{"title":"Implied Volatility Smile with Non-Gaussian Processes","authors":"","doi":"10.1142/9789813276208_0011","DOIUrl":"https://doi.org/10.1142/9789813276208_0011","url":null,"abstract":"","PeriodicalId":227655,"journal":{"name":"Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122318149","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}
{"title":"Stochastic Processes with Jumps","authors":"","doi":"10.1142/9789813276208_0003","DOIUrl":"https://doi.org/10.1142/9789813276208_0003","url":null,"abstract":"","PeriodicalId":227655,"journal":{"name":"Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128322593","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, Frank J. Fabozzi, S. Focardi
{"title":"Extreme Value Theory","authors":"M. L. Bianchi, Stoyan Stoyanov, G. Tassinari, Frank J. Fabozzi, S. Focardi","doi":"10.1142/9789813276208_0009","DOIUrl":"https://doi.org/10.1142/9789813276208_0009","url":null,"abstract":"The main topics covered in this chapter are:what extreme value theory is and how it differs from classical statistics;the two pillars of extreme value theory: Fisher–Tippett–Gnedenko theorem and Pickands–Balkema–de Haan theorem;the three classes that the limit distribution of maxima will fall into: the Frechet, Weibull, or Gumbel distribution;the generalized Pareto distribution;the maximum domain of attraction of an extreme value distribution and the concept of tail equivalence;the theory of maxima for stationary processes;extreme value theory for multivariate distributions;the role of copula in multivariate extreme value theory;the three types of copulas;three estimation methods for distributions: maximum likelihood estimation method, method of moments, and special estimators;the Hill estimator and the Pickands estimator for estimating the shape parameter of a distribution;use and limitations of the quantile plot (QQ-plot) for verifying statistical hypotheses by examining the degree of deviations of the linearity plot of a hypothesized distribution;three different approaches to compute widely-known risk measures (VaR and AVaR).","PeriodicalId":227655,"journal":{"name":"Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116763791","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}
{"title":"The Class of Stable Distributions","authors":"","doi":"10.1142/9789813276208_0005","DOIUrl":"https://doi.org/10.1142/9789813276208_0005","url":null,"abstract":"","PeriodicalId":227655,"journal":{"name":"Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127368645","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}
{"title":"FRONT MATTER","authors":"","doi":"10.1142/9789813276208_fmatter","DOIUrl":"https://doi.org/10.1142/9789813276208_fmatter","url":null,"abstract":"","PeriodicalId":227655,"journal":{"name":"Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134595173","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":"Tempered Stable Distributions","authors":"M. L. Bianchi, Stoyan Stoyanov, G. Tassinari, F. Fabozzi, S. Focardi","doi":"10.1142/9789813276208_0006","DOIUrl":"https://doi.org/10.1142/9789813276208_0006","url":null,"abstract":"The main topics covered in this chapter are:the history of the tempered stable distribution and why this distribution has been applied in finance;the main properties and formulas of tempered stable laws;the evaluation of the characteristic function in a non-trivial case (i.e., for the rapidly decreasing tempered stable law);probability density and cumulative distribution function evaluation when only the characteristic function is available in closed form while the density function is not;how to generate sample draws from a tempered stable distribution;how to estimate the parameters of a tempered stable distribution from a sample;how to evaluate well-known risk measures for a tempered stable stock market model.","PeriodicalId":227655,"journal":{"name":"Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126866473","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}
{"title":"BACK MATTER","authors":"","doi":"10.1142/9789813276208_bmatter","DOIUrl":"https://doi.org/10.1142/9789813276208_bmatter","url":null,"abstract":"","PeriodicalId":227655,"journal":{"name":"Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134055519","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}
{"title":"Random Variables","authors":"박동조","doi":"10.1142/9789813276208_0002","DOIUrl":"https://doi.org/10.1142/9789813276208_0002","url":null,"abstract":"If our atomic events are people, such as survey participants who might walk by our corner, then the height of the next person is a random variable. So are and eye color. If our atomic events are complex numbers, then the real part of the next complex number is a random variable. If our atomic events are cards that we draw from a deck, then the number of pips on the next card is a random variable; so are the suit and whether the card is a face card. If our atomic events are pairs of people (say, the next two participants in our survey), then we can make a random variable by testing whether they have the same birthday, or by squaring the difference between the lengths of their left thumbs.","PeriodicalId":227655,"journal":{"name":"Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128308022","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":"Multivariate Time-Changed Brownian Motion: The Expectation–Maximization Estimation Method","authors":"M. L. Bianchi, Stoyan Stoyanov, G. Tassinari, F. Fabozzi, S. Focardi","doi":"10.1142/9789813276208_0008","DOIUrl":"https://doi.org/10.1142/9789813276208_0008","url":null,"abstract":"The main topics covered in this chapter are:a description of a method to estimate the parameters of models based on the multivariate time-changed Brownian motion;a review of the expectation–maximization (EM) maximum likelihood estimation (MLE) method to estimate the parameters of multivariate generalized hyperbolic distributions;an extension of the EM-based MLE algorithm to normal mean–variance mixture distributions in which only the characteristic function of the mixing distribution is known in closed form, while the density function is not;an error analysis of the estimation method applied to the multivariate normal tempered stable case;an empirical test showing the model performance on a five-and a 30-dimensional series of index (stock) returns;how to evaluate well-known risk measures (i.e., value-at-risk and average value-at-risk) under this framework;how to backtest the value-at-risk by taking into account the number of exceedances.","PeriodicalId":227655,"journal":{"name":"Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management","volume":"13 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":"116180291","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":"A Portfolio Selection Analysis with Non-Gaussian Models","authors":"M. L. Bianchi, Stoyan Stoyanov, G. Tassinari, F. Fabozzi, S. Focardi","doi":"10.1142/9789813276208_0010","DOIUrl":"https://doi.org/10.1142/9789813276208_0010","url":null,"abstract":"The main topics covered in this chapter are:a description of a method to perform portfolio selection based on normal, multivariate generalized hyperbolic, and multivariate normal tempered stable distributions;a review of the main properties of the average value-at-risk measure;a review of the mean–variance and mean-risk portfolio optimization strategies;an implementation of the minimum-variance and equally weighted portfolio criteria;a review of portfolio performance measures to evaluate and backtest different portfolio strategies;an empirical test showing the portfolio selection performance on a 50-dimensional series of stock returns;an evaluation of different portfolio rebalancing frequencies.","PeriodicalId":227655,"journal":{"name":"Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management","volume":"60 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":"127447357","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}