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Fast Valuation of Forward-Starting Basket Default Swaps

by Ken Jackson of the University of Toronto,
Alex Kreinin of Algorithmics, Inc., and
Wanhe Zhang of the University of Toronto

December 13, 2007

Abstract: A basket default swap (BDS) is a credit derivative with contingent payments that are triggered by a combination of default events of the reference entities. A forward-starting basket default swap (FBDS) is a BDS starting at a specified future time. Existing analytic or semi-analytic methods for pricing FBDS are time consuming due to the large number of possible default combinations before the BDS starts. This paper develops a fast approximation method for FBDS based on the conditional independence framework. The method converts the pricing of a FBDS to an equivalent BDS pricing problem and combines Monte Carlo simulation with an analytic approach to achieve an effective method. This hybrid method is a novel technique which can be viewed either as a means to accelerate the convergence of Monte Carlo simulation or as a way to estimate parameters in an analytic method that are difficult to compute directly. Numerical results demonstrate the accuracy and efficiency of the proposed hybrid method.

JEL Classification: G13, C15, C63.

Keywords: Credit derivatives, forward-starting basket default swaps, conditional independence, hybrid methods.

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