Analytic Dynamic Factor Copula Model

The Gaussian factor copula model is the market standard model for multi-name credit derivatives. Its main drawback is that factor copula models exhibit correlation smiles when calibrating against market tranche quotes. To overcome the calibration deficiency, we introduce a multi-period factor copula model by chaining one-period factor copula models. The correlation coefficients in our model are allowed to be timedependent, and hence they are allowed to follow certain stochastic processes. Therefore, we can calibrate against market quotes more consistently. Usually, multi-period factor copula models require multi-dimensional integration, typically computed by Monte Carlo simulation, which makes calibration extremely time consuming. In our model, the portfolio loss of a completely homogeneous pool possesses the Markov property, thus we can compute the portfolio loss distribution analytically without multi-dimensional integration. Numerical results demonstrate the efficiency and flexibility of our model to match market quotes. This research was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada. Department of Computer Science, University of Toronto, 10 King’s College Road, Toronto, ON, M5S 3G4, Canada; [email protected] Algorithmics Inc., 185 Spadina Avenue, Toronto, ON, M5T 2C6, Canada; [email protected] Royal Bank of Canada, 200 Bay Street, Toronto, ON, M5J 2J5, Canada; [email protected]