ajout fichiers manquants et corrections bibliographie

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François Pelletier 2014-01-15 00:52:20 -05:00
parent 92616e09a6
commit 70977e9ee6
43 changed files with 7217 additions and 679 deletions

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## 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()

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@ -385,7 +385,7 @@ titres boursiers, entre 1890 et 1915 (figure \ref{fig:mitchell1}).
Une asymétrie négative des rendements sera alors présente.
\begin{figure}[!ht]
\centering
\includegraphics[scale=0.75]{../varia/mitchell1.pdf}
\includegraphics[scale=0.75]{../graphiques/mitchell1.pdf}
\caption{Distribution des rendements annuels de 40 titres boursiers,
de 1890 à 1915, Table XVIII de \cite{mitchell1916critique}}
\label{fig:mitchell1}

259
memoire/chapitre2.aux Normal file
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@ -548,7 +548,7 @@ avec différents paramètres d'asymétrie et d'aplatissement à la figure
\ref{fig:densiteGAL}.
\begin{figure}[!ht]
\centering
\includegraphics[scale=0.8]{../contenus/r/code/dGAL-exemples.pdf}
\includegraphics[scale=0.8]{../graphiques/dGAL-exemples.pdf}
\caption{Fonction de densité de la distribution Laplace asymétrique
généralisée avec différents paramètres:
$GAL(y;\theta,\sigma,\kappa,\tau)$}

182
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@ -18,7 +18,7 @@ la figure \ref{fig:seriechronoR1} sous forme de série chronologique.
\begin{figure}[!ht]
\centering
\includegraphics[height=4in,
width=4in]{../contenus/r/code/ABBEYN-chronologie.pdf}
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}

