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