Singular Perturbation Methods in Credit Derivative Modeling

Download or read book Singular Perturbation Methods in Credit Derivative Modeling written by Jawon Koo and published by . This book was released on 2010 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis introduces the dynamical pricing model and approximation method in pricing a "Collateralized Debt Obligation" (CDO). For this purpose we use a two-dimensional, self-affecting Markov process of discrete-valued aggregate loss process and stochastic factor process in its intensity. We review several models for pricing of multi-name credit derivative products and explain in detail a two-dimensional Markov intensity model proposed by Halperin and Arnsdorf. Using the model by Halperin and Arnsdorf, we derive the Kolmogorov forward partial differential equation for the transition density function of the underlying two-dimensional Markov process. We use the singular perturbation method to obtain an approximate solution to this partial differential equation in the case of a fast mean reverting stochastic intensity model. We perform an error analysis to determine the accuracy of our approximate solution.