{"id":12379,"date":"2023-10-06T15:25:41","date_gmt":"2023-10-06T14:25:41","guid":{"rendered":"https:\/\/www.simtrade.fr\/blog_simtrade\/?p=12379"},"modified":"2024-02-04T09:10:05","modified_gmt":"2024-02-04T09:10:05","slug":"application-theorie-valeurs-extremes-finance-marches","status":"publish","type":"post","link":"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/","title":{"rendered":"Application de la th\u00e9orie des valeurs extr\u00eames en finance de march\u00e9s"},"content":{"rendered":"<p><a href=\"https:\/\/www.linkedin.com\/in\/gabriel-filja\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" style=\"padding: 5px;\" title=\"\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2023\/10\/img_SimTrade_Photo1_Gabriel_Filja.jpg\" alt=\"Gabriel FILJA\" width=\"133\" align=\"right\" \/><\/a><\/p>\n<p>Dans cet article, <a href=\"https:\/\/www.linkedin.com\/in\/gabriel-filja\" target=\"_blank\" rel=\"noopener\">Gabriel FILJA<\/a> (ESSEC Business School, Executive Master in Senior Bank Management, 2022-2023 &amp; Head of Hedging \u00e0 Convera) pr\u00e9sente des applications de la th\u00e9orie des valeurs extr\u00eames en finance de march\u00e9s et notamment en gestion des risques de march\u00e9s.<\/p>\n<h2>Principe<\/h2>\n<p>La th\u00e9orie des valeurs extr\u00eames (TVE), appel\u00e9 th\u00e9or\u00e8me de Fisher-Tippet-Gnedenko tente de fournir une caract\u00e9risation compl\u00e8te du comportement de la queue pour tous les types de distributions de probabilit\u00e9s.<\/p>\n<p>La th\u00e9orie des valeurs extr\u00eames montre que la loi asymptotique des rentabilit\u00e9s minimale et maximale a une forme bien d\u00e9termin\u00e9e qui est largement ind\u00e9pendante du processus de rentabilit\u00e9s lui-m\u00eame (le lien entre les deux distributions appara\u00eet en particulier dans la valeur de l\u2019indice de queue qui refl\u00e8te le poids des queues de distribution). L\u2019int\u00e9r\u00eat de la TVE dans la gestion du risque c\u2019est de pouvoir calculer le quantile au-del\u00e0 de 99% du seuil de confiance dans le cadre des stress tests ou de la publication des exigences r\u00e9glementaires.<\/p>\n<p>Gnedenko a d\u00e9montr\u00e9 en 1943 par la Th\u00e9orie des valeurs extr\u00eames la propri\u00e9t\u00e9 qui s\u2019applique \u00e0 des nombreuses distributions de probabilit\u00e9s. Soit F(x) la fonction de r\u00e9partition d\u2019une variable x. u est une valeur de x situ\u00e9e dans la partie droite de la queue de distribution.<\/p>\n<p>La probabilit\u00e9 que x soit compris entre u et u+y est de F(y+u) \u2013 F(u) et la probabilit\u00e9 que x soit sup\u00e9rieur \u00e0 u est 1-F(u). Soit F<sub>u<\/sub>(y) la probabilit\u00e9 conditionnelle que x soit compris entre u et u+y sachant que x&gt;u\u2236<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2023\/10\/img_SimTrade_Probabilite_conditionnelle.png\" alt=\"Probabilit\u00e9 conditionnelle\" width=\"300\" \/><\/p>\n<h2>Estimation des param\u00e8tres<\/h2>\n<p>Selon les r\u00e9sultats de Gnedenko, pour un grand nombre de distribution, cela converge vers une distribution g\u00e9n\u00e9ralis\u00e9e de Pareto au fur et \u00e0 mesure que u augmente :<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2023\/10\/img_SimTrade_Distribution_generalisee_Pareto.png\" alt=\"Distribution_g\u00e9n\u00e9ralis\u00e9e_Pareto\" width=\"300\" \/><\/p>\n<p>\u03b2 est le param\u00e8tre d\u2019\u00e9chelle repr\u00e9sente la dispersion de la loi des extr\u00eames<br \/>\n\u03be est l\u2019indice de queue qui mesure l\u2019\u00e9paisseur de la queue et la forme<\/p>\n<p>Selon la valeur de l\u2019indice de queue, on distingue trois formes dedistribiution d\u2019extr\u00eames :<\/p>\n<ul>\n<li>Frechet \u03be &gt; 0<\/li>\n<li>Weibull \u03be &lt; 0<\/li>\n<li>Gumbel \u03be = 0<\/li>\n<\/ul>\n<p>L&#8217;indice de queue \u03be refl\u00e8te le poids des extr\u00eames dans la distribution des rentabilit\u00e9s. Une valeur positive de l&#8217;indice de queue signifie que les extr\u00eames n&#8217;ont pas de r\u00f4le important puisque la variable est born\u00e9e. Une valeur nulle donne relativement peu d&#8217;extr\u00eames alors qu&#8217;une valeur n\u00e9gative implique un grand nombre d&#8217;extr\u00eames (c\u2019est le cas de la loi normale).