez' inversion + Integral", + Volume = 32, + Year = 1961 +} + +@Unpublished{teschl2004topics, + Author = "Gerald Teschl", + Title = "Topics In Real And Functional Analysis", + Year = 2004 +} + +@Article{wolfowitz1957minimum, + Author = "Jacob Wolfowitz", + Journal = "The Annals Of Mathematical Statistics", + Pages = "75--88", + Publisher = "JSTOR", + Title = "The Minimum Distance Method", + Year = 1957 +} + +@Book{wooldridge2001econometric, + Author = "Jeffrey M Wooldridge", + Publisher = "MIT press", + Title = "Econometric Analysis Of Cross Section And Panel + Data", + Year = 2001 +} + +@Article{fama1993common, + Author = "Eugene F Fama and Kenneth R French", + Journal = "Journal Of Financial Economics", + Number = 1, + Pages = "3--56", + Publisher = "Elsevier", + Title = "Common Risk Factors In The Returns On Stocks And + Bonds", + Volume = 33, + Year = 1993 +} + +@InProceedings{walterlevy, + author = {Christian Walter}, + title = {"Levy-Stability Under Addition And Fractal Structure + Of Markets: Implications For The Actuaries And + Emphasized Examination Of Matif National Contract"}, year = 1995, - publisher = {Taylor \& Francis Group} + booktitle = {Proceedings of the 5th AFIR colloquium}, } - -@book{butler2007saddlepoint, - title = {Saddlepoint approximations with applications}, - author = {Butler, Ronald W}, - volume = 22, - year = 2007, - publisher = {Cambridge University Press} -} - -@article{carr1999option, - title = {Option valuation using the fast Fourier transform}, - author = {Carr, Peter and Madan, Dilip}, - journal = {Journal of Computational Finance}, - volume = 2, - number = 4, - pages = {61--73}, - year = 1999 -} - -@article{crowder1986consistency, - title = {On consistency and inconsistency of estimating - equations}, - author = {Crowder, Martin}, - journal = {Econometric Theory}, - pages = {305--330}, - year = 1986, - publisher = {JSTOR} -} - -@article{crowder1987linear, - title = {On linear and quadratic estimating functions}, - author = {Crowder, Martin}, - journal = {Biometrika}, - volume = 74, - number = 3, - pages = {591--597}, - year = 1987, - publisher = {Biometrika Trust} -} - -@article{daniels1954saddlepoint, - title = {Saddlepoint approximations in statistics}, - author = {Daniels, Henry E}, - journal = {The Annals of Mathematical Statistics}, - pages = {631--650}, - year = 1954, - publisher = {JSTOR} -} - -@article{daniels1987tail, - title = {Tail probability approximations}, - author = {Daniels, Henry E}, - journal = {International Statistical Review/Revue - Internationale de Statistique}, - pages = {37--48}, - year = 1987, - publisher = {JSTOR} -} - -@TechReport{derman1996modelrisk, - author = {Derman, Emanuel}, - title = {Model Risk}, - institution = {Goldman Sachs}, - year = 1996 -} - -@book{dodge2004statistique, - title = {Statistique: dictionnaire encyclop{\'e}dique}, - author = {Dodge, Yadolah}, - year = 2004, - publisher = {Springer Verlag France} -} - -@article{epps1983test, - title = {A test for normality based on the empirical - characteristic function}, - author = {Epps, Thomas W and Pulley, Lawrence B}, - journal = {Biometrika}, - volume = 70, - number = 3, - pages = {723--726}, - year = 1983, - publisher = {Biometrika Trust} -} - -@book{epps2007pricing, - title = {Pricing derivative securities}, - author = {Epps, Thomas W}, - year = 2007, - publisher = {World Scientific Publishing Company Incorporated} -} - -@book{everitt2006cambridge, - title = {The Cambridge dictionary of statistics}, - author = {Everitt, Brian and Skrondal, Anders}, - volume = 4, - year = 2006, - publisher = {Cambridge University Press Cambridge} -} - -@article{feuerverger1981efficiency, - title = {On the efficiency of empirical characteristic - function procedures}, - author = {Feuerverger, Andrey and McDunnough, Philip}, - journal = {Journal of the Royal Statistical Society. Series B - (Methodological)}, - pages = {20--27}, - year = 1981, - publisher = {JSTOR} -} - -@article{fox1986large, - title = {Large-sample properties of parameter estimates for - strongly dependent stationary Gaussian time series}, - author = {Fox, Robert and Taqqu, Murad S}, - journal = {The Annals of Statistics}, - volume = 14, - number = 2, - pages = {517--532}, - year = 1986, - publisher = {Institute