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\providecommand{\natexlab}[1]{#1}
\providecommand{\url}[1]{\texttt{#1}}
\expandafter\ifx\csname urlstyle\endcsname\relax
\providecommand{\doi}[1]{doi: #1}\else
\providecommand{\doi}{doi: \begingroup \urlstyle{rm}\Url}\fi
\bibitem[Abramowitz et Stegun(1965)]{abramowitz1965handbook}
Milton Abramowitz et Irene~A. Stegun.
\newblock \emph{Handbook Of Mathematical Functions: With Formulas, Graphs, And
Mathematical Tables}, volume~55.
\newblock Dover Publications, 1965.
\bibitem[Applebaum(2004)]{applebaum2004levy}
David Applebaum.
\newblock Lévy processes: From probability to finance and quantum groups.
\newblock \emph{Notices Of The American Mathematical Society}, 51\penalty0
(11):\penalty0 1336--1347, 2004.
\bibitem[Bachelier(1900)]{bachelier1900theorie}
Louis Bachelier.
\newblock \emph{Th{\'e}orie De La Sp{\'e}culation}.
\newblock Gauthier-Villars, 1900.
\bibitem[Berkson(1980)]{berkson1980minimum}
Joseph Berkson.
\newblock Minimum chi-square, not maximum likelihood!
\newblock \emph{The Annals of Statistics}, pages 457--487, 1980.
\bibitem[Bingham et Kiesel(2004)]{bingham2004risk}
Nicholas~H. Bingham et R{\"u}diger Kiesel.
\newblock \emph{Risk-Neutral Valuation: Pricing And Hedging Of Financial
Derivatives}.
\newblock Springer, 2004.
\bibitem[Black(1976)]{black1976pricing}
Fischer Black.
\newblock The pricing of commodity contracts.
\newblock \emph{Journal Of Financial Economics}, 3\penalty0 (1):\penalty0
167--179, 1976.
\bibitem[Black et Scholes(1973)]{black1973pricing}
Fischer Black et Myron Scholes.
\newblock The pricing of options and corporate liabilities.
\newblock \emph{The Journal Of Political Economy}, pages 637--654, 1973.
\bibitem[Buckle(1995)]{buckle1995bayesian}
D.~J. Buckle.
\newblock Bayesian inference for stable distributions.
\newblock \emph{Journal of the American Statistical Association}, 90\penalty0
(430):\penalty0 605--613, 1995.
\bibitem[Butler(2007)]{butler2007saddlepoint}
Ronald~W. Butler.
\newblock \emph{Saddlepoint Approximations With Applications}, volume~22.
\newblock Cambridge University Press, 2007.
\bibitem[Carr et Madan(1999)]{carr1999option}
Peter Carr et Dilip Madan.
\newblock Option valuation using the fast fourier transform.
\newblock \emph{Journal Of Computational Finance}, 2\penalty0 (4):\penalty0
61--73, 1999.
\bibitem[Crowder(1986)]{crowder1986consistency}
Martin Crowder.
\newblock On consistency and inconsistency of estimating equations.
\newblock \emph{Econometric Theory}, pages 305--330, 1986.
\bibitem[Crowder(1987)]{crowder1987linear}
Martin Crowder.
\newblock On linear and quadratic estimating functions.
\newblock \emph{Biometrika}, 74\penalty0 (3):\penalty0 591--597, 1987.
\bibitem[Daniels(1954)]{daniels1954saddlepoint}
Henry~E Daniels.
\newblock Saddlepoint approximations in statistics.
\newblock \emph{The Annals of Mathematical Statistics}, pages 631--650, 1954.
\bibitem[Derman(1996)]{derman1996modelrisk}
Emanuel Derman.
\newblock Model risk.
\newblock Technical report, Goldman Sachs, 1996.
\bibitem[Dilip B~Madan et Chang(1998)]{madan1998variance}
Peter P~Carr Dilip B~Madan et Eric~C Chang.
\newblock The variance gamma process and option pricing.
\newblock \emph{European Finance Review}, 2\penalty0 (1):\penalty0 79--105,
1998.
\bibitem[Dodge(2004)]{dodge2004statistique}
Yadolah Dodge.
\newblock \emph{Statistique: Dictionnaire Encyclop{\'e}dique}.
\newblock Springer Verlag France, 2004.
\bibitem[Epps(2007)]{epps2007pricing}
Thomas~W Epps.
\newblock \emph{Pricing Derivative Securities}.
\newblock World Scientific Publishing Company Incorporated, 2007.
\bibitem[Epps et Pulley(1983)]{epps1983test}
Thomas~W Epps et Lawrence~B Pulley.
\newblock A test for normality based on the empirical characteristic function.
\newblock \emph{Biometrika}, 70\penalty0 (3):\penalty0 723--726, 1983.
\bibitem[Everitt et Skrondal(2006)]{everitt2006cambridge}
