diff --git a/memoire/annexe1.tex b/memoire/annexe1.tex index 17efb4c..2e3ba1f 100644 --- a/memoire/annexe1.tex +++ b/memoire/annexe1.tex @@ -66,7 +66,7 @@ d'un opérateur intégral, ou à noyau, sur la fonction de densité. Certaines d'entre elles permettent de déterminer entièrement leur distribution. Parmi celles-ci, on retrouve la fonction caractéristique -et les fonctions génératrice des moments et des cumulants, qui sont +et les fonctions génératrices des moments et des cumulants, qui sont les plus couramment utilisées. Certaines transformées permettent de modifier la distribution d'une @@ -226,7 +226,7 @@ distribuées, la fonction caractéristique de $Z$ est la $n^e$ puissance de celle de $X$: \begin{equation} \label{eq:convocaractIID} - \phi_{Z}(s) = \phi_{X_1+\ldots+X_n}(s) = \left[\phi_{X_i}(s)\right]^n. + \phi_{Z}(s) = \phi_{X_1+\ldots+X_n}(s) = \left[\phi_{X}(s)\right]^n. \end{equation} Cette fonction est donc une solution de rechange intéressante à @@ -467,7 +467,7 @@ cas, $N(t,dx)$ est une mesure aléatoire de Poisson. On considère les processus de Lévy $\lbrace X(t) \rbrace$ et $\lbrace Z(t) \rbrace$. Celui qui suit est défini comme étant un processus -subordonné et aussi un processus de Lévy, comme le démontre +subordonné et aussi un processus de Lévy, comme le démontrent \cite{sato1999levy} et \cite{schoutens2003levy}: \begin{equation} \label{eq:processussubordonne} @@ -540,7 +540,8 @@ inférieure ou égale à $g(x)$: g(x). \end{align} -Alors, la fonction $f$ est intégrable. +Alors, la fonction $f$ est intégrable dans l'intervalle +$\mathit{I}$. \subsection{Théorème de Fubini} \label{sec:theoreme-de-fubini} diff --git a/memoire/annexe2.tex b/memoire/annexe2.tex index 2fd1dcd..7d80845 100644 --- a/memoire/annexe2.tex +++ b/memoire/annexe2.tex @@ -78,7 +78,7 @@ vers une variable aléatoire de distribution normale multivariée centrée de matrice de variance-covariance $\mathbf{\Sigma}$: \begin{align} \label{eq:TCLmulti2} - \sqrt{T}\left(\mathbf{Y}_T - \mu\right)\ \stackrel{L}{\rightarrow}\ + \sqrt{T}\left(\mathbf{Y}_T - \boldsymbol{\mu}\right)\ \stackrel{L}{\rightarrow}\ \mathcal{N}_k(0,\mathbf{\Sigma}) \end{align} diff --git a/memoire/chapitre1.tex b/memoire/chapitre1.tex index 5b8aed5..10db086 100644 --- a/memoire/chapitre1.tex +++ b/memoire/chapitre1.tex @@ -119,7 +119,7 @@ retrouver dans le code source. On considère entre autres des erreurs d'arrondissement, de logique et de clarté du code, ainsi que des particularités du matériel qui n'auraient pas été prises en compte par le programmeur. Ces erreurs peuvent être difficiles à détecter, c'est -pourquoi un grand nombre de tests devrait être effectués avant de +pourquoi un grand nombre de tests devraient être effectués avant de publier un logiciel de modélisation financière. \section{Les rendements financiers} @@ -425,7 +425,7 @@ rendements financiers devrait posséder: temps. \end{enumerate} -La famille de distributions L stable semble être celle qui répond le +La famille de distributions L stables semble être celle qui répond le mieux à l'ensemble de ces conditions \citep{walterlevy}. L'équation suivante définit la propriété de L-stabilité de la distribution de la variable aléatoire des rendements sur une période $R$: @@ -442,11 +442,11 @@ la forme suivante: \left[1+\frac{i\beta \xi}{|\xi|} \tan{\frac{\alpha\pi}{2}} \right]. \end{align} -Le domaine et le rôle des paramètres de la distribution L stable est -décrit à la table \ref{tab:roleparam}. La flexibilité apportée par les +Le domaine et le rôle des paramètres de la distribution L stable sont +décrits à la table \ref{tab:roleparam}. La flexibilité apportée par les quatre paramètres permet de remplir les quatre conditions établies au début de cette section. De plus, l'absence, dans