of Mathematical Statistics} -} - -@article{gil1951note, - title = {Note on the inversion theorem}, - author = {Gil-Pelaez, J}, - journal = {Biometrika}, - volume = 38, - number = {3-4}, - pages = {481--482}, - year = 1951, - publisher = {Biometrika Trust} -} - -@book{gourieroux1989statistique, - title = {Statistique et mod{\`e}les {\'e}conom{\'e}triques: - Notions g{\'e}n{\'e}rales, estimation, - pr{\'e}vision, algorithmes}, - author = {Gourieroux, Christian and Monfort, Alain}, - volume = 1, - year = 1989, - publisher = {Economica} -} - -@book{hall2005generalized, - title = {Generalized method of moments}, - author = {Hall, Alastair R}, - year = 2005, - publisher = {Oxford University Press Oxford} -} - -@book{hamilton1994time, - title = {Time series analysis}, - author = {Hamilton, James Douglas}, - volume = 2, - year = 1994, - publisher = {Cambridge Univ Press} -} - -@article{hansen1982large, - title = {Large sample properties of generalized method of - moments estimators}, - author = {Hansen, Lars Peter}, - journal = {Econometrica: Journal of the Econometric Society}, - pages = {1029--1054}, - year = 1982, - publisher = {JSTOR} -} - -@article{henze1990approximation, - title = {An approximation to the limit distribution of the - Epps-Pulley test statistic for normality}, - author = {Henze, N}, - journal = {Metrika}, - volume = 37, - number = 1, - pages = {7--18}, - year = 1990, - publisher = {Springer} -} - -@article{heston1993closed, - title = {A closed-form solution for options with stochastic - volatility with applications to bond and currency - options}, - author = {Heston, Steven L}, - journal = {Review of financial studies}, - volume = 6, - number = 2, - pages = {327--343}, - year = 1993, - publisher = {Soc Financial Studies} -} - -@article{hinkley1977estimation, - title = {Estimation of the Pareto law from underreported - data: A further analysis}, - author = {Hinkley, David V and Revankar, Nagesh S}, - journal = {Journal of Econometrics}, - volume = 5, - number = 1, - pages = {1--11}, - year = 1977, - publisher = {Elsevier} -} - -@book{hogg1978introduction, - title = {Introduction to mathematical statistics}, - author = {Hogg, R.V. and Craig, A.T.}, - isbn = 9780029789902, - lccn = 77002884, - url = {http://books.google.ca/books?id=OZYQAQAAIAAJ}, - year = 1978, - publisher = {Macmillan} -} - -@book{hull1999options, - title = {Options, futures, and other derivatives}, - author = {Hull, John C}, - year = 1999, - publisher = {Pearson Education India} -} - -@article{itkin2005pricing, - title = {Pricing options with VG model using FFT}, - author = {Itkin, Andrey}, - journal = {arXiv preprint physics/0503137}, - year = 2005 -} - -@book{kotz2001laplace, - title = {The Laplace Distribution and Generalizations: A - Revisit With Applications to Communications, - Exonomics, Engineering, and Finance}, - author = {Kotz, S. and Kozubowski, T.J. and Podg{\'o}rski, K.}, - isbn = 9780817641665, - lccn = 00068900, - series = {Progress in Mathematics Series}, - url = {http://books.google.ca/books?id=cb8B07hwULUC}, - year = 2001, - publisher = {Birkh{\"a}user} -} - -@article{kozubowski1999class, - title = {A class of asymmetric distributions}, - author = {Kozubowski, Tomasz J and Podg{\'o}rski, Krzysztof}, - journal = {Actuarial Research Clearing House}, - volume = 1, - pages = {113--134}, - year = 1999, - publisher = {Citeseer} -} - -@article{kozubowski2001asymmetric, - title = {Asymmetric Laplace laws and modeling financial data}, - author = {Kozubowski, Tomasz J and Podg{\'o}rski, Krzysztof}, - journal = {Mathematical and computer modelling}, - volume = 34, - number = 9, - pages = {1003--1021}, - year = 2001, - publisher = {Elsevier} -} - -@book{kyprianou2007introductory, - title = {Introductory lectures on fluctuations of L{\'e}vy - processes with applications}, - author = {Kyprianou, Andreas E}, - year = 2007, - publisher = {Springer} -} - -@article{lugannani1980saddle, - title = {Saddle point approximation for the distribution of - the sum of independent random variables}, - author = {Lugannani, Robert and Rice, Stephen}, - journal = {Advances in applied probability}, - pages = {475--490}, - year = 1980, - publisher = {JSTOR} -} - -@book{lukacs1960characteristic, - title = {Characteristic