Brian Everitt et Anders Skrondal.
\newblock \emph{The Cambridge Dictionary Of Statistics}, volume~4.
\newblock Cambridge University Press Cambridge, 2006.
\bibitem[Fama et French(1993)]{fama1993common}
Eugene~F Fama et Kenneth~R French.
\newblock Common risk factors in the returns on stocks and bonds.
\newblock \emph{Journal Of Financial Economics}, 33\penalty0 (1):\penalty0
3--56, 1993.
\bibitem[Feuerverger et McDunnough(1981)]{feuerverger1981efficiency}
Andrey Feuerverger et Philip McDunnough.
\newblock On the efficiency of empirical characteristic function procedures.
\newblock \emph{Journal Of The Royal Statistical Society. Series B
(methodological)}, pages 20--27, 1981.
\bibitem[Fox et Taqqu(1986)]{fox1986large}
Robert Fox et Murad~S Taqqu.
\newblock Large-sample properties of parameter estimates for strongly dependent
stationary gaussian time series.
\newblock \emph{The Annals of Statistics}, 14\penalty0 (2):\penalty0 517--532,
1986.
\bibitem[Gil-Pelaez(1951)]{gil1951note}
J~Gil-Pelaez.
\newblock Note on the inversion theorem.
\newblock \emph{Biometrika}, 38\penalty0 (3-4):\penalty0 481--482, 1951.
\bibitem[Gourieroux et Monfort(1989)]{gourieroux1989statistique}
Christian Gourieroux et Alain Monfort.
\newblock \emph{Statistique Et Mod{\`e}les {\'E}conom{\'e}triques: Notions
G{\'e}n{\'e}rales, Estimation, Pr{\'e}vision, Algorithmes}, volume~1.
\newblock Economica, 1989.
\bibitem[Hall(2005)]{hall2005generalized}
Alastair~R Hall.
\newblock \emph{Generalized Method Of Moments}.
\newblock Oxford University Press Oxford, 2005.
\bibitem[Hamilton(1994)]{hamilton1994time}
James~Douglas Hamilton.
\newblock \emph{Time Series Analysis}, volume~2.
\newblock Cambridge University Press, 1994.
\bibitem[Hansen(1982)]{hansen1982large}
Lars~Peter Hansen.
\newblock Large sample properties of generalized method of moments estimators.
\newblock \emph{Econometrica: Journal Of The Econometric Society}, pages
1029--1054, 1982.
\bibitem[Henze(1990)]{henze1990approximation}
N~Henze.
\newblock An approximation to the limit distribution of the epps-pulley test
statistic for normality.
\newblock \emph{Metrika}, 37\penalty0 (1):\penalty0 7--18, 1990.
\bibitem[Heston(1993)]{heston1993closed}
Steven~L Heston.
\newblock A closed-form solution for options with stochastic volatility with
applications to bond and currency options.
\newblock \emph{Review Of Financial Studies}, 6\penalty0 (2):\penalty0
327--343, 1993.
\bibitem[Hinkley et Revankar(1977)]{hinkley1977estimation}
David~V Hinkley et Nagesh~S Revankar.
\newblock Estimation of the pareto law from underreported data: A further
analysis.
\newblock \emph{Journal Of Econometrics}, 5\penalty0 (1):\penalty0 1--11, 1977.
\bibitem[Hogg et Craig(1978)]{hogg1978introduction}
R.V. Hogg et A.T. Craig.
\newblock \emph{Introduction To Mathematical Statistics}.
\newblock Macmillan, 1978.
\newblock ISBN 9780029789902.
\bibitem[Itkin(2005)]{itkin2005pricing}
Andrey Itkin.
\newblock Pricing options with vg model using fft.
\newblock \emph{arXiv preprint physics/0503137}, 2005.
\bibitem[Jingbo~Wang et Marsaglia(2003)]{wang2003evaluating}
Wai Wan~Tsang Jingbo~Wang et George Marsaglia.
\newblock Evaluating kolmogorov's distribution.
\newblock \emph{Journal of Statistical Software}, 8\penalty0 (18):\penalty0
1--4, 2003.
\bibitem[Kotz et~al.(2001)Kotz, Kozubowski, et Podg{\'o}rski]{kotz2001laplace}
S.~Kotz, T.J. Kozubowski, et K.~Podg{\'o}rski.
\newblock \emph{The Laplace Distribution And Generalizations: A Revisit With
Applications To Communications, Exonomics, Engineering, And Finance}.
\newblock Progress in Mathematics Series. Birkh{\"a}user, 2001.
\newblock ISBN 9780817641665.
\bibitem[Koutrouvelis(1980)]{KOUTROUVELIS01011980}
I.~A. Koutrouvelis.
\newblock {A Goodness-Of-Fit Test Of Simple Hypotheses Based On The Empirical
Characteristic Function}.
\newblock \emph{Biometrika}, 67\penalty0 (1):\penalty0 238--240, 1980.
