M. L. Bianchi, Stoyan Stoyanov, G. Tassinari, F. Fabozzi, S. Focardi
{"title":"Multivariate Time-Changed Brownian Motion","authors":"M. L. Bianchi, Stoyan Stoyanov, G. Tassinari, F. Fabozzi, S. Focardi","doi":"10.1142/9789813276208_0007","DOIUrl":"https://doi.org/10.1142/9789813276208_0007","url":null,"abstract":"The main topics covered in this chapter are:the history of time-changed Brownian motion and why this process has been applied to finance;the main properties and formulas for different parametric examples of multivariate time-changed Brownian motion;the relation between multivariate time-changed Brownian motion and multivariate normal mean–variance mixture distributions;the derivation of the closed formula for the density function of some multivariate normal mean–variance mixture laws;the evaluation of the probability density function of a multivariate normal mean–variance mixture law when only the characteristic function of the mixing distribution is available in closed form while the density function is not;how to generate sample draws from a multivariate normal mean–variance mixture law.","PeriodicalId":227655,"journal":{"name":"Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management","volume":"159 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123076561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. L. Bianchi, Stoyan Stoyanov, G. Tassinari, F. Fabozzi, S. Focardi
{"title":"Application of Extreme Value Theory to Estimate Tail Thickness for Asset Return Distributions","authors":"M. L. Bianchi, Stoyan Stoyanov, G. Tassinari, F. Fabozzi, S. Focardi","doi":"10.1142/9789813276208_0012","DOIUrl":"https://doi.org/10.1142/9789813276208_0012","url":null,"abstract":"The main topics covered in this chapter are:assessment of value-at-risk (VaR) and average value-at-risk (AVaR) through extreme value theory (EVT) using the peaks-over-threshold method;how to combine the standard GARCH model which takes into account the clustering of volatility with EVT for risk estimation;extensive in-sample and out-of-sample analysis of the upper and the lower tail thickness of the return distributions of market indices;AVaR-based and standard VaR-based statistical tests to assess the out-of-sample behavior of the risk model.","PeriodicalId":227655,"journal":{"name":"Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management","volume":"128 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128168312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. L. Bianchi, Stoyan Stoyanov, G. Tassinari, F. Fabozzi, S. Focardi
{"title":"The Generalized Hyperbolic Distribution","authors":"M. L. Bianchi, Stoyan Stoyanov, G. Tassinari, F. Fabozzi, S. Focardi","doi":"10.1142/9789813276208_0004","DOIUrl":"https://doi.org/10.1142/9789813276208_0004","url":null,"abstract":"The main topics covered in this chapter are:the definition and the main properties of the class of generalized hyperbolic distributions including different parameterizations, tail behavior, and central and non-central moments common in applications in finance;special subclasses which represent popular models in finance including the hyperbolic, the normal inverse Gaussian, the hyperbolic skewed t, the variance gamma, and other distributions;a random number generator for the general case and the most important subclasses;the method of maximum likelihood for parameter estimation for the general case and the most important subclasses;an empirical comparison of the fits of the generalized hyperbolic class and the most important subclasses based on the daily returns of the SPthe intuition behind the multivariate generalized hyperbolic distribution.","PeriodicalId":227655,"journal":{"name":"Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116243960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}