Valuation of Basket Default Swaps (BDS), equivalent to calculation of the fair premium, is a challenging task in practice. The closed form solution of such contract is usually hard to find, thus we must resort to Monte Carlo (MC) method. Under ordinary scenarios, the MC method works well and yields an acceptable estimator. However, when high-rating assets are in one basket, naïve Monte Carlo is no more efficient (slow in convergence), or not effective
at all (providing uninformative zero estimators.)

To improve the quality of valuation, we propose two algorithms to refine the crude Monte Carlo. Both algorithms rely on conditional expectation and importance sampling (IS) techniques. The first algorithm is conditional on all
marginal factors, and then choose an appropriate IS
distribution carefully for the common factor. The second algorithm, however, does things reversely. We condition on the common factor in the first step, and shift every factor mean to “important” regions, by the conditional independence property. We find that conditioning on all trivial factors and changing the measures of principal
factors is the best strategy. Both algorithms greatly outperform basic MC, measured in variances, when the default events are very rare.

Besides, sensitivity analysis and comparisons of both algorithms’ performances are also presented. We also show that precise estimations from our algorithms are beneficial to both valuation (pricing) and Greek calculation (hedging.)

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