Projet de lecture dirigée portant sur l'estimation des modèles de taux d'intérêts basés sur des processus stochastiques. En collaboration avec mon superviseur de mémoire Andrew Luong.
You can not select more than 25 topics Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.

rapport.aux 9.0KB

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109
  1. \relax
  2. \catcode`:\active
  3. \catcode`;\active
  4. \catcode`!\active
  5. \catcode`?\active
  6. \providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
  7. \HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
  8. \global\let\oldcontentsline\contentsline
  9. \gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
  10. \global\let\oldnewlabel\newlabel
  11. \gdef\newlabel#1#2{\newlabelxx{#1}#2}
  12. \gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
  13. \AtEndDocument{\ifx\hyper@anchor\@undefined
  14. \let\contentsline\oldcontentsline
  15. \let\newlabel\oldnewlabel
  16. \fi}
  17. \fi}
  18. \global\let\hyper@last\relax
  19. \gdef\HyperFirstAtBeginDocument#1{#1}
  20. \providecommand\HyField@AuxAddToFields[1]{}
  21. \select@language{french}
  22. \@writefile{toc}{\select@language{french}}
  23. \@writefile{lof}{\select@language{french}}
  24. \@writefile{lot}{\select@language{french}}
  25. \citation{james2000interest}
  26. \citation{lai2008statistical}
  27. \@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{3}{section.1}}
  28. \@writefile{toc}{\contentsline {section}{\numberline {2}Courbes param\IeC {\'e}triques}{4}{section.2}}
  29. \@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Survol de la m\IeC {\'e}thode et utilisation}{4}{subsection.2.1}}
  30. \@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Courbe de Nelson-Siegel}{4}{subsection.2.2}}
  31. \@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Analyse empirique}{5}{subsection.2.3}}
  32. \@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Conclusion}{9}{subsection.2.4}}
  33. \@writefile{toc}{\contentsline {section}{\numberline {3}Analyse de composantes principales}{10}{section.3}}
  34. \@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Survol de la m\IeC {\'e}thode et utilisation}{10}{subsection.3.1}}
  35. \@writefile{toc}{\contentsline {paragraph}{Diff\IeC {\'e}renciation}{10}{section*.2}}
  36. \@writefile{toc}{\contentsline {paragraph}{Matrice de variance-covariance}{10}{section*.3}}
  37. \@writefile{toc}{\contentsline {paragraph}{Valeurs et vecteurs propres}{10}{section*.4}}
  38. \@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Analyse empirique}{11}{subsection.3.2}}
  39. \@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.1}Approche avec covariances}{12}{subsubsection.3.2.1}}
  40. \@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.2}Approche avec corr\IeC {\'e}lation}{13}{subsubsection.3.2.2}}
  41. \@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.3}Comparaison des deux approches}{14}{subsubsection.3.2.3}}
  42. \@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.4}Volatilit\IeC {\'e} expliqu\IeC {\'e}e par composante (score)}{14}{subsubsection.3.2.4}}
  43. \@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Conclusion}{15}{subsection.3.3}}
  44. \@writefile{toc}{\contentsline {section}{\numberline {4}M\IeC {\'e}thode des moments}{16}{section.4}}
