In this paper, we suggest a ¯rst-passage-time model which can explain default probability and default correlation dynamics under stochastic market environment. We add a Markov regime-switching market condition to a ¯rst-passage-time model of Zhou (2001). Using this model, we try to explain various relationship between default probability, default correlation, and market condition. We also suggest a valuation method for credit default swap (CDS) with(or without) counterparty default risk (CDR) and basket default swap under this model.
Our numerical results provide us with several meaningful implications. First, default swap spread is higher under economic recession than under economic expansion across default swap maturity. Second, as the di®erence of asset return volatility between under bear market and under bull market increases, CDS spread increases regardless of maturity. Third, the bigger the intensity shifting from bull market to bear market, the higher the spread for both CDS without CDR and basket default swap. However, the spread of CDS with CDR may decline against the intensity when the default risk of counterparty is higher than that of reference
entity under economic recession.