la majorité des cas, -de moments finis d'ordre supérieur à l'espérance, permet de tenir +de moments finis d'ordre supérieur à l'espérance permet de tenir compte du mouvement erratique des prix et ainsi produire de larges discontinuités de son processus. Elle permet aussi d'expliquer l'apparence de corrélation sérielle, en considérant une probabilité diff --git a/memoire/chapitre2.tex b/memoire/chapitre2.tex index a6963ed..a6fa87e 100644 --- a/memoire/chapitre2.tex +++ b/memoire/chapitre2.tex @@ -46,7 +46,7 @@ stationnaires. Cependant, la plupart des caractéristiques diffèrent: \begin{itemize} \item Discontinuité des trajectoires (processus de sauts); \item Distribution asymétrique des accroissements; -\item Paramètre d'échelle et de temps entièrement dissociés. +\item Paramètres d'échelle et de temps entièrement dissociés. \end{itemize} Enfin, il possède une représentation alternative qui n'implique aucun @@ -125,7 +125,7 @@ Cette distribution est définie par la fonction de densité $f_{\mu,\sigma}(x)$ et la fonction caractéristique $\phi_{\mu,\sigma}(\xi)$: \begin{align} - f_{\mu,\sigma}(x) &= \frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left\{\frac{1}{2} \left(\frac{x-\mu}{\sigma} \right)^2\right\}} \label{eq:fndensitenormale} \\ + f_{\mu,\sigma}(x) &= \frac{1}{\sqrt{2\pi\sigma^2}}\exp{-\left\{\frac{1}{2} \left(\frac{x-\mu}{\sigma} \right)^2\right\}} \label{eq:fndensitenormale} \\ \phi_{\mu,\sigma}(\xi) &= \exp\left\{ i\mu\xi-\frac{\sigma^2\xi^2}{2} \right\} \label{eq:fncaractnormale}. diff --git a/memoire/chapitre4.tex b/memoire/chapitre4.tex index 7debc62..8dba1fa 100644 --- a/memoire/chapitre4.tex +++ b/memoire/chapitre4.tex @@ -17,11 +17,11 @@ suivant une distribution particulière. Le vecteur de paramètres de celle-ci, $\theta$, de longueur $a$, appartenant à l'espace $\Omega \subset \mathbb{R}^a$, doit être estimé à partir de l'échantillon. Une première approche consiste à maximiser la fonction de vraisemblance -$LL(\theta;\mathbf{y})$, qui équivaut au produit de la densité +$L(\theta;\mathbf{y})$, qui équivaut au produit de la densité $f(y;\theta)$ évaluée à chacune des réalisations $y(t)$: \begin{align} \label{eq:vraisemblance} - LL(\theta;\mathbf{y}) = \prod_{t=1}^T + L(\theta;\mathbf{y}) = \prod_{t=1}^T f(y(t);\theta),\quad\theta\in\Omega. \end{align} @@ -872,12 +872,12 @@ que la somme de deux variables aléatoires normales l'est aussi: E\left[\sqrt{T}\left(\hat\theta - \tilde\theta\right) \right] &= E\left[\sqrt{T}\left(\hat\theta - \theta_0\right) \right] - E\left[\sqrt{T}\left(\tilde\theta - \theta_0\right) \right]\nonumber\\ - &= \theta_0 - \theta_0 \nonumber\\ + &= 0 - 0 \nonumber\\ &= 0 \\ V\left[\sqrt{T}\left(\hat\theta - \tilde\theta\right) \right] &= - V\left[\sqrt{T}\left(\hat\theta - \theta_0\right) \right] - - V\left[\sqrt{T}\left(\tilde\theta - \theta_0\right) \right]\nonumber\\ - &= \left(I-(I-P)\right)\mathcal{J}_0^{-1}\nonumber\\ + V\left[\sqrt{T}\left(\hat\theta - \theta_0\right) \right] + + V\left[\sqrt{T}\left(\theta_0 - \tilde\theta\right) \right]\nonumber\\ + &= \left(I+(P-I)\right)\mathcal{J}_0^{-1}\nonumber\\ &= P\mathcal{J}_0^{-1}. \end{align} diff --git a/memoire/chapitre6.tex b/memoire/chapitre6.tex index 257592e..639d1a2 100644 --- a/memoire/chapitre6.tex +++ b/memoire/chapitre6.tex @@ -180,9 +180,12 @@ où \subsection{Variance-covariance des paramètres} On obtient la variance-covariance asymptotique des paramètres à partir -de la variance-covariance associée aux conditions de moment, en -utilisant la méthode delta multivariée. Pour ce faire, on évalue -d'abord la valeur théorique du gradient $D(\theta)$. +de la variance-covariance associée aux conditions de moment en +utilisant la méthode delta multivariée (Annexe +\ref{sec:deltamethod}). + +Pour