\newblock \doi{10.1093/biomet/67.1.238}.
\bibitem[Kozubowski et Podg{\'o}rski(1999)]{kozubowski1999class}
Tomasz~J Kozubowski et Krzysztof Podg{\'o}rski.
\newblock A class of asymmetric distributions.
\newblock \emph{Actuarial Research Clearing House}, 1:\penalty0 113--134, 1999.
\bibitem[Kozubowski et Podg{\'o}rski(2001)]{kozubowski2001asymmetric}
Tomasz~J Kozubowski et Krzysztof Podg{\'o}rski.
\newblock Asymmetric laplace laws and modeling financial data.
\newblock \emph{Mathematical And Computer Modeling}, 34\penalty0 (9):\penalty0
1003--1021, 2001.
\bibitem[Kyprianou(2007)]{kyprianou2007introductory}
Andreas~E Kyprianou.
\newblock \emph{Introductory Lectures On Fluctuations Of L{\'e}Vy Processes
With Applications}.
\newblock Springer, 2007.
\bibitem[Lugannani et Rice(1980)]{lugannani1980saddle}
Robert Lugannani et Stephen Rice.
\newblock Saddle point approximation for the distribution of the sum of
independent random variables.
\newblock \emph{Advances In Applied Probability}, pages 475--490, 1980.
\bibitem[Lukacs(1960)]{lukacs1960characteristic}
Eugene Lukacs.
\newblock \emph{Characteristic Functions}, volume~4.
\newblock Griffin London, 1960.
\bibitem[Luong et Thompson(1987)]{luong1987minimum}
Andrew Luong et Mary~E. Thompson.
\newblock Minimum-distance methods based on quadratic distances for transforms.
\newblock \emph{Canadian Journal of Statistics}, 15\penalty0 (3):\penalty0
239--251, 1987.
\bibitem[Madan et Seneta(1990)]{madan1990variance}
Dilip~B Madan et Eugene Seneta.
\newblock The variance gamma model for share market returns.
\newblock \emph{Journal Of Business}, pages 511--524, 1990.
\bibitem[Mandelbrot(1963)]{mandelbrot1963variation}
Benoit Mandelbrot.
\newblock The variation of certain speculative prices.
\newblock \emph{Journal Of Business}, pages 394--419, 1963.
\bibitem[Merton(1976)]{merton1976option}
Robert~C Merton.
\newblock Option pricing when underlying stock returns are discontinuous.
\newblock \emph{Journal Of Financial Economics}, 3\penalty0 (1):\penalty0
125--144, 1976.
\bibitem[Mitchell(1916)]{mitchell1916critique}
Wesley~C Mitchell.
\newblock A critique of index numbers of the prices of stocks.
\newblock \emph{The Journal Of Political Economy}, pages 625--693, 1916.
\bibitem[Newey et McFadden(1994)]{newey1994large}
Whitney~K Newey et Daniel McFadden.
\newblock Large sample estimation and hypothesis testing.
\newblock \emph{Handbook Of Econometrics}, 4:\penalty0 2111--2245, 1994.
\bibitem[Newey et West(1987)]{newey1987hypothesis}
Whitney~K Newey et Kenneth~D West.
\newblock Hypothesis testing with efficient method of moments estimation.
\newblock \emph{International Economic Review}, 28\penalty0 (3):\penalty0
777--787, 1987.
\bibitem[O.E.E. 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. Cambridge University
Press, 1999.
\newblock ISBN 9780521553025.
\bibitem[Schoutens(2003)]{schoutens2003levy}
Wim Schoutens.
\newblock \emph{L{\'e}vy Processes In Finance}.
\newblock Wiley, 2003.
\bibitem[Scott et Dong(2012)]{RpackageVarianceGamma}
David Scott et Christine~Yang Dong.
\newblock \emph{{Variancegamma: The Variance Gamma Distribution}}, 2012.
\newblock URL \url{http://CRAN.R-project.org/package=VarianceGamma}.
\newblock R package version 0.3-1.
\bibitem[Seneta(2004)]{seneta2004fitting}
Eugene Seneta.
\newblock Fitting the variance-gamma model to financial data.
\newblock \emph{Journal Of Applied Probability}, pages 177--187, 2004.
\bibitem[Shapiro et Wilk(1965)]{shapiro1965analysis}
Samuel~Sanford Shapiro et Martin~B Wilk.
\newblock An analysis of variance test for normality (complete samples).
\newblock \emph{Biometrika}, 52\penalty0 (3/4):\penalty0 591--611, 1965.
\bibitem[Shephard(1991)]{shephard1991characteristic}
Neil~G Shephard.
\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.
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A level-1 auxiliary file: annexe3.aux