functions}, - author = {Lukacs, Eugene}, - volume = 4, - year = 1960, - publisher = {Griffin London} -} - -@article{luong1987minimum, - title = {Minimum-distance methods based on quadratic - distances for transforms}, - author = {Luong, A and Thompson, ME}, - journal = {Canadian Journal of Statistics}, - volume = 15, - number = 3, - pages = {239--251}, - year = 1987, - publisher = {Wiley Online Library} -} - -@article{madan1990variance, - title = {The variance gamma (VG) model for share market - returns}, - author = {Madan, Dilip B and Seneta, Eugene}, - journal = {Journal of business}, - pages = {511--524}, - year = 1990, - publisher = {JSTOR} -} - -@article{madan1998variance, - title = {The variance gamma process and option pricing}, - author = {Madan, Dilip B and Carr, Peter P and Chang, Eric C}, - journal = {European Finance Review}, - volume = 2, - number = 1, - pages = {79--105}, - year = 1998, - publisher = {Kluwer Academic Publishers} -} - -@article{mandelbrot1963variation, - title = {The variation of certain speculative prices}, - author = {Mandelbrot, B.}, - journal = {Journal of business}, - pages = {394--419}, - year = 1963, - publisher = {University of Chicago Press} -} - -@article{merton1976option, - title = {Option pricing when underlying stock returns are - discontinuous}, - author = {Merton, Robert C}, - journal = {Journal of financial economics}, - volume = 3, - number = 1, - pages = {125--144}, - year = 1976, - publisher = {Elsevier} -} - -@article{mitchell1916critique, - title = {A critique of index numbers of the prices of stocks}, - author = {Mitchell, Wesley C}, - journal = {The Journal of Political Economy}, - pages = {625--693}, - year = 1916, - publisher = {JSTOR} -} - -@book{musiela2005martingale, - title = {Martingale methods in financial modelling}, - author = {Musiela, Marek and Rutkowski, Marek}, - volume = 36, - year = 2005, - publisher = {Springer} -} - -@article{newey1987hypothesis, - title = {Hypothesis testing with efficient method of moments - estimation}, - author = {Newey, Whitney K and West, Kenneth D}, - journal = {International Economic Review}, - volume = 28, - number = 3, - pages = {777--787}, - year = 1987, - publisher = {JSTOR} -} - -@article{newey1994large, - title = {Large sample estimation and hypothesis testing}, - author = {Newey, Whitney K and McFadden, Daniel}, - journal = {Handbook of econometrics}, - volume = 4, - pages = {2111--2245}, - year = 1994, - publisher = {Elsevier} -} - -@article{praetz1972distribution, - title = {The distribution of share price changes}, - author = {Praetz, Peter D}, - journal = {Journal of business}, - pages = {49--55}, - year = 1972, - publisher = {JSTOR} -} - -@article{press1967compound, - title = {A compound events model for security prices}, - author = {Press, S James}, - journal = {Journal of Business}, - pages = {317--335}, - year = 1967, - publisher = {JSTOR} -} - -@article{randal2004non, - title = {Non-parametric estimation of historical volatility}, - author = {Randal, John A and Thomson, Peter J and Lally, - Martin T}, - journal = {Quantitative Finance}, - volume = 4, - number = 4, - pages = {427--440}, - year = 2004, - publisher = {Taylor \& Francis} -} - -@book{sato1999levy, - title = {L{\'e}vy Processes and Infinitely Divisible - Distributions}, - author = {Sato, K.}, - isbn = 9780521553025, - lccn = 99015232, - series = {Cambridge Studies in Advanced Mathematics}, - url = {http://books.google.ca/books?id=CwT5BNG0-owC}, - year = 1999, - publisher = {Cambridge University Press} -} - -@book{schoutens2003levy, - title = {L{\'e}vy processes in Finance}, - author = {Schoutens, Wim}, - year = 2003, - publisher = {Wiley} -} - -@article{seneta2004fitting, - title = {Fitting the variance-gamma model to financial data}, - author = {Seneta, Eugene}, - journal = {Journal of Applied Probability}, - pages = {177--187}, - year = 2004, - publisher = {JSTOR} -} - -@article{shapiro1965analysis, - title = {An analysis of variance test for normality (complete - samples)}, - author = {Shapiro, Samuel Sanford and Wilk, Martin B}, - journal = {Biometrika}, - volume = 52, - number = {3/4}, - pages = {591--611}, - year = 1965, - publisher = {JSTOR} -} - -@article{shephard1991characteristic, - title = {From characteristic