ce faire, on évalue d'abord la valeur +théorique du gradient $D(\theta)$: \begin{align} D(\theta) &= E \left[ \begin{array}{cc} -1 & -2\,\left( Y-\theta-\mu\,\tau\right) \\ diff --git a/memoire/chapitre8.tex b/memoire/chapitre8.tex index 2471048..bf8dd3c 100644 --- a/memoire/chapitre8.tex +++ b/memoire/chapitre8.tex @@ -19,13 +19,13 @@ En se référant à \cite{bingham2004risk}, on définit: \item Une \textbf{option d'achat (de vente) européenne} donne le \textbf{droit} d'acheter (de vendre) un actif au \textbf{prix d'exercice} $K$ au temps $T$. -\item Lorsque la valeur actuelle du titre est, par rapport au prix +\item Lorsque sa valeur actuelle est, par rapport au prix d'exercice: \begin{itemize} - \item supérieure $(S(t)>K)$, l'option est dite \textbf{dans le + \item supérieure $(S(t)>K)$, l'option d'achat est dite \textbf{dans le cours}; - \item égale $(S(t)=K)$, l'option est dite \textbf{au cours}; - \item inférieure $(S(t) \ln(S(0))$). Dans ce contexte particulier, +est hors du cours ($k > \ln(S(t))$). Dans ce contexte particulier, \cite{carr1999option} développent une formule alternative à l'équation \eqref{eq:prixoptionCarr} pour évaluer le prix de l'option d'achat : \begin{align} @@ -436,7 +436,7 @@ $\left[-K,K\right]$, le théorème de Fubini (section En remplaçant le résultat \eqref{eq:fubini-integrale-a-EPPS} dans l'équation de départ \eqref{eq:putepps-1}, on obtient ainsi une -expression particulièrement simple pour le prix de l'option d'achat: +expression particulièrement simple pour le prix de l'option de vente: \begin{align} P(S(t),K,T) &= B(t,T)K\left[\frac{1}{2}-\frac{1}{2\pi} \int_{-c}^c K^{-i\nu} \frac{\phi(\nu)}{\nu(i+\nu)} diff --git a/memoire/chapitre9.tex b/memoire/chapitre9.tex index 0bc0de6..67559dc 100644 --- a/memoire/chapitre9.tex +++ b/memoire/chapitre9.tex @@ -39,7 +39,7 @@ premiers moments. Minimum & -0.027500\\ 1er quartile & -0.009790\\ Médiane & -0.003260\\ - 3e Quartile & 0.006620\\ + 3e quartile & 0.006620\\ Maximum & 0.043400\\ \hline @@ -674,8 +674,8 @@ pour les méthodes des moments généralisée et de l'équation d'estimation optimale aux figures \ref{fig:prix1R1-1} et \ref{fig:prix1R1-3}. On peut facilement remarquer le manque de précision de l'approche de Carr-Madan, qui s'approche de la courbe de Black-Scholes lorsque le -titre est dans la monnaie et qui se met à osciller dès que le titre -est hors de la monnaie. Les méthodes de Epps et de Heston donnent des +titre est dans le cours et qui se met à osciller dès que le titre +est hors le cours. Les méthodes de Epps et de Heston donnent des résultats très similaires, et l'approximation du point de selle d'ordre 1 est très précise dans ce contexte. \begin{figure}[!ht] diff --git a/memoire/gabarit-maitrise.aux b/memoire/gabarit-maitrise.aux index b3da01f..ce8ea44 100644 --- a/memoire/gabarit-maitrise.aux +++ b/memoire/gabarit-maitrise.aux @@ -85,26 +85,26 @@ \bibcite{heston1993closed}{{29}{1993}{{Heston}}{{}}} \bibcite{hinkley1977estimation}{{30}{1977}{{Hinkley et Revankar}}{{}}} \bibcite{hogg1978introduction}{{31}{1978}{{Hogg et Craig}}{{}}} -\bibcite{sato1999levy}{{32}{1999}{{iti Sato}}{{}}} -\bibcite{itkin2005pricing}{{33}{2005}{{Itkin}}{{}}} -\bibcite{wang2003evaluating}{{34}{2003}{{{Jingbo Wang} et Marsaglia}}{{}}} -\bibcite{kotz2001laplace}{{35}{2001}{{Kotz et~al.}}{{Kotz, Kozubowski, et Podg{\'o}rski}}} -\bibcite{KOUTROUVELIS01011980}{{36}{1980}{{Koutrouvelis}}{{}}} -\bibcite{kozubowski1999class}{{37}{1999}{{Kozubowski et Podg{\'o}rski}}{{}}} -\bibcite{kozubowski2001asymmetric}{{38}{2001}{{Kozubowski et Podg{\'o}rski}}{{}}} -\bibcite{kyprianou2007introductory}{{39}{2007}{{Kyprianou}}{{}}} -\bibcite{lugannani1980saddle}{{40}{1980}{{Lugannani et Rice}}{{}}} -\bibcite{lukacs1960characteristic}{{41}{1960}{{Lukacs}}{{}}} -\bibcite{luong1987minimum}{{42}{1987}{{Luong et Thompson}}{{}}} -\bibcite{madan1990variance}{{43}{1990}{{Madan et Seneta}}{{}}} -\bibcite{mandelbrot1963variation}{{44}{1963}{{Mandelbrot}}{{}}} -\bibcite{merton1976option}{{45}{1976}{{Merton}}{{}}} -\bibcite{barndorff2001levy}{{46}{2001}{{Mikosch et~al.}}{{Mikosch, Resnick, et Barndorff-Nielsen}}} -\bibcite{mitchell1916critique}{{47}{1916}{{Mitchell}}{{}}} -\bibcite{newey1994large}{{48}{1994}{{Newey et McFadden}}{{}}} -\bibcite{newey1987hypothesis}{{49}{1987}{{Newey et West}}{{}}} -\bibcite{praetz1972distribution}{{50}{1972}{{Praetz}}{{}}} -\bibcite{press1967compound}{{51}{1967}{{Press}}{{}}} +\bibcite{itkin2005pricing}{{32}{2005}{{Itkin}}{{}}} +\bibcite{wang2003evaluating}{{33}{2003}{{{Jingbo Wang} et Marsaglia}}{{}}} +\bibcite{kotz2001laplace}{{34}{2001}{{Kotz et~al.}}{{Kotz, Kozubowski, et Podg{\'o}rski}}} +\bibcite{KOUTROUVELIS01011980}{{35}{1980}{{Koutrouvelis}}{{}}} +\bibcite{kozubowski1999class}{{36}{1999}{{Kozubowski et Podg{\'o}rski}}{{}}} +\bibcite{kozubowski2001asymmetric}{{37}{2001}{{Kozubowski et Podg{\'o}rski}}{{}}} +\bibcite{kyprianou2007introductory}{{38}{2007}{{Kyprianou}}{{}}} +\bibcite{lugannani1980saddle}{{39}{1980}{{Lugannani et Rice}}{{}}} +\bibcite{lukacs1960characteristic}{{40}{1960}{{Lukacs}}{{}}} +\bibcite{luong1987minimum}{{41}{1987}{{Luong et Thompson}}{{}}} +\bibcite{madan1990variance}{{42}{1990}{{Madan et Seneta}}{{}}} +\bibcite{mandelbrot1963variation}{{43}{1963}{{Mandelbrot}}{{}}} +\bibcite{merton1976option}{{44}{1976}{{Merton}}{{}}} +\bibcite{barndorff2001levy}{{45}{2001}{{Mikosch et~al.}}{{Mikosch, Resnick, et Barndorff-Nielsen}}} +\bibcite{mitchell1916critique}{{46}{1916}{{Mitchell}}{{}}} +\bibcite{newey1994large}{{47}{1994}{{Newey et McFadden}}{{}}} +\bibcite{newey1987hypothesis}{{48}{1987}{{Newey et West}}{{}}} +\bibcite{praetz1972distribution}{{49}{1972}{{Praetz}}{{}}} +\bibcite{press1967compound}{{50}{1967}{{Press}}{{}}} +\bibcite{sato1999levy}{{51}{1999}{{Sato}}{{}}} \bibcite{schoutens2003levy}{{52}{2003}{{Schoutens}}{{}}} \bibcite{RpackageVarianceGamma}{{53}{2012}{{Scott et Dong}}{{}}} \bibcite{seneta2004fitting}{{54}{2004}{{Seneta}}{{}}} diff --git a/memoire/gabarit-maitrise.bbl b/memoire/gabarit-maitrise.bbl index 63a951f..4f4b053 100644 --- a/memoire/gabarit-maitrise.bbl +++ b/memoire/gabarit-maitrise.bbl @@ -180,13 +180,6 @@ Robert~V. Hogg et Allen Craig. \newblock \emph{{I}ntroduction to {M}athematical {S}tatistics}. \newblock Macmillan, 1978. -\bibitem[iti Sato(1999)]{sato1999levy} -Ken iti Sato. -\newblock \emph{{L}{\'e}vy {P}rocesses and {I}nfinitely {D}ivisible - {D}istributions}. -\newblock Cambridge Studies in Advanced Mathematics. Cambridge University - Press, 1999. - \bibitem[Itkin(2005)]{itkin2005pricing} Andrey Itkin. \newblock {P}ricing {O}ptions with {VG} {M}odel {U}sing {FFT}. @@ -296,6 +289,13 @@ S.~James Press. \newblock {A} {C}ompound {E}vents {M}odel for {S}ecurity {P}rices. \newblock \emph{Journal of Business}, pages 317--335, 1967. +\bibitem[{Sato}(1999)]{sato1999levy} +{Ken-Iti} {Sato}. +\newblock \emph{{L}{\'e}vy {P}rocesses and {I}nfinitely {D}ivisible + {D}istributions}. +\newblock Cambridge Studies in Advanced Mathematics. Cambridge University + Press, 1999. + \bibitem[Schoutens(2003)]{schoutens2003levy} Wim Schoutens. \newblock \emph{{L}{\'e}vy {P}rocesses in {F}inance}. @@ -306,7 +306,7 @@ David Scott et Christine~Yang Dong. \newblock \emph{{{v}ariancegamma: {T}he {V}ariance {G}amma {D}istribution}}, 2012. \newblock URL \url{http://CRAN.R-project.org/package=VarianceGamma}. -\newblock R package version 0.3-1. +\newblock Consulté le 24 janvier 2014. \bibitem[Seneta(2004)]{seneta2004fitting} Eugene Seneta. @@ -339,7 +339,7 @@ Alan Stuart et J.