Pricing Correlation-Dependent Derivatives Based on Exponential Approximations to the Hockey Stick Function

Correlation-dependent derivatives, such as Asset-Backed Securities (ABS) and Collateralized Debt Obligations (CDO), have grown rapidly. Factor models in the conditional independence framework are widely used in practice to capture the correlated default events of the underlying obligors. An essential part of these models is the accurate and efficient evaluation of the expected loss of the specified tranche, conditional on a given value of a systematic factor (or values of a set of systematic factors). Unlike other papers that focus on how to evaluate the loss distribution of the underlying pool, in this paper we focus on the tranche loss function itself. It is approximated by a sum of This research was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada. Algorithmics Inc., 185 Spadina Avenue, Toronto, ON, M5T 2C6, Canada; [email protected] Department of Computer Science, University of Toronto, 10 King’s College Rd, Toronto, ON, M5S 3G4, Canada; [email protected] Algorithmics Inc., 185 Spadina Avenue, Toronto, ON, M5T 2C6, Canada; [email protected] Department of Computer Science, University of Toronto, 10 King’s College Rd, Toronto, ON, M5S 3G4, Canada; [email protected]