function to distribution - function: a simple framework for the theory}, - author = {Shephard, Neil G}, - journal = {Econometric Theory}, - volume = 7, - number = 04, - pages = {519--529}, - year = 1991, - publisher = {Cambridge Univ Press} -} - -@book{spiegel1999schaum, - title = {Schaum's mathematical handbook of formulas and - tables}, - author = {Spiegel, Murray R and Liu, John}, - volume = 1000, - year = 1999, - publisher = {McGraw-Hill} -} - -@book{stuart1987kendall, - title = {Kendall’s advanced theory of statistics, Vol. 1}, - author = {Stuart, Alan and Ord, J Keith}, - year = 1987, - publisher = {Oxford University Press, New York} -} - -@Manual{thevolskew, - title = {The Volatility Skew}, - author = {Alan Verga}, - year = 2013, - url = {http://www.thevolatilityskew.com} -} - -@phdthesis{torczon1989multi, - title = {Multi-directional search: a direct search algorithm - for parallel machines}, - author = {Torczon, Virginia Joanne}, - year = 1989, - school = {Citeseer} -} - -@article{wang2003evaluating, - title = {Evaluating Kolmogorov's distribution}, - author = {Wang, Jingbo and Tsang, Wai Wan and Marsaglia, - George}, - journal = {Journal of Statistical Software}, - volume = 8, - number = 18, - pages = {1--4}, - year = 2003, - publisher = {American Statistical Association} -} - -@article{wendel1961non, - title = {The non-absolute convergence of Gil-Pelaez'inversion - integral}, - author = {Wendel, JG}, - journal = {The Annals of Mathematical Statistics}, - volume = 32, - number = 1, - pages = {338--339}, - year = 1961, - publisher = {Institute of Mathematical Statistics} -} - -@article{teschl2004topics, - title={Topics in Real and Functional analysis}, - author={Teschl, Gerald}, - journal={unpublished, available online at \url{http://www.mat.univie.ac.at/\~gerald}}, - year={2004} -} - -@article{wolfowitz1957minimum, - title = {The minimum distance method}, - author = {Wolfowitz, Jacob}, - journal = {The Annals of Mathematical Statistics}, - pages = {75--88}, - year = 1957, - publisher = {JSTOR} -} - -@book{wooldridge2001econometric, - title = {Econometric analysis of cross section and panel - data}, - author = {Wooldridge, Jeffrey M}, - year = 2001, - publisher = {MIT press} -} - -@article{fama1993common, - title={Common risk factors in the returns on stocks and bonds}, - author={Fama, Eugene F and French, Kenneth R}, - journal={Journal of financial economics}, - volume={33}, - number={1}, - pages={3--56}, - year={1993}, - publisher={Elsevier} -} - -@inproceedings{walterlevy, - title={Levy-stability-under-addition and fractal structure of markets: imlications for the actuaries and emphasized axamination of MATIF national contract}, - author={Walter, Christian} -} \ No newline at end of file diff --git a/memoire/memoire.bib~ b/memoire/memoire.bib~ new file mode 100644 index 0000000..7e536df --- /dev/null +++ b/memoire/memoire.bib~ @@ -0,0 +1,697 @@ +@article{KOUTROUVELIS01011980, + author = {Koutrouvelis, I. A.}, + title = {A goodness-of-fit test of simple hypotheses based on + the empirical characteristic function}, + volume = 67, + number = 1, + pages = {238-240}, + year = 1980, + doi = {10.1093/biomet/67.1.238}, + abstract = {SUMMARY The empirical characteristic function φn(t) + and its asymptotic distribution are utilized to find + a chi-squared goodness-of-fit test for simple null + hypotheses. In addition the optimum number and + location of points t at which φn(t) has to be + evaluated is investigated for specified alternative + hypotheses.}, + URL = + {http://biomet.oxfordjournals.org/content/67/1/238.abstract}, + eprint = + {http://biomet.oxfordjournals.org/content/67/1/238.full.pdf+html}, + journal = {Biometrika} +} + +@Manual{RpackageVarianceGamma, + title = {VarianceGamma: The Variance Gamma Distribution}, + author = {David Scott and Christine Yang Dong}, + year = 2012, + note = {R package version 0.3-1}, + url = {http://CRAN.R-project.org/package=VarianceGamma}, +} + +@Manual{Rsoftware, + title = {R: A Language and Environment for Statistical + Computing}, + author = {{R Core Team}}, + organization = {R Foundation for Statistical Computing}, + address = {Vienna, Austria}, + year = 2012, + note = {{ISBN} 3-900051-07-0}, + url = {http://www.R-project.org/}, +} + +@ARTICLE{Singer:2009, + AUTHOR = {Singer, S. and Nelder, J. }, + TITLE = {Nelder-Mead algorithm}, + YEAR = 2009, + JOURNAL = {Scholarpedia}, + VOLUME = 4, + NUMBER = 7, + PAGES = 2928, + URL = {http://dx.doi.org/10.4249/scholarpedia.2928} +} + +@book{abramowitz1965handbook, + title = {Handbook of mathematical functions: with formulas, + graphs, and mathematical tables}, + author = {Abramowitz, Milton and Stegun, Irene A}, + volume = 55, + year = 1965, + publisher = {Dover publications} +} + +@article{applebaum2004levy, + title = {L{\'e}vy processes: From probability to finance and + quantum groups}, + author = {Applebaum, David}, + journal = {Notices of the AMS}, + volume = 51, + number = 11, + pages = {1336--1347}, + year = 2004 +} + +@book{bachelier1900theorie, + title = {Th{\'e}orie de la sp{\'e}culation}, + author = {Bachelier, Louis}, + year = 1900, + publisher = {Gauthier-Villars} +} + +@book{barndorff2001levy, + title = {L{\'e}vy Processes: Theory and Applications}, + author = {Barndorff-Nielsen, O.E.E. and Mikosch, T.E. and + Resnick, S.I.E.}, + isbn = 9780817641672, + lccn = {lc00068064}, + url = {http://books.google.ca/books?id=ExpTdTauXMwC}, + year = 2001, + publisher = {Birkhäuser} +} + +@article{berkson1980minimum, + title = {Minimum chi-square, not maximum likelihood!}, + author = {Berkson, Joseph}, + journal = {The Annals of Statistics}, + pages = {457--487}, + year = 1980, + publisher = {JSTOR} +} + +@book{bingham2004risk, + title = {Risk-neutral valuation: Pricing and hedging of + financial derivatives}, + author = {Bingham, Nicholas H and Kiesel, R{\"u}diger}, + year = 2004, + publisher = {Springer} +} + +@article{black1973pricing, + title = {The pricing of options and corporate liabilities}, + author = {Black, Fischer and Scholes, Myron}, + journal = {The journal of political economy}, + pages = {637--654}, + year = 1973, + publisher = {JSTOR} +} + +@article{black1976pricing, + title = {The pricing of commodity contracts}, + author = {Black, Fischer}, + journal = {Journal of financial economics}, + volume = 3, + number = 1, + pages = {167--179}, + year = 1976, + publisher = {Elsevier} +} + +@article{buckle1995bayesian, + title = {Bayesian inference for stable distributions}, + author = {Buckle, DJ}, + journal = {Journal of the American Statistical Association}, + volume = 90, + number = 430, + pages = {605--613}, + year = 1995, + publisher = {Taylor \& Francis Group} +} + +@book{butler2007saddlepoint, + title = {Saddlepoint approximations with applications}, + author = {Butler, Ronald W}, + volume = 22, + year = 2007, + publisher = {Cambridge University Press} +} + +@article{carr1999option, + title = {Option valuation using the fast Fourier transform}, + author = {Carr, Peter and Madan, Dilip}, + journal = {Journal of Computational Finance}, + volume = 2, + number = 4, + pages = {61--73}, + year = 1999 +} + +@article{crowder1986consistency, + title = {On consistency and inconsistency of estimating + equations}, + author = {Crowder, Martin}, + journal = {Econometric Theory}, + pages = {305--330}, + year = 1986, + publisher = {JSTOR} +} + +@article{crowder1987linear, + title = {On linear and quadratic estimating functions}, + author = {Crowder, Martin}, + journal = {Biometrika}, + volume = 74, + number = 3, + pages = {591--597}, + year = 1987, + publisher = {Biometrika Trust} +} + +@article{daniels1954saddlepoint, + title = {Saddlepoint approximations in statistics}, + author = {Daniels, Henry E}, + journal = {The Annals of Mathematical Statistics}, + pages = {631--650}, + year = 1954, + publisher = {JSTOR} +} + +@article{daniels1987tail, + title = {Tail probability approximations}, + author = {Daniels, Henry E}, + journal = {International Statistical Review/Revue + Internationale de Statistique}, + pages = {37--48}, + year = 1987, + publisher = {JSTOR} +} + +@TechReport{derman1996modelrisk, + author = {Derman, Emanuel}, + title = {Model Risk}, + institution = {Goldman Sachs}, + year = 1996 +} + +@book{dodge2004statistique, + title = {Statistique: dictionnaire encyclop{\'e}dique}, + author = {Dodge, Yadolah}, + year = 2004, + publisher = {Springer Verlag France} +} + +@article{epps1983test, + title = {A test for normality based on the empirical + characteristic function}, + author = {Epps, Thomas W and Pulley, Lawrence B}, + journal = {Biometrika}, + volume = 70, + number = 3, + pages = {723--726}, + year = 1983, + publisher = {Biometrika Trust} +} + +@book{epps2007pricing, + title = {Pricing derivative securities}, + author = {Epps, Thomas W}, + year = 2007, + publisher = {World Scientific Publishing Company Incorporated} +} + +@book{everitt2006cambridge, + title = {The Cambridge dictionary of statistics}, + author = {Everitt, Brian and Skrondal, Anders}, + volume = 4, + year = 2006, + publisher = {Cambridge University Press Cambridge} +} + +@article{feuerverger1981efficiency, + title = {On the efficiency of empirical characteristic + function procedures}, + author = {Feuerverger, Andrey and McDunnough, Philip}, + journal = {Journal of the Royal Statistical Society. Series B + (Methodological)}, + pages = {20--27}, + year = 1981, + publisher = {JSTOR} +} + +@article{fox1986large, + title = {Large-sample properties of parameter estimates for + strongly dependent stationary Gaussian time series}, + author = {Fox, Robert and Taqqu, Murad S}, + journal = {The Annals of Statistics}, + volume = 14, + number = 2, + pages = {517--532}, + year = 1986, + publisher = {Institute of Mathematical Statistics} +} + +@article{gil1951note, + title = {Note on the inversion theorem}, + author = {Gil-Pelaez, J}, + journal = {Biometrika}, + volume = 38, + number = {3-4}, + pages = {481--482}, + year = 1951, + publisher = {Biometrika Trust} +} + +@book{gourieroux1989statistique, + title = {Statistique et mod{\`e}les {\'e}conom{\'e}triques: + Notions g{\'e}n{\'e}rales, estimation, + pr{\'e}vision, algorithmes}, + author = {Gourieroux, Christian and Monfort, Alain}, + volume = 1, + year = 1989, + publisher = {Economica} +} + +@book{hall2005generalized, + title = {Generalized method of moments}, + author = {Hall, Alastair R}, + year = 2005, + publisher = {Oxford University Press Oxford} +} + +@book{hamilton1994time, + title = {Time series analysis}, + author = {Hamilton, James Douglas}, + volume = 2, + year = 1994, + publisher = {Cambridge Univ Press} +} + +@article{hansen1982large, + title = {Large sample properties of generalized method of + moments estimators}, + author = {Hansen, Lars Peter}, + journal = {Econometrica: Journal of the Econometric Society}, + pages = {1029--1054}, + year = 1982, + publisher = {JSTOR} +} + +@article{henze1990approximation, + title = {An approximation to the limit distribution of the + Epps-Pulley test statistic for normality}, + author = {Henze, N}, + journal = {Metrika}, + volume = 37, + number = 1, + pages = {7--18}, + year = 1990, + publisher = {Springer} +} + +@article{heston1993closed, + title = {A closed-form solution for options with stochastic + volatility with applications to bond and currency + options}, + author = {Heston, Steven L}, + journal = {Review of financial studies}, + volume = 6, + number = 2, + pages = {327--343}, + year = 1993, + publisher = {Soc Financial Studies} +} + +@article{hinkley1977estimation, + title = {Estimation of the Pareto law from underreported + data: A further analysis}, + author = {Hinkley, David V and Revankar, Nagesh S}, + journal = {Journal of Econometrics}, + volume = 5, + number = 1, + pages = {1--11}, + year = 1977, + publisher = {Elsevier} +} + +@book{hogg1978introduction, + title = {Introduction to mathematical statistics}, + author = {Hogg, R.V. and Craig, A.T.}, + isbn = 9780029789902, + lccn = 77002884, + url = {http://books.google.ca/books?id=OZYQAQAAIAAJ}, + year = 1978, + publisher = {Macmillan} +} + +@book{hull1999options, + title = {Options, futures, and other derivatives}, + author = {Hull, John C}, + year = 1999, + publisher = {Pearson Education India} +} + +@article{itkin2005pricing, + title = {Pricing options with VG model using FFT}, + author = {Itkin, Andrey}, + journal = {arXiv preprint physics/0503137}, + year = 2005 +} + +@book{kotz2001laplace, + title = {The Laplace Distribution and Generalizations: A + Revisit With Applications to Communications, + Exonomics, Engineering, and Finance}, + author = {Kotz, S. and Kozubowski, T.J. and Podg{\'o}rski, K.