A first-passage-time model under regime-switching market environment

In this paper, we suggest a first-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 the first-passage-time model of Zhou [Zhou, C., 2001. An analysis of default correlations and multiple defaults. Review of Financial Studies 14, 555-576]. 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 in economic recession than in economic expansion across default swap maturity. Second, as the difference 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.