Analytical Pricing of Defaultable Bond with Stochastic Default Intensity

TL;DR

This paper derives analytical formulas for pricing defaultable bonds and credit default swaps considering stochastic default intensity, using PDE methods under various interest rate and default recovery assumptions.

Contribution

It introduces new analytical pricing formulas for defaultable bonds and credit default swaps with stochastic default intensity and various interest rate models.

Findings

Provided formulas under constant short rate and Vasicek model

Derived credit spread analysis

Formulas assume uncorrelated default intensity and firm value

Abstract

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.