}, + isbn = 9780817641665, + lccn = 00068900, + series = {Progress in Mathematics Series}, + url = {http://books.google.ca/books?id=cb8B07hwULUC}, + year = 2001, + publisher = {Birkh{\"a}user} +} + +@article{kozubowski1999class, + title = {A class of asymmetric distributions}, + author = {Kozubowski, Tomasz J and Podg{\'o}rski, Krzysztof}, + journal = {Actuarial Research Clearing House}, + volume = 1, + pages = {113--134}, + year = 1999, + publisher = {Citeseer} +} + +@article{kozubowski2001asymmetric, + title = {Asymmetric Laplace laws and modeling financial data}, + author = {Kozubowski, Tomasz J and Podg{\'o}rski, Krzysztof}, + journal = {Mathematical and computer modelling}, + volume = 34, + number = 9, + pages = {1003--1021}, + year = 2001, + publisher = {Elsevier} +} + +@book{kyprianou2007introductory, + title = {Introductory lectures on fluctuations of L{\'e}vy + processes with applications}, + author = {Kyprianou, Andreas E}, + year = 2007, + publisher = {Springer} +} + +@article{lugannani1980saddle, + title = {Saddle point approximation for the distribution of + the sum of independent random variables}, + author = {Lugannani, Robert and Rice, Stephen}, + journal = {Advances in applied probability}, + pages = {475--490}, + year = 1980, + publisher = {JSTOR} +} + +@book{lukacs1960characteristic, + title = {Characteristic functions}, + author = {Lukacs, Eugene}, + volume = 4, + year = 1960, + publisher = {Griffin London} +} + +@article{luong1987minimum, + title = {Minimum-distance methods based on quadratic + distances for transforms}, + author = {Luong, A and Thompson, ME}, + journal = {Canadian Journal of Statistics}, + volume = 15, + number = 3, + pages = {239--251}, + year = 1987, + publisher = {Wiley Online Library} +} + +@article{madan1990variance, + title = {The variance gamma (VG) model for share market + returns}, + author = {Madan, Dilip B and Seneta, Eugene}, + journal = {Journal of business}, + pages = {511--524}, + year = 1990, + publisher = {JSTOR} +} + +@article{madan1998variance, + title = {The variance gamma process and option pricing}, + author = {Madan, Dilip B and Carr, Peter P and Chang, Eric C}, + journal = {European Finance Review}, + volume = 2, + number = 1, + pages = {79--105}, + year = 1998, + publisher = {Kluwer Academic Publishers} +} + +@article{mandelbrot1963variation, + title = {The variation of certain speculative prices}, + author = {Mandelbrot, B.}, + journal = {Journal of business}, + pages = {394--419}, + year = 1963, + publisher = {University of Chicago Press} +} + +@article{merton1976option, + title = {Option pricing when underlying stock returns are + discontinuous}, + author = {Merton, Robert C}, + journal = {Journal of financial economics}, + volume = 3, + number = 1, + pages = {125--144}, + year = 1976, + publisher = {Elsevier} +} + +@article{mitchell1916critique, + title = {A critique of index numbers of the prices of stocks}, + author = {Mitchell, Wesley C}, + journal = {The Journal of Political Economy}, + pages = {625--693}, + year = 1916, + publisher = {JSTOR} +} + +@book{musiela2005martingale, + title = {Martingale methods in financial modelling}, + author = {Musiela, Marek and Rutkowski, Marek}, + volume = 36, + year = 2005, + publisher = {Springer} +} + +@article{newey1987hypothesis, + title = {Hypothesis testing with efficient method of moments + estimation}, + author = {Newey, Whitney K and West, Kenneth D}, + journal = {International Economic Review}, + volume = 28, + number = 3, + pages = {777--787}, + year = 1987, + publisher = {JSTOR} +} + +@article{newey1994large, + title = {Large sample estimation and hypothesis testing}, + author = {Newey, Whitney K and McFadden, Daniel}, + journal = {Handbook of econometrics}, + volume = 4, + pages = {2111--2245}, + year = 1994, + publisher = {Elsevier} +} + +@article{praetz1972distribution, + title = {The distribution of share price changes}, + author = {Praetz, Peter D}, + journal = {Journal of business}, + pages = {49--55}, + year = 1972, + publisher = {JSTOR} +} + +@article{press1967compound, + title = {A compound events model for security prices}, + author = {Press, S James}, + journal = {Journal of Business}, + pages = {317--335}, + year = 1967, + publisher = {JSTOR} +} + +@article{randal2004non, + title = {Non-parametric estimation of historical volatility}, + author = {Randal, John A and Thomson, Peter J and Lally, + Martin T}, + journal = {Quantitative Finance}, + volume = 4, + number = 4, + pages = {427--440}, + year = 2004, + publisher = {Taylor \& Francis} +} + +@book{sato1999levy, + title = {L{\'e}vy Processes and Infinitely Divisible + Distributions}, + author = {Sato, K.