A jump-diffusion model for pricing corporate debt securities in a complex capital structure

This paper proposes a jump-diffusion model, in closed form, to price corporate debt securities, senior and junior, with the same maturity and violation of the absolute priority rule. We take the structural approach that the firm's asset value follows a jump-diffusion process in a stochastic interest rate economy. Default occurs only if the firm value at the maturity of the corporate debts is less than the sum of the prespecified face values. Unlike previous models in the structural approach, our model is consistent with the current term structures of credit spreads for both senior and junior debts. In particular, it captures realistic short maturity credit spreads observed in the market. The key idea is to allow the jump intensity to be a time-dependent function. As an application, valuation of credit spread options is presented.