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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.