The Pricing of Credit Securities with Counterparty Risk using a Contagion Model

In this paper, we study the pricing of defaultable bonds and credit default swaps with counterparty risk using a contagion model. We present a contagion model of correlated defaults in a reduced model. The model assumes the intensities of default processes depend on the stochastic interest rate process driven by a stochastic differential equation and the default process of a counterparty. These are extensions of the models in Jarrow and Yu (2001) and Hao and Ye (2011). Moreover, we derive the explicit formulae for the pricing of defaultable bonds and credit default swap with counterparty risk using the properties of stochastic exponentials and make some numerical analysis on the explicit formulae.