Modeling Default Dependence with the Mixture of Calendar Time and Business Time

摘要

Evaluating default correlation between securities in a portfolio is very important for credit derivatives pricing and risk management. Under the framework of the structural model proposed by Black and Cox, we assume that the asset values of companies are driven by Brownian motions in the worlds of the calendar time and the business time; they then could evolve continuously or by leap. We build the dynamic default correlations using the time-varying correlated Brownian motions in these processes. The sensitivity of default correlations to the key parameters is explored in the paper by numerical examples, and we apply the model to risk management as well. Because default times are unpredictable in the proposed model, the defaults might occur suddenly. Independent defaults and complete correlated defaults can be described in the model as well.