Pricing securities subject to credit risk and regime switching
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This thesis begins with an introduction of credit risk and a review of credit risk models. A modi ed credit risk model which is subject to adjustable counterparty risks is then present, i.e. these counterparty risks are controlled by an exponential distribution. Following are two applications of this modi ed model on pricing credit derivatives: default swap of rst-to-default baskets and collateralized bond obligations. Then a broader framework for the valuation of credit risk is introduced, i.e. incorporating Markov-modulated regime switching into the underlying factors of credit risk models. Under this generalized credit risk mode, two numerical methods: nite di erence method and Markov Chain Monte Carlo simulation are used to calculate the prices of defaultable bonds. Finally, perpetual American put options subject to regime switching are studied. A stochastic approximation method is provided to nd the optimal selling points for perpetual American put options.