<\/p>\n<p style=\"text-align: center;\">Figure 1 : Densit\u00e9 des lois des valeurs extr\u00eames<br \/>\n<img decoding=\"async\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2023\/10\/img_Densite_lois_valeurs_extremes.png\" alt=\" Densit\u00e9 des lois des valeurs extr\u00eames\" width=\"500\" \/><br \/>\nSource : auteur.<\/p>\n<p style=\"text-align: center;\">Tableau 1 : Fonctions de distribution des valeurs extr\u00eames pour un \u03be &gt; 0, loi de Frechet, \u03be &lt; 0 loi de Weibull et \u03be = 0, loi de Gumbel. <img decoding=\"async\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2023\/10\/img_Fonctions_distribution_valeurs_extremes.png\" alt=\"Fonctions de distribution des valeurs extr\u00eames \" width=\"500\" \/><br \/>\nSource : auteur.<\/p>\n<p>Les param\u00e8tres \u03b2 et \u03be sont estim\u00e9s par la m\u00e9thode de maximum de vraisemblance. D\u2019abord il faut d\u00e9finir u (valeur proche du 95e centile par exemple). Une des m\u00e9thodes pour d\u00e9terminer ce seuil, c\u2019est la technique appel\u00e9e Peak Over Threshold (POT), ou m\u00e9thode des exc\u00e8s au-del\u00e0 d&#8217;un seuil qui se focalise sur les observations qui d\u00e9passent un certain seuil donn\u00e9. Au lieu de consid\u00e9rer les valeurs maximales ou les plus grandes valeurs, cette m\u00e9thode consiste \u00e0 examiner toutes les observations qui franchissent un seuil \u00e9lev\u00e9 pr\u00e9alablement fix\u00e9.<br \/>\nL&#8217;objectif est de s\u00e9lectionner un seuil ad\u00e9quat et d&#8217;analyser les exc\u00e8s qui en d\u00e9coulent. Ensuite nous trions les r\u00e9sultats par ordre d\u00e9croissant pour obtenir les observations telles que x&gt;u et leur nombre total.<\/p>\n<p>Nous \u00e9tudions maintenant les rentabilit\u00e9s extr\u00eames pour l\u2019action Soci\u00e9t\u00e9 G\u00e9n\u00e9rale sur la p\u00e9riode 2011-2021. La Figure 2 repr\u00e9sentes rentabilit\u00e9s journali\u00e8res de l\u2019action et les rentabilit\u00e9s extr\u00eames n\u00e9gatives obtenues avec l\u2019approche des d\u00e9passements de seuil (Peak Over Threshold ou POT). Avec le seuil retenu de -7%, on obtient 33 d\u00e9passements sur 2 595 rentabilit\u00e9s journali\u00e8res de la p\u00e9riode 2011 \u00e0 2021.<\/p>\n<p style=\"text-align: center;\">Figure 2 : S\u00e9lection des rentabilit\u00e9s extr\u00eames n\u00e9gatives pour l\u2019action Soci\u00e9t\u00e9 G\u00e9n\u00e9rale selon l\u2019approche Peak Over Threshold (POT)<br \/>\n<img decoding=\"async\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2023\/10\/img_Societe_generale_valeurs_extremes.png\" alt=\"S\u00e9lection des rentabilit\u00e9s extr\u00eames pour le titre Soci\u00e9t\u00e9 Gen\u00e9rale \" width=\"500\" \/><br \/>\nSource : auteur.<\/p>\n<h2>M\u00e9thode d\u2019estimation statistique<\/h2>\n<p>Nous allons maintenant voir comment d\u00e9terminer les \u03b2 et \u03be en utilisant la fonction de maximum de vraisemblance qui s\u2019\u00e9crit :<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2023\/10\/img_SimTrade_Fonction_vraisemblance.png\" alt=\"Fonction de vraisemblance\" width=\"300\" \/><\/p>\n<p>Pour un \u00e9chantillon de n observations, l\u2019estimation de 1-F(u) est n<sub>u<\/sub>\/n. Dans ce cas, la probabilit\u00e9 inconditionnelle de x&gt;u+y vaut :<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2023\/10\/img_SimTrade_Probabilite_inconditionnelle.png\" alt=\"Fonction de vraisemblance\" width=\"300\" \/><\/p>\n<p>Et