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We provide analytical pricing formula of corporate defaultable bond with bothexpected and unexpected default in the case with stochastic default intensity.In the case with constant short rate and exogenous default recovery using PDEmethod, we gave some pricing formula of the defaultable bond under theconditions that 1)expected default recovery is the same with unexpected defaultrecovery; 2) default intensity follows one of 3 special cases of Willmottmodel; 3) default intensity is uncorrelated with firm value. Then we derived apricing formula of a credit default swap. And in the case of stochastic shortrate and exogenous default recovery using PDE method, we gave some pricingformula of the defaultable bond under the conditions that 1) expected defaultrecovery is the same with unexpected default recovery; 2) the short ratefollows Vasicek model; 3) default intensity follows one of 3 special cases ofWillmott model; 4) default intensity is uncorrelated with firm value; 5)default intensity is uncorrelated with short rate. Then we derived a pricingformula of a credit default swap. We give some credit spread analysis, too.

Analytical Pricing of Defaultable Bond with Stochastic Default Intensity