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Calibration of Multivariate Generalized Hyperbolic Distributions Using the EM Algorithm, with Applications in Risk Management, Portfolio Optimization and Portfolio Credit Risk

Title: Calibration of Multivariate Generalized Hyperbolic Distributions Using the EM Algorithm, with Applications in Risk Management, Portfolio Optimization and Portfolio Credit Risk.
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Name(s): Hu, Wenbo, author
Kercheval, Alec, professor directing dissertation
Huffer, Fred, outside committee member
Case, Bettye, committee member
Nichols, Warren, committee member
Nolder, Craig, committee member
Department of Mathematics, degree granting department
Florida State University, degree granting institution
Type of Resource: text
Genre: Text
Issuance: monographic
Date Issued: 2005
Publisher: Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource
Language(s): English
Abstract/Description: The distributions of many financial quantities are well-known to have heavy tails, exhibit skewness, and have other non-Gaussian characteristics. In this dissertation we study an especially promising family: the multivariate generalized hyperbolic distributions (GH). This family includes and generalizes the familiar Gaussian and Student t distributions, and the so-called skewed t distributions, among many others. The primary obstacle to the applications of such distributions is the numerical difficulty of calibrating the distributional parameters to the data. In this dissertation we describe a way to stably calibrate GH distributions for a wider range of parameters than has previously been reported. In particular, we develop a version of the EM algorithm for calibrating GH distributions. This is a modification of methods proposed in McNeil, Frey, and Embrechts (2005), and generalizes the algorithm of Protassov (2004). Our algorithm extends the stability of the calibration procedure to a wide range of parameters, now including parameter values that maximize log-likelihood for our real market data sets. This allows for the first time certain GH distributions to be used in modeling contexts when previously they have been numerically intractable. Our algorithm enables us to make new uses of GH distributions in three financial applications. First, we forecast univariate Value-at-Risk (VaR) for stock index returns, and we show in out-of-sample backtesting that the GH distributions outperform the Gaussian distribution. Second, we calculate an efficient frontier for equity portfolio optimization under the skewed-t distribution and using Expected Shortfall as the risk measure. Here, we show that the Gaussian efficient frontier is actually unreachable if returns are skewed t distributed. Third, we build an intensity-based model to price Basket Credit Default Swaps by calibrating the skewed t distribution directly, without the need to separately calibrate xi the skewed t copula. To our knowledge this is the first use of the skewed t distribution in portfolio optimization and in portfolio credit risk.
Identifier: FSU_migr_etd-3694 (IID)
Submitted Note: A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Degree Awarded: Fall Semester, 2005.
Date of Defense: October 28, 2005.
Keywords: Basket Credit Default Swaps, Skewed T Distribution, Generalized Hyperbolic Distributions, Portfolio Credit Risk, Portfolio Optimization, Risk Management, EM Algorithm
Bibliography Note: Includes bibliographical references.
Advisory Committee: Alec Kercheval, Professor Directing Dissertation; Fred Huffer, Outside Committee Member; Bettye Case, Committee Member; Warren Nichols, Committee Member; Craig Nolder, Committee Member.
Subject(s): Mathematics
Persistent Link to This Record: http://purl.flvc.org/fsu/fd/FSU_migr_etd-3694
Owner Institution: FSU

Choose the citation style.
Hu, W. (2005). Calibration of Multivariate Generalized Hyperbolic Distributions Using the EM Algorithm, with Applications in Risk Management, Portfolio Optimization and Portfolio Credit Risk. Retrieved from http://purl.flvc.org/fsu/fd/FSU_migr_etd-3694