  45. \@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Description de la m\IeC {\'e}thode}{16}{subsection.4.1}}
  46. \@writefile{toc}{\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}}
  47. \@writefile{toc}{\contentsline {paragraph}{Mod\IeC {\`e}le de Vasicek}{16}{section*.5}}
  48. \newlabel{eq:vasicek}{{1}{16}{Modèle de Vasicek\relax }{equation.4.1}{}}
  49. \@writefile{toc}{\contentsline {paragraph}{Mod\IeC {\`e}le de Cox, Ingersoll et Ross}{17}{section*.6}}
  50. \newlabel{eq:CIR}{{2}{17}{Modèle de Cox, Ingersoll et Ross\relax }{equation.4.2}{}}
  51. \@writefile{toc}{\contentsline {paragraph}{Mod\IeC {\`e}le de Chan, Karolyi, Longstaff et Sanders}{17}{section*.7}}
  52. \newlabel{eq:CKLS}{{3}{17}{Modèle de Chan, Karolyi, Longstaff et Sanders\relax }{equation.4.3}{}}
  53. \@writefile{toc}{\contentsline {subsection}{\numberline {4.3}Discr\IeC {\'e}tisation}{18}{subsection.4.3}}
  54. \newlabel{eq:discretisationCKLS}{{4}{18}{Discrétisation\relax }{equation.4.4}{}}
  55. \@writefile{toc}{\contentsline {subsection}{\numberline {4.4}Conditions de moments utilis\IeC {\'e}s}{18}{subsection.4.4}}
  56. \newlabel{eq:moments1}{{5}{18}{Conditions de moments utilisés\relax }{equation.4.5}{}}
  57. \newlabel{eq:moments2}{{6}{18}{Conditions de moments utilisés\relax }{equation.4.5}{}}
  58. \newlabel{eq:momentscr1}{{7}{18}{Conditions de moments utilisés\relax }{equation.4.7}{}}
  59. \newlabel{eq:momentscr2}{{8}{18}{Conditions de moments utilisés\relax }{equation.4.7}{}}
  60. \citation{Newey_West_1987}
  61. \newlabel{eq:momentsemp1}{{9}{19}{Conditions de moments utilisés\relax }{equation.4.9}{}}
  62. \newlabel{eq:momentsemp2}{{10}{19}{Conditions de moments utilisés\relax }{equation.4.9}{}}
  63. \newlabel{eq:momentsemp3}{{11}{19}{Conditions de moments utilisés\relax }{equation.4.9}{}}
  64. \newlabel{eq:momentsemp4}{{12}{19}{Conditions de moments utilisés\relax }{equation.4.9}{}}
  65. \newlabel{eq:objectif1}{{13}{19}{Conditions de moments utilisés\relax }{equation.4.13}{}}
  66. \newlabel{eq:objectif2}{{14}{19}{Conditions de moments utilisés\relax }{equation.4.14}{}}
  67. \newlabel{eq:omega0}{{15}{19}{Conditions de moments utilisés\relax }{equation.4.15}{}}
  68. \@writefile{toc}{\contentsline {subsection}{\numberline {4.5}Matrice de pond\IeC {\'e}ration de Newey-West}{19}{subsection.4.5}}
  69. \newlabel{eq:neweywest}{{16}{19}{Matrice de pondération de Newey-West\relax }{equation.4.16}{}}
  70. \newlabel{eq:neweywestac}{{17}{19}{Matrice de pondération de Newey-West\relax }{equation.4.16}{}}
  71. \@writefile{toc}{\contentsline {subsection}{\numberline {4.6}Jacobien des moments}{21}{subsection.4.6}}
  72. \@writefile{toc}{\contentsline {subsection}{\numberline {4.7}Statistique de Student (t)}{22}{subsection.4.7}}
  73. \newlabel{eq:varparam}{{18}{22}{Statistique de Student (t)\relax }{equation.4.18}{}}
  74. \@writefile{toc}{\contentsline {subsection}{\numberline {4.8}Donn\IeC {\'e}es utilis\IeC {\'e}es}{23}{subsection.4.8}}
  75. \@writefile{toc}{\contentsline {subsection}{\numberline {4.9}Applications}{24}{subsection.4.9}}
  76. \@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Mod\IeC {\`e}le CKLS estim\IeC {\'e} avec GMM}}{24}{table.1}}
  77. \@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Mod\IeC {\`e}le Vasicek estim\IeC {\'e} avec GMM}}{24}{table.2}}
