On computational methods for the valuation of credit derivatives by Wanhe Zhang A thesis submitted in conformity with the requirements

On computational methods for the valuation of credit derivatives Wanhe Zhang Doctor of Philosophy Graduate Department of Computer Science University of Toronto 2010 A credit derivative is a financial instrument whose value depends on the credit risk of an underlying asset or assets. Credit risk is the possibility that the obligor fails to honor any payment obligation. This thesis proposes four new computational methods for the valuation of credit derivatives. Compared with synthetic collateralized debt obligations (CDOs) or basket default swaps (BDS), the value of which depends on the defaults of a prescribed underlying portfolio, a forward-starting CDO or BDS has a random underlying portfolio, as some “names” may default before the CDO or BDS starts. We develop an approach to convert a forward product to an equivalent standard one. Therefore, we avoid having to consider the default combinations in the period between the start of the forward contract and the start of the associated CDO or BDS. In addition, we propose a hybrid method combining Monte Carlo simulation with an analytical method to obtain an effective method for pricing forward-starting BDS. Current factor copula models are static and fail to calibrate consistently against market quotes. To overcome this deficiency, we develop a novel chaining technique to build a multi-period factor copula model from several one-period factor copula models. This allows the default correlations to be time-dependent, thereby allowing the model to fit market quotes consistently. Previously developed multi-period factor copula models require multi-dimensional integration, usually computed by Monte Carlo simulation,