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Title: Adaptive Monte Carlo Variance Reduction for Lévy Processes with Two-Time-Scale Stochastic Approximation
Authors: Kawai, Reiichiro
First Published: Jun-2008
Publisher: Springer Verlag
Citation: Methodology and Computing in Applied Probability, 2008, 10 (2), pp. 199-223.
Abstract: We propose an approach to a twofold optimal parameter search for a combined variance reduction technique of the control variates and the important sampling in a suitable pure-jump Lévy process framework. The parameter search procedure is based on the two-time-scale stochastic approximation algorithm with equilibrated control variates component and with quasi-static importance sampling one. We prove the almost sure convergence of the algorithm to a unique optimum. The parameter search algorithm is further embedded in adaptive Monte Carlo simulations in the case of the gamma distribution and process. