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Efficient algorithms for basket default swap pricing with multivariate Archimedean copulas. (English) Zbl 1233.91296
Summary: We introduce a new importance sampling method for pricing basket default swaps employing exchangeable Archimedean copulas and nested Gumbel copulas. We establish more realistic dependence structures than existing copula models for credit risks in the underlying portfolio, and propose an appropriate density for importance sampling by analyzing multivariate Archimedean copulas. To justify efficiency and accuracy of the proposed algorithms, we present numerical examples and compare them with the crude Monte Carlo simulation, and finally show that our proposed estimators produce considerably smaller variances.

MSC:
91G40 Credit risk
91G70 Statistical methods; risk measures
62H20 Measures of association (correlation, canonical correlation, etc.)
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