Measuring Credit Risk under Multidimensional Affine Jump-Diffusion Model

Credit risk is a major issue for Banks, other financial institutions and anyone involved in the transaction of financial contracts. It is particularly important to model an effective pricing approach for managing the credit risk. This paper establishes a credit risk model using the structural model in which the corporate's total asset value follows multidimensional affine jump diffusion processes, and measures the corporate's credit risk value in terms of default probability. The closed-form explicit solutions for the corporate's default probability, distance to default and zero-coupon credit bond are obtained by means of some methods including the characteristics of affine structure, the semi-martingale It\^o formula, the Feynman-Kac theorem and the Fourier inverse transformation technique. Numerical experiments are used to analyze the impacts of volatility, interest rate, jump densities, related coefficients and other parameters on the default probability. These conclusions have some key reference values for pricing the defaultable bonds and credit derivatives.