A level-1 auxiliary file: deed.aux
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\contentsline {figure}{\numberline {1.1}{\ignorespaces Mod\IeC {\`e}le de Bachelier: probabilit\IeC {\'e} compos\IeC {\'e}e\relax }}{8}{figure.caption.12}
\contentsline {figure}{\numberline {1.2}{\ignorespaces Distribution des rendements annuels de 40 titres boursiers, de 1890 \IeC {\`a} 1915, Table XVIII de \cite {mitchell1916critique}\relax }}{10}{figure.caption.13}
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\contentsline {figure}{\numberline {2.1}{\ignorespaces Premier incr\IeC {\'e}ment d'un processus subordonn\IeC {\'e}\relax }}{23}{figure.caption.16}
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\contentsline {figure}{\numberline {2.3}{\ignorespaces Fonction de densit\IeC {\'e} de la distribution Laplace asym\IeC {\'e}trique g\IeC {\'e}n\IeC {\'e}ralis\IeC {\'e}e avec diff\IeC {\'e}rents param\IeC {\`e}tres: $GAL(y;\theta ,\sigma ,\kappa ,\tau )$\relax }}{31}{figure.caption.19}
\contentsline {figure}{\numberline {2.4}{\ignorespaces Histogramme et estimateur de densit\IeC {\'e} par noyau de 2500 r\IeC {\'e}alisations de la variable al\IeC {\'e}atoire $Y\sim GAL(\theta =0,\sigma =1,\kappa =2,\tau =1)$\relax }}{34}{figure.caption.20}
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\contentsline {figure}{\numberline {9.1}{\ignorespaces Repr\IeC {\'e}sentation en s\IeC {\'e}rie chronologique de l'\IeC {\'e}chantillon $R_1$\relax }}{98}{figure.caption.28}
\contentsline {figure}{\numberline {9.2}{\ignorespaces Distribution de la variable al\IeC {\'e}atoire $R_1$\relax }}{99}{figure.caption.31}
\contentsline {figure}{\numberline {9.3}{\ignorespaces Graphique Quantile-Quantile\relax }}{100}{figure.caption.33}
\contentsline {figure}{\numberline {9.4}{\ignorespaces \IeC {\'E}quation du point de selle pour $r=0.01$\relax }}{104}{figure.caption.37}
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\contentsline {table}{\numberline {1.2}{\ignorespaces Respect des conditions \IeC {\'e}mises par Madan et Seneta pour les diff\IeC {\'e}rents mod\IeC {\`e}les pr\IeC {\'e}sent\IeC {\'e}s\relax }}{17}{table.caption.15}
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\contentsline {table}{\numberline {6.1}{\ignorespaces Contraintes lin\IeC {\'e}aires pour les cas particuliers de la distribution de Laplace asym\IeC {\'e}trique g\IeC {\'e}n\IeC {\'e}ralis\IeC {\'e}e $GAL(\theta ,\sigma ,\mu ,\tau )$\relax }}{77}{table.caption.27}
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\contentsline {table}{\numberline {9.1}{\ignorespaces Statistiques 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}
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\contentsline {table}{\numberline {9.11}{\ignorespaces Test du $\chi ^2$\relax }}{108}{table.caption.44}
\contentsline {table}{\numberline {9.12}{\ignorespaces Test de Kolmogorov-Smirnov\relax }}{108}{table.caption.45}
\contentsline {table}{\numberline {9.13}{\ignorespaces Test de distance minimale bas\IeC {\'e} sur la fonction g\IeC {\'e}n\IeC {\'e}ratrice des moments\relax }}{109}{table.caption.46}
\contentsline {table}{\numberline {9.14}{\ignorespaces Caract\IeC {\'e}ristiques de l'option\relax }}{109}{table.caption.47}
\contentsline {table}{\numberline {9.15}{\ignorespaces Param\IeC {\`e}tres neutres au risque\relax }}{109}{table.caption.48}
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\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}

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\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

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\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}

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@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 = {Kendalls 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}
}

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