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Title: Application of Perturbation Methods to Modeling Correlated Defaults in Financial Markets
Authors: Zhou, Xianwen
Advisors: Kazufumi Ito, Committee Member
Tao Pang, Committee Member
Jean-Pierre Fouque, Committee Chair
John Seater, Committee Member
Keywords: copula
option pricing
credit derivatives
Monte Carlo
singular perturbation
regular perturbation
stochastic volatility
Issue Date: 21-Mar-2007
Degree: PhD
Discipline: Applied Mathematics
Abstract: In recent years people have seen a rapidly growing market for credit derivatives. Among these traded credit derivatives, a growing interest has been shown on multi-name credit derivatives, whose underlying assets are a pool of defaultable securities. For a multi-name credit derivative, the key is the default dependency structure among the underlying portfolio of reference entities, instead of the individual term structure of default probabilities for each single reference entity as in the case of single-name derivative. So far, however, default dependency modeling is still the most demanding open problem in the pricing of credit derivatives. The research in this dissertation is trying to model the default dependency with aid of perturbation method, which was first proposed by Fouque, Papanicolaou and Sircar (2000) as a powerful tool to pricing options under stochastic volatility. Specifically, after a theoretic result regarding the approximation accuracy of the perturbation method and an application of this method to pricing American options under stochastic volatility by Monte Carlo approach, a multi-dimensional Merton model under stochastic volatility is studied first, and then the multi-dimensional generalization of the first-passage model under stochastic volatility comes next, which is then followed by a copula perturbed from the standard Gaussian copula.
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