Credit Risks with Lévy Processes under a Stochastic Interest Rate: A Structural Form Model

Abstract

Merton (1974) proposes a structural form model to evaluate the default bond, and Zhou (2001) investigates a credit spread under a jump diffusion model, in which the jump risk is non-system risk. Empirical analysis finds the leptokurtic feature in the dynamic process of the firm’s value. Based on the structural form model, we investigate the firm value with the exponential Lévy processes to evaluate the default bond and default probability under the Vasicek’s stochastic interest rate model (taking the jump diffusion model as a special case). Empirical studies have also found the volatility clustering phenomenon in the dynamic of asset return. Therefore, in particular, we give Markov modulated Poisson Processes to describe the dynamics of the firm value and evaluate the default bond and default probability in some simple results theoretically and numerically.