Application of Perturbation Methods to Modeling Correlated Defaults in Financial Markets

copula;option pricing;credit derivatives;Monte Carlo;singular perturbation;regular perturbation;stochastic volatility

Zhou, Xianwen ; Kazufumi Ito, Committee Member,Tao Pang, Committee Member,Jean-Pierre Fouque, Committee Chair,John Seater, Committee Member,Zhou, Xianwen ; Kazufumi Ito ; Committee Member ; Tao Pang ; Committee Member ; Jean-Pierre Fouque ; Committee Chair ; John Seater ; Committee Member

University:North Carolina State University

关键词: copula;    option pricing;    credit derivatives;    Monte Carlo;    singular perturbation;    regular perturbation;    stochastic volatility;   

Others  :  https://repository.lib.ncsu.edu/bitstream/handle/1840.16/4247/etd.pdf?sequence=1&isAllowed=y

美国|英语

来源: null

【 摘 要 】

In recent years peoplehave 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 theindividual 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 perturbationmethod, which was first proposed by Fouque, Papanicolaou andSircar (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 byacopulaperturbed from the standard Gaussian copula.