Pricing Derivatives using the Asymptotic Expansion Approach: Credit Migration Models with Stochastic Credit Spreads

The purpose of this paper is to evaluate the asymptotic approximation formulas for the price of contingent claims with credit risk, such as credit default swaps and options on defaultable bonds, in a Markovian credit migration model. Often the generator matrix of a credit migration process is assumed to be deterministic; however, a stochastically varying generator matrix is used in this paper. To apply such a model to the valuation of options on defaultable bonds, the small disturbance asymptotic expansion approach of Kunitomo and Takahashi is used in this study.