NJIT eTD: The New Jersey Institute of Technology's electronic Theses & Dissertations
 Title: Modeling and quasi-Monte Carlo simulation of risk in credit portfolios Author: Ren, Bo Document Type: Dissertation Department: Department of Mathematical Sciences Degree: Doctor of Philosophy Major: Mathematical Sciences Advisory Committee: Horntrop, David James Morokoff, William J. Michalopoulou, Eliza Zoi-Heleni Ehrlich, Michael A. Goodman, Roy Thesis Date: 2010, January Keywords: Credit portfolios modelling Simulation analysis Quasi-Monte Carlo methods Monte Carlo methods Availability: Unrestricted Abstract: Credit risk is the risk of losing contractually obligated cash flows promised by a coun­terparty such as a corporation, financial institution, or government due to default on its debt obligations. The need for accurate pricing and hedging of complex credit derivatives and for active management of large credit portfolios calls for an accurate assessment of the risk inherent in the underlying credit portfolios. An important chal­lenge for modeling a credit portfolio is to capture the correlations within the credit portfolio. For very large and homogeneous portfolios, analytic and semi-analytic approaches can be used to derive limiting distributions. However, for portfolios of inhomogeneous default probabilities, default correlations, recovery values, or position sizes, Monte Carlo methods are necessary to capture their underlying dynamic evolu­tions. Since the feasibility of the Monte Carlo methods is limited by their relatively slow convergence rate, methods to improve the efficiency of simulations for credit portfolios are highly desired. In this dissertation, a comparison of the commonly employed single step models for credit portfolios, referred to as the copula-based default time approach, with our novel applications of multi-step models was made at first. Comparison of simulation results indicates that the dependency structure may be better incorporated by the multi-step models, since the default time models can introduce substantially skewed correlations within credit portfolios, a shortcoming which has become more evident in the recent subprime crisis. Next, to improve the efficiency of simulations, quasi- random sequences were introduced into both the single step and multi-step models by devising several new algorithms involving the Brownian bridge construction and principal component analysis. The simulation results from tests under various sce­narios suggest that quasi-Monte Carlo methods can substantially improve simulation effectiveness not only for the problems of computing integrals but also for those of order statistics, indicating significant advantage when calculating a number of risk quantities such as Value at Risk (VaR). Finally, the performance of the simulations based on the above credit portfolio models and the quasi-Monte Carlo methods was examined in the context of modeling and valuation of credit portfolio derivatives. The results suggest that these methods can considerably improve the simulation of complex financial instruments involving portfolio credit risk. Complete Thesis: njit-etd2010-042 (148 pages ~ 13,040 KB pdf) Feedback: Please complete this Feedback Form to inform us about your experience using this website. It will assist us in better serving your information needs in the future. Thank You!
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