This thesis develops the no arbitrage approach for pricing credit spread derivatives which have the payoff depending on the terminal value of the credit spread of a reference entity. In my pricing model, the spot rate is assumed to follow the Hull-White model while the spot spread correlated to the spot rate is taken to follow either the Hull-White model or the Black-Karasinsky model. The time dependent drift terms in the mean reversion stochastic processes are determined by fitting the current term structures of the default free and defaultable bond prices. I manage to derive the analytic representation for the time dependent drift functions and analytic price formula for credit spread options if the spot rate and spot spread both follow the Hull-White model. I also construct the fitti...[ Read more ]

This thesis develops the no arbitrage approach for pricing credit spread derivatives which have the payoff depending on the terminal value of the credit spread of a reference entity. In my pricing model, the spot rate is assumed to follow the Hull-White model while the spot spread correlated to the spot rate is taken to follow either the Hull-White model or the Black-Karasinsky model. The time dependent drift terms in the mean reversion stochastic processes are determined by fitting the current term structures of the default free and defaultable bond prices. I manage to derive the analytic representation for the time dependent drift functions and analytic price formula for credit spread options if the spot rate and spot spread both follow the Hull-White model. I also construct the fitting algorithms to value numerically the credit spread derivatives if the spot spread follows the Black-Karasinsky model. Moreover, the pricing behaviors of some credit spread options are examined.