Credit Securitisations and Derivatives: Challenges for the Global Markets

11

Analytic Dynamic Factor Copula Model*

Ken Jackson1, Alex Kreinin2 and Wanhe Zhang3

1University of Toronto

2Risk Analytics, Business Analytics, IBM, Toronto

3Royal Bank of Canada, Toronto

11.1 INTRODUCTION

Due to their computational efficiency, factor copula models are popular for pricing multi-name credit derivatives. Within this class of models, the Gaussian factor copula model is the market standard model. However, it cannot match market quotes consistently without violating the model assumptions as explained in Hull and White (2006) and Torresetti et al. (2006). For example, it has to use different correlation factor loadings for different tranches based on the same underlying portfolio. To better match the observable spreads, several modifications have been proposed based on the conditional independence framework. See, for example, Andersen and Sidenius (2004), Baxter (2007) and Hull and White (2008). Most of these approaches are static one-period models that generate a portfolio loss distribution at a fixed maturity. They may not be flexible enough to match market quotes or applicable for new products with strong time-dependent features, such as forward-starting tranches, tranche options and leveraged super-senior tranches as pointed out in Andersen (2006). Another popular approach to calibrate factor copula models is base correlation, as, for example, discussed in McGinty et al. (2004), which calibrates the correlation for the first loss tranche, i.e. the sum of all tranches ...