1 Pricing Corporate Bonds with Risk Adjustable Default Barrier

This paper develops a corporate bond valuation model that incorporates a default barrier with dynamics depending on stochastic interest rates and variance of the corporate bond function. The volatility of the firm value affects the level of the barrier over time through the variance of the corporate bond function and its contribution to the barrier's dynamics is adjusted by a free parameter. We derive a closed-form solution of the corporate bond price as a function of firm value and interest rate, with time-dependent model parameters governing the dynamics of firm value and interest rate. The numerical results calculated from the solution show that the dynamics of the barrier has material impact on the term structures of credit spreads. The model incorporating the risk adjustable default barrier, deviations from the absolute priority rule, and time-dependent model parameters is capable of producing diverse shape of term structures of credit spreads. This model provides new insight for future research on corporate bonds analysis and credit risk modelling.