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Fast Pricing of Basket Default Swaps

Financial Analytics and Structured Transactions Group, Bear Stearns and Company Inc., New York, New York 10179
Graduate School of Business, Columbia University, New York, New York 10027
zchen1{at}bear.com
pg20{at}columbia.edu

A basket default swap is a derivative security tied to an underlying basket of corporate bonds or other assets subject to credit risk. The value of the contract depends on the joint distribution of the default times of the underlying assets. Valuing a basket default swap often entails Monte Carlo simulation of these default times. For baskets of high-quality credits and for swaps that require multiple defaults to trigger payment, pricing the swap is a rare-event simulation problem. The Joshi-Kainth algorithm is an innovative importance-sampling technique for this problem that forces a predetermined number of defaults to occur on each path. This paper analyzes, extends, and improves the Joshi-Kainth algorithm. We show that, in its original form, the algorithm can actually increase variance; we present an alternative that is guaranteed to reduce variance, even when defaults are not rare. Along the way, we provide a rigorous underpinning in a setting sufficiently general to include both the original method and the version proposed here.

Subject classifications: finance; securities; simulation; efficiency; applications.
History: Received March 2006; revision received July 2006; accepted January 2007.