A First Passage Time Model for Counterparty Default

Counterparty risk is becoming an important issue for over the counter trades. However, valuation of counterparty risk is still in its early stage. The previous studies often ignore the wrong way risk which is a key aspect of counterparty risk valuation. In this paper, we develop a tractable first passage time model, which is able to capture the correlation between the default and market risk factor, particularly interest rates. We derive closed form solutions for survival and marginal default probability in the presence of correlation between the default event and interest rate based on the model assumptions. The numerical results for pricing credit default swap illustrate that the closed form solutions are exact when the volatilities for default driver and risk factor are constant and a good approximation when the volatilities are piece-wise constant. We also showed how sensitive the CDS spread is to different model parameters. In particular, we found the correlation between the default and market factors has a significant impact on the default probability and CDS spread.