Approximations and control variates for pricing portfolio credit derivatives
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
Risk Analysis of Collateralized Debt Obligations
Operations Research
Exact and Efficient Simulation of Correlated Defaults
SIAM Journal on Financial Mathematics
Computing mean first exit times for stochastic processes using multi-level Monte Carlo
Proceedings of the Winter Simulation Conference
Numerical methods to quantify the model risk of basket default swaps
Journal of Computational and Applied Mathematics
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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.