  78. \@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces Mod\IeC {\`e}le CIR estim\IeC {\'e} avec GMM}}{24}{table.3}}
  79. \@writefile{toc}{\contentsline {subsection}{\numberline {4.10}Conclusion}{24}{subsection.4.10}}
  80. \@writefile{lot}{\contentsline {table}{\numberline {4}{\ignorespaces Matrice de Var-Cov des par. pour mod\IeC {\`e}le CKLS avec GMM}}{25}{table.4}}
  81. \@writefile{lot}{\contentsline {table}{\numberline {5}{\ignorespaces Matrice de Var-Cov des par. pour mod\IeC {\`e}le Vasicek avec GMM}}{25}{table.5}}
  82. \@writefile{toc}{\contentsline {section}{\numberline {5}M\IeC {\'e}thode du maximum de vraisemblance}{25}{section.5}}
  83. \@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Description de la m\IeC {\'e}thode}{25}{subsection.5.1}}
  84. \@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Application au mod\IeC {\`e}le de Vasicek}{25}{subsection.5.2}}
  85. \newlabel{eq:distVas}{{19}{25}{Application au modèle de Vasicek\relax }{equation.5.19}{}}
  86. \newlabel{eq:objVas}{{20}{25}{Application au modèle de Vasicek\relax }{equation.5.20}{}}
  87. \@writefile{lot}{\contentsline {table}{\numberline {6}{\ignorespaces Matrice de Var-Cov des par. pour mod\IeC {\`e}le CIR avec GMM}}{26}{table.6}}
  88. \@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Application au mod\IeC {\`e}le CIR}{26}{subsection.5.3}}
  89. \newlabel{eq:distCIR}{{21}{26}{Application au modèle CIR\relax }{equation.5.21}{}}
  90. \newlabel{eq:chisqCIR}{{22}{26}{Application au modèle CIR\relax }{equation.5.22}{}}
  91. \newlabel{eq:objCIR}{{23}{26}{Application au modèle CIR\relax }{equation.5.23}{}}
  92. \@writefile{toc}{\contentsline {subsection}{\numberline {5.4}Application au mod\IeC {\`e}le CIR avec approximation normale}{27}{subsection.5.4}}
  93. \@writefile{toc}{\contentsline {subsection}{\numberline {5.5}Analyse empirique}{27}{subsection.5.5}}
  94. \@writefile{lot}{\contentsline {table}{\numberline {7}{\ignorespaces Param\IeC {\`e}tres estim\IeC {\'e}s par maximum de vraiemblance pour 2 mod\IeC {\`e}les}}{27}{table.7}}
  95. \newlabel{tab:estimParam}{{7}{27}{Paramètres estimés par maximum de vraiemblance pour 2 modèles\relax }{table.7}{}}
  96. \@writefile{toc}{\contentsline {subsection}{\numberline {5.6}Conclusion}{27}{subsection.5.6}}
  97. \bibdata{biblio}
  98. \bibcite{james2000interest}{1}
  99. \bibcite{lai2008statistical}{2}
  100. \bibcite{Newey_West_1987}{3}
  101. \bibstyle{plain}
  102. \@writefile{toc}{\contentsline {section}{\numberline {6}Bibliographie}{28}{section.6}}
  103. \@writefile{toc}{\contentsline {section}{\numberline {7}Annexes}{29}{section.7}}
  104. \@writefile{toc}{\contentsline {subsection}{\numberline {7.1}Fichier source R pour courbes de Nelson Siegel}{29}{subsection.7.1}}
  105. \@writefile{toc}{\contentsline {subsection}{\numberline {7.2}Fichier source R pour PCA}{30}{subsection.7.2}}
  106. \@writefile{toc}{\contentsline {subsection}{\numberline {7.3}Fichiers source R pour MMG}{33}{subsection.7.3}}
  107. \@writefile{toc}{\contentsline {subsubsection}{\numberline {7.3.1}Fonctions}{33}{subsubsection.7.3.1}}
  108. \@writefile{toc}{\contentsline {subsubsection}{\numberline {7.3.2}Fichier d'ex\IeC {\'e}cution}{39}{subsubsection.7.3.2}}
  109. \@writefile{toc}{\contentsline {subsection}{\numberline {7.4}Fichiers source R pour EMV}{41}{subsection.7.4}}