}, + isbn = 9780521553025, + lccn = 99015232, + series = {Cambridge Studies in Advanced Mathematics}, + url = {http://books.google.ca/books?id=CwT5BNG0-owC}, + year = 1999, + publisher = {Cambridge University Press} +} + +@book{schoutens2003levy, + title = {L{\'e}vy processes in Finance}, + author = {Schoutens, Wim}, + year = 2003, + publisher = {Wiley} +} + +@article{seneta2004fitting, + title = {Fitting the variance-gamma model to financial data}, + author = {Seneta, Eugene}, + journal = {Journal of Applied Probability}, + pages = {177--187}, + year = 2004, + publisher = {JSTOR} +} + +@article{shapiro1965analysis, + title = {An analysis of variance test for normality (complete + samples)}, + author = {Shapiro, Samuel Sanford and Wilk, Martin B}, + journal = {Biometrika}, + volume = 52, + number = {3/4}, + pages = {591--611}, + year = 1965, + publisher = {JSTOR} +} + +@article{shephard1991characteristic, + title = {From characteristic function to distribution + function: a simple framework for the theory}, + author = {Shephard, Neil G}, + journal = {Econometric Theory}, + volume = 7, + number = 04, + pages = {519--529}, + year = 1991, + publisher = {Cambridge Univ Press} +} + +@book{spiegel1999schaum, + title = {Schaum's mathematical handbook of formulas and + tables}, + author = {Spiegel, Murray R and Liu, John}, + volume = 1000, + year = 1999, + publisher = {McGraw-Hill} +} + +@book{stuart1987kendall, + title = {Kendall’s advanced theory of statistics, Vol. 1}, + author = {Stuart, Alan and Ord, J Keith}, + year = 1987, + publisher = {Oxford University Press, New York} +} + +@Manual{thevolskew, + title = {The Volatility Skew}, + author = {Alan Verga}, + year = 2013, + url = {http://www.thevolatilityskew.com} +} + +@phdthesis{torczon1989multi, + title = {Multi-directional search: a direct search algorithm + for parallel machines}, + author = {Torczon, Virginia Joanne}, + year = 1989, + school = {Citeseer} +} + +@article{wang2003evaluating, + title = {Evaluating Kolmogorov's distribution}, + author = {Wang, Jingbo and Tsang, Wai Wan and Marsaglia, + George}, + journal = {Journal of Statistical Software}, + volume = 8, + number = 18, + pages = {1--4}, + year = 2003, + publisher = {American Statistical Association} +} + +@article{wendel1961non, + title = {The non-absolute convergence of Gil-Pelaez'inversion + integral}, + author = {Wendel, JG}, + journal = {The Annals of Mathematical Statistics}, + volume = 32, + number = 1, + pages = {338--339}, + year = 1961, + publisher = {Institute of Mathematical Statistics} +} + +@article{teschl2004topics, + title={Topics in Real and Functional analysis}, + author={Teschl, Gerald}, + journal={unpublished, available online at \url{http://www.mat.univie.ac.at/\~gerald}}, + year={2004} +} + +@article{wolfowitz1957minimum, + title = {The minimum distance method}, + author = {Wolfowitz, Jacob}, + journal = {The Annals of Mathematical Statistics}, + pages = {75--88}, + year = 1957, + publisher = {JSTOR} +} + +@book{wooldridge2001econometric, + title = {Econometric analysis of cross section and panel + data}, + author = {Wooldridge, Jeffrey M}, + year = 2001, + publisher = {MIT press} +} + +@article{fama1993common, + title={Common risk factors in the returns on stocks and bonds}, + author={Fama, Eugene F and French, Kenneth R}, + journal={Journal of financial economics}, + volume={33}, + number={1}, + pages={3--56}, + year={1993}, + publisher={Elsevier} +} + +@inproceedings{walterlevy, + title={Levy-stability-under-addition and fractal structure of markets: imlications for the actuaries and emphasized axamination of MATIF national contract}, + author={Walter, Christian} +} \ No newline at end of file diff --git a/memoire/remerciements.aux b/memoire/remerciements.aux new file mode 100644 index 0000000..a8d4360 --- /dev/null +++ b/memoire/remerciements.aux @@ -0,0 +1,80 @@ +\relax +\providecommand\hyper@newdestlabel[2]{} +\@writefile{toc}{\contentsline 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