~Keith Ord. \bibitem[Teschl(2004)]{teschl2004topics} Gerald Teschl. \newblock {T}opics in {R}eal and {F}unctional {A}nalysis. -\newblock 2004. +\newblock Consulté le 24 janvier 2014, 2004. \newblock URL \url{http://www.mat.univie.ac.at/~gerald/ftp/book-fa/index.html}. \bibitem[Walter(1995)]{walterlevy} diff --git a/memoire/gabarit-maitrise.blg b/memoire/gabarit-maitrise.blg index 645f42e..cc74c55 100644 --- a/memoire/gabarit-maitrise.blg +++ b/memoire/gabarit-maitrise.blg @@ -21,33 +21,32 @@ A level-1 auxiliary file: annexe2.aux A level-1 auxiliary file: annexe3.aux A level-1 auxiliary file: deed.aux Database file #1: memoire.bib -Warning--empty note in teschl2004topics You've used 63 entries, 2773 wiz_defined-function locations, - 966 strings with 14129 characters, -and the built_in function-call counts, 25310 in all, are: -= -- 2354 + 966 strings with 14138 characters, +and the built_in function-call counts, 25309 in all, are: += -- 2355 > -- 954 < -- 81 + -- 342 - -- 279 -* -- 1694 -:= -- 3811 +* -- 1692 +:= -- 3812 add.period$ -- 194 call.type$ -- 63 change.case$ -- 262 chr.to.int$ -- 63 -cite$ -- 127 +cite$ -- 126 duplicate$ -- 1372 empty$ -- 2353 format.name$ -- 390 -if$ -- 5428 +if$ -- 5429 int.to.chr$ -- 1 int.to.str$ -- 1 missing$ -- 80 newline$ -- 325 num.names$ -- 252 -pop$ -- 593 +pop$ -- 592 preamble$ -- 1 purify$ -- 219 quote$ -- 0 @@ -59,8 +58,7 @@ text.length$ -- 21 text.prefix$ -- 0 top$ -- 0 type$ -- 593 -warning$ -- 1 +warning$ -- 0 while$ -- 279 width$ -- 0 -write$ -- 815 -(There was 1 warning) +write$ -- 816 diff --git a/memoire/gabarit-maitrise.log b/memoire/gabarit-maitrise.log index 17c0a61..9a3e882 100644 --- a/memoire/gabarit-maitrise.log +++ b/memoire/gabarit-maitrise.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/Debian) (format=pdflatex 2013.11.30) 18 JAN 2014 11:16 +This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/Debian) (format=pdflatex 2013.11.30) 24 JAN 2014 20:14 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -1969,7 +1969,7 @@ it/10.95 ; ^^[; ^^V; ^^\\OT1/cmr/m/n/10.95 )$\T1/cmr/m/n/10.95 . ] -<../graphiques/ABBEYN-chronologie.pdf, id=2152, 433.62pt x 433.62pt> +<../graphiques/ABBEYN-chronologie.pdf, id=2153, 433.62pt x 433.62pt> File: ../graphiques/ABBEYN-chronologie.pdf Graphic file (type pdf) @@ -1977,7 +1977,7 @@ Package pdftex.def Info: ../graphiques/ABBEYN-chronologie.pdf used on input lin e 21. 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Koutrouvelis", - Doi = "10.1093/biomet/67.1.238", - Journal = "{B}iometrika", - Number = 1, - Pages = "238--240", - Title = "{{A} {G}oodness-{O}f-{F}it {T}est of {S}imple {H}ypotheses {B}ased on the {E}mpirical {C}haracteristic {F}unction}", - Volume = 67, - Year = 1980 -} - -@Manual{RpackageVarianceGamma, - Author = "David Scott and Christine Yang Dong", - Note = "R package version 0.3-1", - Title = "{{v}ariancegamma: {T}he {V}ariance {G}amma {D}istribution}", - Url = "http://CRAN.R-project.org/package=VarianceGamma", - Year = 2012 -} - -@Manual{Rsoftware, - Address = "Vienna, Austria", - Author = "{R Core Team}", - Isbn = "3-900051-07-0", - Organization = "R Foundation for Statistical Computing", - Title = "{{R}: A {L}anguage and {E}nvironment for {S}tatistical {C}omputing}", - Url = "http://www.R-project.org", - Year = 2012 -} - -@Article{Singer:2009, - Author = "Sa\v{s}a Singer and John Nelder", - Doi = "10.4249/scholarpedia.2928", - Journal = "Scholarpedia", - Number = 7, - Pages = 2928, - Title = "{N}elder-{M}ead {A}lgorithm", - Volume = 4, - Year = 2009 -} - -@Book{abramowitz1965handbook, - Author = "Milton Abramowitz and Irene A. Stegun", - Publisher = "Dover Publications", - Title = "{H}andbook of {M}athematical {F}unctions: with {F}ormulas, {G}raphs, and {M}athematical {T}ables", - Volume = 55, - Year = 1965 -} - -@Article{applebaum2004levy, - Author = "David Applebaum", - Journal = "Notices of the American Mathematical Society", - Number = 11, - Pages = "1336--1347", - Title = "{L}{\'e}vy {P}rocesses: {F}rom {P}robability to {F}inance and {Q}uantum {G}roups", - Volume = 51, - Year = 2004 -} - -@Book{bachelier1900theorie, - Author = "Louis Bachelier", - Publisher = "Gauthier-Villars", - Title = "{T}h{\'e}orie de la sp{\'e}culation", - Year = 1900 -} - -@Book{barndorff2001levy, - Author = "Thomas Mikosch and Sidney I. Resnick and Ole E. Barndorff-Nielsen", - Isbn = 9780817641672, - Publisher = "Birkh{\"a}user", - Title = "{L}{\'e}vy {P}rocesses: {T}heory and {A}pplications", - Year = 2001 -} - -@Article{berkson1980minimum, - Author = "Joseph Berkson", - Journal = "the Annals of Statistics", - Pages = "457--487", - Publisher = "JSTOR", - Title = "{M}inimum {C}hi-Square, not {M}aximum {L}ikelihood!", - Year = 1980 -} - -@Book{bingham2004risk, - Author = "Nicholas H. Bingham and R{\"u}diger Kiesel", - Publisher = "Springer", - Title = "{R}isk-Neutral {V}aluation: {P}ricing and {H}edging of {F}inancial {D}erivatives", - Year = 2004 -} - -@Article{black1973pricing, - Author = "Fischer Black and Myron Scholes", - Journal = "the Journal of Political Economy", - Pages = "637--654", - Publisher = "JSTOR", - Title = "{T}he {P}ricing of {O}ptions and {C}orporate {L}iabilities", - Year = 1973 -} - -@Article{black1976pricing, - Author = "Fischer Black", - Journal = "Journal of Financial Economics", - Number = 1, - Pages = "167--179", - Publisher = "Elsevier", - Title = "{T}he {P}ricing of {C}ommodity {C}ontracts", - Volume = 3, - Year = 1976 -} - -@Article{buckle1995bayesian, - Author = "D. J. Buckle", - Journal = "Journal of the American Statistical Association", - Number = 430, - Pages = "605--613", - Publisher = "Taylor \& Francis Group", - Title = "{B}ayesian {I}nference for {S}table {D}istributions", - Volume = 90, - Year = 1995 -} - -@Book{butler2007saddlepoint, - Author = "Ronald W. Butler", - Publisher = "Cambridge University Press", - Title = "{S}addlepoint {A}pproximations with {A}pplications", - Volume = 22, - Year = 2007 -} - -@Article{carr1999option, - Author = "Peter P. Carr and Dilip B. Madan", - Journal = "Journal of Computational Finance", - Number = 4, - Pages = "61--73", - Title = "{O}ption {V}aluation {U}sing the {F}ast {F}ourier {T}ransform", - Volume = 2, - Year = 1999 -} - -@Article{crowder1986consistency, - Author = "Martin Crowder", - Journal = "Econometric theory", - Pages = "305--330", - Publisher = "JSTOR", - Title = "{O}n {C}onsistency and {I}nconsistency of {E}stimating {E}quations", - Year = 1986 -} - -@Article{crowder1987linear, - Author = "Martin Crowder", - Journal = "Biometrika", - Number = 3, - Pages = "591--597", - Publisher = "Biometrika Trust", - Title = "{O}n {L}inear and {Q}uadratic {E}stimating {F}unctions", - Volume = 74, - Year = 1987 -} - -@Article{daniels1954saddlepoint, - Author = "Henry E. Daniels", - Journal = "the Annals of Mathematical Statistics", - Pages = "631--650", - Publisher = "JSTOR", - Title = "{S}addlepoint {A}pproximations in {S}tatistics", - Year = 1954 -} - -@Article{daniels1987tail, - Author = "Henry E. 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Epps", - Publisher = "World Scientific Publishing Company incorporated", - Title = "{P}ricing {D}erivative {S}ecurities", - Year = 2007 -} - -@Book{everitt2006cambridge, - Author = "Brian Everitt and Anders Skrondal", - Publisher = "Cambridge University Press Cambridge", - Title = "{T}he {C}ambridge {D}ictionary of {S}tatistics", - Volume = 4, - Year = 2006 -} - -@Article{fama1993common, - Author = "Eugene F. Fama and Kenneth R. French", - Journal = "Journal of Financial Economics", - Number = 1, - Pages = "3--56", - Publisher = "Elsevier", - Title = "{C}ommon {R}isk {F}actors in the {R}eturns on {S}tocks and {B}onds", - Volume = 33, - Year = 1993 -} - -@Article{feuerverger1981efficiency, - Author = "Andrey Feuerverger and Philip McDunnough", - Journal = "Journal of the Royal Statistical Society. 