Evaluation of yield spread for credit risk

We study the rational evaluation of yield spread for defaultable credit with fixed maturity. The default occurs when the asset value hits a given fraction of the nominal credit value. The yield spread is continuously accumulated to the initial credit as an insurance fee for future default. By the rational credit pricing, we prove the unique existence of equilibrium yield spread which satisfies the arbitrage free property. Furthermore we show that this spread yield is independent of the choice of interest rate process. For the quantitative study of rational yield spread, we derive an explicit analytic formula for the equilibrium and show numerical example for various parameters.