科研之友
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摘要
Importance sampling (IS), as an efficiency improvement technique for Monte Carlo simulations, is particularly well-suited for correlation products which have payoffs contingent on the occurrence of rare events. An appropriate choice of the IS distribution is of absolute necessity to ensure variance reduction. Without being chosen carefully, the use of IS can result in ineffective variance reduction, or at the worse cases, even increase the variance of the Monte Carlo estimators. Hence, it is highly desirable to be able to select the right IS distribution that guarantees variance reduction.. In this paper, we propose an effective IS algorithm for the valuation of k-th to default basket default swaps. The algorithm is simple to implement and guarantees variance reduction. We have established a way of ensuring that for every simulation path generated, the desired default events always take place, and this is achieved tinder an appropriate choice of the IS distribution among the set of possible measures that can force the required events of interest to occur. Our numerical results show that the proposed algorithm is considerably more efficient than the crude simulation method. The gain in variance-reduction efficiency is particularly prominent when the possibility of the k-th default event is remote.
- 出版日期2007
- 单位中央民族大学