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Gil-Pelaez", - Journal = "Biometrika", - Number = "3-4", - Pages = "481--482", - Publisher = "Biometrika Trust", - Title = "{N}ote on the {I}nversion {T}heorem", - Volume = 38, - Year = 1951 -} - -@Book{gourieroux1989statistique, - Author = "Christian Gourieroux and Alain Monfort", - Publisher = "Economica", - Title = "{S}tatistique 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 = "{G}eneralized {M}ethod of {M}oments", - Year = 2005 -} - -@Book{hamilton1994time, - Author = "James Douglas Hamilton", - Publisher = "Cambridge University Press", - Title = "{T}ime {S}eries {A}nalysis", - Volume = 2, - Year = 1994 -} - -@Article{hansen1982large, - Author = "Lars Peter Hansen", - Journal = "Econometrica: Journal of the Econometric Society", - Pages = "1029--1054", - Publisher = "JSTOR", - Title = "{L}arge {S}ample {P}roperties of {G}eneralized {M}ethod of {M}oments {E}stimators", - Year = 1982 -} - -@Article{henze1990approximation, - Author = "Norbert Henze", - Journal = "Metrika", - Number = 1, - Pages = "7--18", - Publisher = "Springer", - Title = "{A}n {A}pproximation to the {L}imit {D}istribution of the {E}pps-{P}ulley {T}est {S}tatistic for {N}ormality", - 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} {C}losed-{F}orm {S}olution for {O}ptions with {S}tochastic {V}olatility with {A}pplications to {B}ond and {C}urrency {O}ptions", - 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 = "{E}stimation of the {P}areto {L}aw from {U}nderreported {D}ata: {A} {F}urther {A}nalysis", - Volume = 5, - Year = 1977 -} - -@Book{hogg1978introduction, - Author = "Robert V. Hogg and Allen Craig", - Isbn = 9780029789902, - Publisher = "Macmillan", - Title = "{I}ntroduction to {M}athematical {S}tatistics", - Year = 1978 -} - -@Book{hull1999options, - Author = "John C. Hull", - Publisher = "Pearson Education india", - Title = "{O}ptions, {F}utures, and {O}ther {D}erivatives", - Year = 1999 -} - -@Article{itkin2005pricing, - Author = "Andrey Itkin", - Journal = "arXiv preprint physics/0503137", - Title = "{P}ricing {O}ptions with {VG} {M}odel {U}sing {FFT}", - Year = 2005 -} - -@Book{kotz2001laplace, - Author = "Samuel Kotz and Tomasz J. Kozubowski and Krzystof Podg{\'o}rski", - Isbn = 9780817641665, - Publisher = "Birkh{\"a}user", - Series = "Progress in Mathematics Series", - Title = "{T}he {L}aplace {D}istribution and {G}eneralizations: {A} {R}evisit with {A}pplications to {C}ommunications, {E}conomics, {E}ngineering, and {F}inance", - 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} {C}lass of {A}symmetric {D}istributions", - Volume = 1, - Year = 1999 -} - -@Article{kozubowski2001asymmetric, - Author = "Tomasz J. Kozubowski and Krzysztof Podg{\'o}rski", - Journal = "{M}athematical and {C}omputer {M}odeling", - Number = 9, - Pages = "1003--1021", - Publisher = "Elsevier", - Title = "{A}symmetric {L}aplace {L}aws and {M}odeling {F}inancial {D}ata", - Volume = 34, - Year = 2001 -} - -@Book{kyprianou2007introductory, - Author = "Andreas E. Kyprianou", - Publisher = "Springer", - Title = "{I}ntroductory {L}ectures on {F}luctuations of {L}{\'e}vy {P}rocesses with {A}pplications", - Year = 2007 -} - -@Article{lugannani1980saddle, - Author = "Robert Lugannani and Stephen Rice", - Journal = "Advances in Applied Probability", - Pages = "475--490", - Publisher = "JSTOR", - Title = "{S}addle {P}oint {A}pproximation for the {D}istribution of the {S}um of {I}ndependent {R}andom {V}ariables", - Year = 1980 -} - -@Book{lukacs1960characteristic, - Author = "Eugene Lukacs", - Publisher = "Griffin London", - Title = "{C}haracteristic {F}unctions", - Volume = 4, - Year = 1960 -} - -@Article{luong1987minimum, - Author = "Andrew Luong and Mary E. 