l&#8217;estimateur de la queue de distribution de probabilit\u00e9 cumul\u00e9e de x (pour un grand) est :<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2023\/10\/img_SimTrade_Estimateur_queue_distribution.png\" alt=\"Estimateur queue distribution\" width=\"300\" \/><\/p>\n<p>Mon travail personnel a consist\u00e9 \u00e0 estimer le param\u00e8tre d\u2019\u00e9chelle \u03b2 et le param\u00e8tre de queue \u03be \u00e0 partir de la formule par le maximum de vraisemblance en utilisant le solveur Excel. Nous avons pr\u00e9c\u00e9demment d\u00e9termin\u00e9 n=0,07 par la m\u00e9thode de POT en Figure 2, et n_u= 2595<\/p>\n<p>Ainsi nous obtenons \u03b2=0,0378 et \u03be=0,0393 ce qui maximise par la m\u00e9thode du maximum de vraisemblance la somme du logarithme des valeurs extr\u00eames \u00e0 un total de 73,77.<\/p>\n<h2>Estimation de la VaR TVE<\/h2>\n<p>Pour calculer le VaR au seuil q, nous obtenons F(VaR) = q<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2023\/10\/img_SimTrade_VaR_TVE.png\" alt=\"VaR TVE\" width=\"300\" \/><\/p>\n<p>Mon travail personnel a consist\u00e9 \u00e0 estimer la VaR du titre de la Soci\u00e9t\u00e9 G\u00e9n\u00e9rale de la p\u00e9riode de 2011 \u00e0 2021 sur un total de 2595 cotations avec 33 d\u00e9passements de seuil (-7%). En appliquant les donn\u00e9es obtenues \u00e0 la formule nous obtenons :<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2023\/10\/img_SimTrade_VaR_99_Societe_Generale.png\" alt=\"VaR 99% Soci\u00e9t\u00e9 G\u00e9n\u00e9rale\" width=\"500\" \/><\/p>\n<p>Puis nous estimons la VaR \u00e0 99,90% et 99,95% :<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2023\/10\/img_SimTrade_VaR_99_90_Societe_Generale.png\" alt=\"VaR 99,90% Soci\u00e9t\u00e9 G\u00e9n\u00e9rale\" width=\"300\" \/><\/p>\n<p>Il n\u2019est pas surprenant que l\u2019extrapolation \u00e0 la queue d\u2019une distribution de probabilit\u00e9 soit difficile, pas parce qu\u2019il est difficile d\u2019identifier des distributions de probabilit\u00e9 possibles qui pourraient correspondre aux donn\u00e9es observ\u00e9es (il est relativement facile de trouver de nombreuses distributions possibles diff\u00e9rentes), mais parce que l\u2019\u00e9ventail des r\u00e9ponses qui peuvent vraisemblablement \u00eatre obtenues peut \u00eatre tr\u00e8s large, en particulier si nous voulons extrapoler dans la queue lointaine o\u00f9 il peut y avoir peu ou pas de points d\u2019observation directement applicables.<\/p>\n<p>La th\u00e9orie des valeurs extr\u00eames, si elle est utilis\u00e9e pour mod\u00e9liser le comportement de la queue au-del\u00e0 de la port\u00e9e de l\u2019ensemble de donn\u00e9es observ\u00e9es, est une forme d\u2019extrapolation. Une partie de la cause du comportement \u00e0 queue \u00e9paisse (fat tail) est l\u2019impact que le comportement humain (y compris le sentiment des investisseurs) a sur le comportement du march\u00e9.<\/p>\n<h2>En quoi \u00e7a peut m&#8217;int\u00e9resser ?<\/h2>\n<p>Nous pouvons ainsi mener des stress tests en utilisant la th\u00e9orie des valeurs extr\u00eames et \u00e9valuer les impacts sur le bilan de la banque ou encore d\u00e9terminer les limites de risques pour le trading et obtenir ainsi une meilleure estimation du worst case scenario.<\/p>\n<h2>Autres articles sur le blog SimTrade<\/h2>\n<p>\u25b6 Shengyu ZHENG <a href=\"https:\/\/www.simtrade.fr\/blog_simtrade\/categories-de-mesures-de-risque\/\" target=\"_parent\" rel=\"noopener\">Cat\u00e9gories de mesures de risques<\/a><\/p>\n<p>\u25b6 Shengyu ZHENG <a href=\"https:\/\/www.simtrade.fr\/blog_simtrade\/moments-de-la-distribution\/\" target=\"_parent\" rel=\"noopener\">Moments de la distribution<\/a><\/p>\n<p>\u25b6 Shengyu ZHENG <a href=\"https:\/\/www.simtrade.fr\/blog_simtrade\/extreme-value-theory-block-maxima-peak-threshold\/\" target=\"_parent\" rel=\"noopener\">Extreme Value Theory: the Block-Maxima approach and the Peak-Over-Threshold approach<\/a><\/p>\n<h2>Ressources<\/h2>\n<h3>Articles acad\u00e9miques<\/h3>\n<p>Falk M., J. H\u00fcsler, et R.