Pricing of Multi-Defaultable Bonds with a Two-Correlated-Factor Hull-White Model

This research attempts to propose closed-form solutions for prices of credit-risky bonds, assuming a nonzero correlation between interest rates and credit spreads. The times of default of a credit-risky bond are modelled as the jump times of a Cox process, following the method of Lando, with an intensity that follows a Hull and White model, correlated with a similar model of the risk-free interest rate. Under the fractional recovery of market value assumption of Duffie and Singleton, the partial differential equation (PDE) for the price of the zero-coupon credit-risky bond is derived. Then this PDE is analytically solved, using the method of separation of variables, and easy-to-implement closed-form solutions are found. Finally, numerical examples are presented to show how these closed-form solutions can identify the magnitude and the direction of the credit-risky bond mispricing under different parameter assumptions.