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An Efficient Algorithm for Basket Default Swap Valuation

Mi-Hsiu Chiang, Meng-Lan Yueh and Ming-Hua Hsieh
The Journal of Derivatives Winter 2007, 15 (2) 8-19; DOI: https://doi.org/10.3905/jod.2007.699043
Mi-Hsiu Chiang
An assistant professor in the department of money and banking at National Chengchi University in Taiwan.
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  • For correspondence: mhchiang@nccu.edu.tw
Meng-Lan Yueh
An assistant professor in the department of finance at National Central University in Taiwan.
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  • For correspondence: mlyueh@cc.ncu.edu.tw
Ming-Hua Hsieh
An associate professor in the department of management information systems at National Chengchi University in Taiwan.
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  • For correspondence: mhsieh@mis.nccu.edu.tw
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Abstract

Monte Carlo simulation has become a workhorse of practical derivatives valuation because it is often impossible to construct theoretical pricing models for real world instruments in closed form. Credit derivatives are a case in point. But a major problem in the use of simulation methods for securities tied to default risk is that they are often written on baskets of individual credits, meaning that the number of correlated random variables to simulate can be very large, and the derivative's value depends heavily on the correlations among defaults. Individual defaults are very low probability events, so joint defaults are rare indeed. Often, a great many Monte Carlo paths must be simulated to produce even a single credit event for a contract like a k-th-to-default basket swap. Importance sampling, which focuses the simulation effort on the most important paths for a given problem, is a useful variance reduction technique. In this article, the authors present an importance sampling methodology that is easy to implement and guarantees variance reduction for k-th-to-default basket swaps. A set of numerical examples using 1st-, 2nd- and 3rd-to-default contracts based on industry portfolios, each containing five bonds, demonstrates how powerful the approach is. The amount of variance reduction depends on the level of correlation among the credits, which is substantial, and can be an order of magnitude, or even more, for highly correlated risks.

TOPICS: Credit default swaps, simulations, technical analysis

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The Journal of Derivatives
Vol. 15, Issue 2
Winter 2007
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An Efficient Algorithm for Basket Default Swap Valuation
Mi-Hsiu Chiang, Meng-Lan Yueh, Ming-Hua Hsieh
The Journal of Derivatives Nov 2007, 15 (2) 8-19; DOI: 10.3905/jod.2007.699043

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An Efficient Algorithm for Basket Default Swap Valuation
Mi-Hsiu Chiang, Meng-Lan Yueh, Ming-Hua Hsieh
The Journal of Derivatives Nov 2007, 15 (2) 8-19; DOI: 10.3905/jod.2007.699043
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