-D. Reiss, Laws of Small Numbers: Extremes and Rare Events. Basel: Springer Basel, 2011. doi: 10.1007\/978-3-0348-0009-9.<\/p>\n<p>Gilli M. et E. K\u00ebllezi, \u00ab An Application of Extreme Value Theory for Measuring Financial Risk \u00bb, Comput Econ, vol. 27, no 2, p. 207\u2011228, mai 2006, doi: 10.1007\/s10614-006-9025-7.<\/p>\n<p>Gkillas K. and F. Longin (2018) <a href=\"https:\/\/www.longin.fr\/Recherche_Publications\/recherche_publications_financial_market_capital_control_us.htm\" target=\"_blank\" rel=\"noopener\">Financial market activity under capital controls: lessons from extreme events<\/a> <i>Economics Letters<\/i>, 171, 10-13.<\/p>\n<p>Gnedenko B., \u00ab Sur La Distribution Limite Du Terme Maximum D\u2019Une Serie Aleatoire \u00bb, Annals of Mathematics, vol. 44, no 3, p. 423\u2011453, 1943, doi: 10.2307\/1968974.<\/p>\n<p>Hull J.et A. White, \u00ab Optimal delta hedging for options \u00bb, Journal of Banking &amp; Finance, vol. 82, p. 180\u2011190, sept. 2017, doi: 10.1016\/j.jbankfin.2017.05.006.<\/p>\n<p>Longin F. (1996) <a href=\"https:\/\/www.longin.fr\/Recherche_Publications\/recherche_publications_asymptotic_distribution_us.htm\" target=\"_blank\" rel=\"noopener\">The asymptotic distribution of extreme stock market returns<\/a> <i>Journal of Business<\/i>, 63, 383-408.<\/p>\n<p>Longin F. (2000) <a href=\"https:\/\/www.longin.fr\/Recherche_Publications\/recherche_publications_var_stress_testing_us.htm\" target=\"_blank\" rel=\"noopener\">From VaR to stress testing : the extreme value approach<\/a> <i>Journal of Banking and Finance<\/i>, 24, 1097-1130.<\/p>\n<p>Longin F. (2016) <a href=\"https:\/\/extreme-events-finance.net\/wiley-handbook\/\" target=\"_blank\" rel=\"noopener\">Extreme events in finance: a handbook of extreme value theory and its applications<\/a> Wiley Editions.<\/p>\n<p>Longin F. and B. Solnik (2001) <a href=\"https:\/\/longin.fr\/Recherche_Publications\/Articles_pdf\/Longin_Solnik_Extreme_corelation_of_international_equity_market.pdf\" target=\"_blank\" rel=\"noopener\">Extreme Correlation of International Equity Markets<\/a>, <i>The Journal of Finance<\/i>, 56, 649-676.<\/p>\n<p>Roncalli T. et G. Riboulet, \u00ab Stress testing et th\u00e9orie des valeurs extr\u00eames : une vision quantit\u00e9e du risque extr\u00eame \u00bb.<\/p>\n<h3>Sites internet<\/h3>\n<p><a href=\"https:\/\/extreme-events-finance.net\/\" target=\"_blank\" rel=\"noopener\">Extreme Events in Finance<\/a><\/p>\n<h2>A propos de l&#8217;auteur<\/h2>\n<p>Cet article a \u00e9t\u00e9 \u00e9crit en juillet 2023 par <a href=\"https:\/\/www.linkedin.com\/in\/gabriel-filja\" target=\"_blank\" rel=\"noopener\">Gabriel FILJA<\/a> (ESSEC Business School, Executive Master in Senior Bank Management, 2022-2023 &amp; Head of Hedging \u00e0 Convera).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Dans cet article, Gabriel FILJA (ESSEC Business School, Executive Master in Senior Bank Management, 2022-2023 &amp; Head of Hedging \u00e0 Convera) pr\u00e9sente des applications de la th\u00e9orie des valeurs extr\u00eames en finance de march\u00e9s et notamment en gestion des risques de march\u00e9s. Principe La th\u00e9orie des valeurs extr\u00eames (TVE), appel\u00e9 th\u00e9or\u00e8me de Fisher-Tippet-Gnedenko tente de &#8230; <a title=\"Application de la th\u00e9orie des valeurs extr\u00eames en finance de march\u00e9s\" class=\"read-more\" href=\"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/\" aria-label=\"Read more about Application de la th\u00e9orie des valeurs extr\u00eames en finance de march\u00e9s\">Read