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Madan", - Journal = "European Finance Review", - Number = 1, - Pages = "79--105", - Publisher = "Kluwer Academic Publishers", - Title = "{T}he {V}ariance {G}amma {P}rocess and {O}ption {P}ricing", - Volume = 2, - Year = 1998 -} - -@Article{mandelbrot1963variation, - Author = "Benoit Mandelbrot", - Journal = "Journal of Business", - Pages = "394--419", - Publisher = "University of Chicago Press", - Title = "{T}he {V}ariation of {C}ertain {S}peculative {P}rices", - Year = 1963 -} - -@Article{merton1976option, - Author = "Robert C. Merton", - Journal = "Journal of Financial Economics", - Number = 1, - Pages = "125--144", - Publisher = "Elsevier", - Title = "{O}ption {P}ricing when {U}nderlying {S}tock {R}eturns {A}re {D}iscontinuous", - Volume = 3, - Year = 1976 -} - -@Article{mitchell1916critique, - Author = "Wesley C. Mitchell", - Journal = "The Journal of Political Economy", - Pages = "625--693", - Publisher = "JSTOR", - Title = "{A} {C}ritique of {I}ndex {N}umbers of the {P}rices of {S}tocks", - Year = 1916 -} - -@Book{musiela2005martingale, - Author = "Marek Musiela and Marek Rutkowski", - Publisher = "Springer", - Title = "{M}artingale {M}ethods in {F}inancial {M}odelling", - 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 = "{H}ypothesis {T}esting with {E}fficient {M}ethod of {M}oments {E}stimation", - Volume = 28, - Year = 1987 -} - -@Article{newey1994large, - Author = "Whitney K. 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Keith Ord", - Publisher = "Oxford University Press, New York", - Title = "{K}endall{\rq}s {A}dvanced {T}heory of {S}tatistics, {V}ol. 1", - Year = 1987 -} - -@Unpublished{teschl2004topics, - Author = "Gerald Teschl", - Title = "{T}opics in {R}eal and {F}unctional {A}nalysis", - Year = 2004 -} - -@Phdthesis{torczon1989multi, - Author = "Virginia Joanne Torczon", - Title = "{M}ulti-directional {S}earch: {A} {D}irect {S}earch {A}lgorithm for {P}arallel {M}achines", - Year = 1989 -} - -@Inproceedings{walterlevy, - Author = "Christian Walter", - Booktitle = "Proceedings of the 5th AFIR colloquium", - Title = "{L}{\'e}vy-{S}tability {U}nder {A}ddition and {F}ractal {S}tructure of {M}arkets: {I}mplications for the {A}ctuaries and {E}mphasized {E}xamination of {MATIF} {N}ational {C}ontract", - Year = 1995 -} - -@Article{wang2003evaluating, - Author = "Wai Wan Tsang {Jingbo Wang} and George Marsaglia", - Journal = "Journal of Statistical Software", - Number = 18, - Pages = "1--4", - Publisher = "American Statistical Association", - Title = "{E}valuating {K}olmogorov's {D}istribution", - Volume = 8, - Year = 2003 -} - -@Article{wendel1961non, - Author = "J. G. Wendel", - Journal = "The Annals of Mathematical Statistics", - Number = 1, - Pages = "338--339", - Publisher = "institute of Mathematical Statistics", - Title = "{T}he {N}on-{A}bsolute {C}onvergence of {G}il-{P}elaez' {I}nversion {I}ntegral", - Volume = 32, - Year = 1961 -} - -@Article{wolfowitz1957minimum, - Author = "Jacob Wolfowitz", - Journal = "The Annals of Mathematical Statistics", - Pages = "75--88", - Publisher = "JSTOR", - Title = "{T}he {M}inimum {D}istance {M}ethod", - Year = 1957 -} - -@Book{wooldridge2001econometric, - Author = "Jeffrey M. Wooldridge", - Publisher = "MIT press", - Title = "{E}conometric {A}nalysis of {C}ross {S}ection and {P}anel {D}ata", - Year = 2001 -} -