48 lines
4.2 KiB
TeX
48 lines
4.2 KiB
TeX
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\select@language {french}
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\contentsline {section}{\numberline {1}Introduction}{3}{section.1}
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\contentsline {section}{\numberline {2}Courbes param\IeC {\'e}triques}{4}{section.2}
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\contentsline {subsection}{\numberline {2.1}Survol de la m\IeC {\'e}thode et utilisation}{4}{subsection.2.1}
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\contentsline {subsection}{\numberline {2.2}Courbe de Nelson-Siegel}{4}{subsection.2.2}
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\contentsline {subsection}{\numberline {2.3}Analyse empirique}{5}{subsection.2.3}
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\contentsline {subsection}{\numberline {2.4}Conclusion}{9}{subsection.2.4}
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\contentsline {section}{\numberline {3}Analyse de composantes principales}{10}{section.3}
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\contentsline {subsection}{\numberline {3.1}Survol de la m\IeC {\'e}thode et utilisation}{10}{subsection.3.1}
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\contentsline {paragraph}{Diff\IeC {\'e}renciation}{10}{section*.2}
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\contentsline {paragraph}{Matrice de variance-covariance}{10}{section*.3}
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\contentsline {paragraph}{Valeurs et vecteurs propres}{10}{section*.4}
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\contentsline {subsection}{\numberline {3.2}Analyse empirique}{11}{subsection.3.2}
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\contentsline {subsubsection}{\numberline {3.2.1}Approche avec covariances}{12}{subsubsection.3.2.1}
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\contentsline {subsubsection}{\numberline {3.2.2}Approche avec corr\IeC {\'e}lation}{13}{subsubsection.3.2.2}
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\contentsline {subsubsection}{\numberline {3.2.3}Comparaison des deux approches}{14}{subsubsection.3.2.3}
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\contentsline {subsubsection}{\numberline {3.2.4}Volatilit\IeC {\'e} expliqu\IeC {\'e}e par composante (score)}{14}{subsubsection.3.2.4}
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\contentsline {subsection}{\numberline {3.3}Conclusion}{15}{subsection.3.3}
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\contentsline {section}{\numberline {4}M\IeC {\'e}thode des moments}{16}{section.4}
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\contentsline {subsection}{\numberline {4.1}Description de la m\IeC {\'e}thode}{16}{subsection.4.1}
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\contentsline {subsection}{\numberline {4.2}Mod\IeC {\`e}les de taux d'int\IeC {\'e}r\IeC {\^e}t court-terme}{16}{subsection.4.2}
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\contentsline {paragraph}{Mod\IeC {\`e}le de Vasicek}{16}{section*.5}
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\contentsline {paragraph}{Mod\IeC {\`e}le de Cox, Ingersoll et Ross}{17}{section*.6}
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\contentsline {paragraph}{Mod\IeC {\`e}le de Chan, Karolyi, Longstaff et Sanders}{17}{section*.7}
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\contentsline {subsection}{\numberline {4.3}Discr\IeC {\'e}tisation}{18}{subsection.4.3}
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\contentsline {subsection}{\numberline {4.4}Conditions de moments utilis\IeC {\'e}s}{18}{subsection.4.4}
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\contentsline {subsection}{\numberline {4.5}Matrice de pond\IeC {\'e}ration de Newey-West}{19}{subsection.4.5}
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\contentsline {subsection}{\numberline {4.6}Jacobien des moments}{21}{subsection.4.6}
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\contentsline {subsection}{\numberline {4.7}Statistique de Student (t)}{22}{subsection.4.7}
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\contentsline {subsection}{\numberline {4.8}Donn\IeC {\'e}es utilis\IeC {\'e}es}{23}{subsection.4.8}
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\contentsline {subsection}{\numberline {4.9}Applications}{24}{subsection.4.9}
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\contentsline {subsection}{\numberline {4.10}Conclusion}{24}{subsection.4.10}
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\contentsline {section}{\numberline {5}M\IeC {\'e}thode du maximum de vraisemblance}{25}{section.5}
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\contentsline {subsection}{\numberline {5.1}Description de la m\IeC {\'e}thode}{25}{subsection.5.1}
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\contentsline {subsection}{\numberline {5.2}Application au mod\IeC {\`e}le de Vasicek}{25}{subsection.5.2}
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\contentsline {subsection}{\numberline {5.3}Application au mod\IeC {\`e}le CIR}{26}{subsection.5.3}
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\contentsline {subsection}{\numberline {5.4}Application au mod\IeC {\`e}le CIR avec approximation normale}{27}{subsection.5.4}
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\contentsline {subsection}{\numberline {5.5}Analyse empirique}{27}{subsection.5.5}
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\contentsline {subsection}{\numberline {5.6}Conclusion}{27}{subsection.5.6}
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\contentsline {section}{\numberline {6}Bibliographie}{28}{section.6}
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\contentsline {section}{\numberline {7}Annexes}{29}{section.7}
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\contentsline {subsection}{\numberline {7.1}Fichier source R pour courbes de Nelson Siegel}{29}{subsection.7.1}
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\contentsline {subsection}{\numberline {7.2}Fichier source R pour PCA}{30}{subsection.7.2}
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\contentsline {subsection}{\numberline {7.3}Fichiers source R pour MMG}{33}{subsection.7.3}
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\contentsline {subsubsection}{\numberline {7.3.1}Fonctions}{33}{subsubsection.7.3.1}
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\contentsline {subsubsection}{\numberline {7.3.2}Fichier d'ex\IeC {\'e}cution}{39}{subsubsection.7.3.2}
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\contentsline {subsection}{\numberline {7.4}Fichiers source R pour EMV}{41}{subsection.7.4}
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