more<\/a><\/p>\n","protected":false},"author":101,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[5,10],"tags":[565,598,607],"class_list":["post-12379","post","type-post","status-publish","format-standard","hentry","category-contributors","category-financial-techniques","tag-stress-testing","tag-tve","tag-value-at-risk"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v26.3 (Yoast SEO v27.2) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Application de la th\u00e9orie des valeurs extr\u00eames en finance de march\u00e9s - SimTrade blog<\/title>\n<meta name=\"description\" content=\"D\u00e9couvrir la th\u00e9orie des valeurs extr\u00eames et ses applications en finance - Insights sur les risques de march\u00e9s avec Gabriel FILJA | SimTrade Blog\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Application de la th\u00e9orie des valeurs extr\u00eames en finance de march\u00e9s\" \/>\n<meta property=\"og:description\" content=\"D\u00e9couvrir la th\u00e9orie des valeurs extr\u00eames et ses applications en finance - Insights sur les risques de march\u00e9s avec Gabriel FILJA | SimTrade Blog\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/\" \/>\n<meta property=\"og:site_name\" content=\"SimTrade blog\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/fr-fr.facebook.com\/simtrade.fr\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-10-06T14:25:41+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-02-04T09:10:05+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2023\/10\/img_SimTrade_Photo1_Gabriel_Filja.jpg\" \/>\n<meta name=\"author\" content=\"Gabriel FILJA\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@simtrade\" \/>\n<meta name=\"twitter:site\" content=\"@simtrade\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Gabriel FILJA\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"9 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/\"},\"author\":{\"name\":\"Gabriel FILJA\",\"@id\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/#\/schema\/person\/66d864792328021c95af6c12cb8fbcd6\"},\"headline\":\"Application de la th\u00e9orie des valeurs extr\u00eames en finance de march\u00e9s\",\"datePublished\":\"2023-10-06T14:25:41+00:00\",\"dateModified\":\"2024-02-04T09:10:05+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/\"},\"wordCount\":1434,\"publisher\":{\"@id\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/#organization\"},\"image\":{\"@id\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2023\/10\/img_SimTrade_Photo1_Gabriel_Filja.jpg\",\"keywords\":[\"Stress testing\",\"TVE\",\"Value at risk\"],\"articleSection\":[\"Contributors\",\"Financial techniques\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/\",\"url\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/\",\"name\":\"Application de la th\u00e9orie des valeurs extr\u00eames en finance de march\u00e9s - SimTrade blog\",\"isPartOf\":{\"@id\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2023\/10\/img_SimTrade_Photo1_Gabriel_Filja.jpg\",\"datePublished\":\"2023-10-06T14:25:41+00:00\",\"dateModified\":\"2024-02-04T09:10:05+00:00\",\"description\":\"D\u00e9couvrir la th\u00e9orie des valeurs extr\u00eames et ses applications en finance - Insights sur les risques de march\u00e9s avec Gabriel FILJA | SimTrade Blog\",\"breadcrumb\":{\"@id\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/#primaryimage\",\"url\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2023\/10\/img_SimTrade_Photo1_Gabriel_Filja.jpg\",\"contentUrl\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2023\/10\/img_SimTrade_Photo1_Gabriel_Filja.jpg\",\"width\":800,\"height\":800},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Application de la th\u00e9orie des valeurs extr\u00eames en finance de march\u00e9s\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/#website\",\"url\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/\",\"name\":\"SimTrade