Large Deviations And Rare Event Simulation For Portfolio Credit Risk




de Silva, Lokuge Hasitha Eranda

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Estimating the loss distribution of a credit portfolio is an important problem in credit risk management. When dealing with credit portfolios, correlations between defaults play an important role. "Threshold based factor models" is a widely used method of modeling this phenomenon. Both the well know industry models, KMV and CreditMetrics fall into this category. We begin this thesis by deriving sharp large deviation asymptotics for a single factor model as the number of obligors go to infinity. Both the systematic and idiosyncratic risk factors are allowed to take general distributions. We derive our asymptotics under a unified framework, and they can be applied to many different probability distributions. Some of the distributions that we consider for the risk factors are Gaussian, Exponential, Pareto, Gamma, and Stretched Exponential.



Mathematics, Credit Risk, Large Deviation, Mathematical Finance, Rare Event Simulation