blog\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/#organization\",\"name\":\"SimTrade\",\"url\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2014\/01\/cropped-cropped-Banner_blog_SimTrade2.jpg\",\"contentUrl\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2014\/01\/cropped-cropped-Banner_blog_SimTrade2.jpg\",\"width\":940,\"height\":126,\"caption\":\"SimTrade\"},\"image\":{\"@id\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/fr-fr.facebook.com\/simtrade.fr\/\",\"https:\/\/x.com\/simtrade\",\"https:\/\/www.linkedin.com\/company\/sim-trade\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/#\/schema\/person\/66d864792328021c95af6c12cb8fbcd6\",\"name\":\"Gabriel FILJA\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/secure.gravatar.com\/avatar\/9c86283f368b8073daec3d261972043cc555f7e919252a657d323b4960c794ff?s=96&d=mm&r=g\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/9c86283f368b8073daec3d261972043cc555f7e919252a657d323b4960c794ff?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/9c86283f368b8073daec3d261972043cc555f7e919252a657d323b4960c794ff?s=96&d=mm&r=g\",\"caption\":\"Gabriel FILJA\"},\"url\":\"https:\/\/www.simtrade.fr\/blog_simtrade\/author\/gfilja\/\"}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Application de la th\u00e9orie des valeurs extr\u00eames en finance de march\u00e9s - SimTrade blog","description":"D\u00e9couvrir la th\u00e9orie des valeurs extr\u00eames et ses applications en finance - Insights sur les risques de march\u00e9s avec Gabriel FILJA | SimTrade Blog","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/","og_locale":"en_US","og_type":"article","og_title":"Application de la th\u00e9orie des valeurs extr\u00eames en finance de march\u00e9s","og_description":"D\u00e9couvrir la th\u00e9orie des valeurs extr\u00eames et ses applications en finance - Insights sur les risques de march\u00e9s avec Gabriel FILJA | SimTrade Blog","og_url":"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/","og_site_name":"SimTrade blog","article_publisher":"https:\/\/fr-fr.facebook.com\/simtrade.fr\/","article_published_time":"2023-10-06T14:25:41+00:00","article_modified_time":"2024-02-04T09:10:05+00:00","og_image":[{"url":"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2023\/10\/img_SimTrade_Photo1_Gabriel_Filja.jpg","type":"","width":"","height":""}],"author":"Gabriel FILJA","twitter_card":"summary_large_image","twitter_creator":"@simtrade","twitter_site":"@simtrade","twitter_misc":{"Written by":"Gabriel FILJA","Est. reading time":"9 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/#article","isPartOf":{"@id":"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/"},"author":{"name":"Gabriel FILJA","@id":"https:\/\/www.simtrade.fr\/blog_simtrade\/#\/schema\/person\/66d864792328021c95af6c12cb8fbcd6"},"headline":"Application de la th\u00e9orie des valeurs extr\u00eames en finance de march\u00e9s","datePublished":"2023-10-06T14:25:41+00:00","dateModified":"2024-02-04T09:10:05+00:00","mainEntityOfPage":{"@id":"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/"},"wordCount":1434,"publisher":{"@id":"https:\/\/www.simtrade.fr\/blog_simtrade\/#organization"},"image":{"@id":"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/#primaryimage"},"thumbnailUrl":"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2023\/10\/img_SimTrade_Photo1_Gabriel_Filja.jpg","keywords":["Stress testing","TVE","Value at risk"],"articleSection":["Contributors","Financial techniques"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/","url":"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/","name":"Application de la th\u00e9orie des valeurs extr\u00eames en finance de march\u00e9s - SimTrade blog","isPartOf":{"@id":"https:\/\/www.simtrade.fr\/blog_simtrade\/#website"},"primaryImageOfPage":{"@id":"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/#primaryimage"},"image":{"@id":"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/#primaryimage"},"thumbnailUrl":"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2023\/10\/img_SimTrade_Photo1_Gabriel_Filja.jpg","datePublished":"2023-10-06T14:25:41+00:00","dateModified":"2024-02-04T09:10:05+00:00","description":"D\u00e9couvrir la th\u00e9orie des valeurs extr\u00eames et ses applications en finance - Insights sur les risques de march\u00e9s avec Gabriel FILJA | SimTrade Blog","breadcrumb":{"@id":"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/#primaryimage","url":"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2023\/10\/img_SimTrade_Photo1_Gabriel_Filja.jpg","contentUrl":"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2023\/10\/img_SimTrade_Photo1_Gabriel_Filja.jpg","width":800,"height":800},{"@type":"BreadcrumbList","@id":"https:\/\/www.simtrade.fr\/blog_simtrade\/application-theorie-valeurs-extremes-finance-marches\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.simtrade.fr\/blog_simtrade\/"},{"@type":"ListItem","position":2,"name":"Application de la th\u00e9orie des valeurs extr\u00eames en finance de march\u00e9s"}]},{"@type":"WebSite","@id":"https:\/\/www.simtrade.fr\/blog_simtrade\/#website","url":"https:\/\/www.simtrade.fr\/blog_simtrade\/","name":"SimTrade blog","description":"","publisher":{"@id":"https:\/\/www.simtrade.fr\/blog_simtrade\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.simtrade.fr\/blog_simtrade\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/www.simtrade.fr\/blog_simtrade\/#organization","name":"SimTrade","url":"https:\/\/www.simtrade.fr\/blog_simtrade\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/www.simtrade.fr\/blog_simtrade\/#\/schema\/logo\/image\/","url":"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2014\/01\/cropped-cropped-Banner_blog_SimTrade2.jpg","contentUrl":"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2014\/01\/cropped-cropped-Banner_blog_SimTrade2.jpg","width":940,"height":126,"caption":"SimTrade"},"image":{"@id":"https:\/\/www.simtrade.fr\/blog_simtrade\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/fr-fr.facebook.com\/simtrade.fr\/","https:\/\/x.com\/simtrade","https:\/\/www.linkedin.com\/company\/sim-trade"]},{"@type":"Person","@id":"https:\/\/www.simtrade.fr\/blog_simtrade\/#\/schema\/person\/66d864792328021c95af6c12cb8fbcd6","name":"Gabriel FILJA","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/secure.gravatar.com\/avatar\/9c86283f368b8073daec3d261972043cc555f7e919252a657d323b4960c794ff?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/9c86283f368b8073daec3d261972043cc555f7e919252a657d323b4960c794ff?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/9c86283f368b8073daec3d261972043cc555f7e919252a657d323b4960c794ff?s=96&d=mm&r=g","caption":"Gabriel FILJA"},"url":"https:\/\/www.simtrade.fr\/blog_simtrade\/author\/gfilja\/"}]}},"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-json\/wp\/v2\/posts\/12379","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-json\/wp\/v2\/users\/101"}],"replies":[{"embeddable":true,"href":"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-json\/wp\/v2\/comments?post=12379"}],"version-history":[{"count":6,"href":"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-json\/wp\/v2\/posts\/12379\/revisions"}],"predecessor-version":[{"id":13220,"href":"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-json\/wp\/v2\/posts\/12379\/revisions\/13220"}],"wp:attachment":[{"href":"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-json\/wp\/v2\/media?parent=12379"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-json\/wp\/v2\/categories?post=12379"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-json\/wp\/v2\/tags?post=12379"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}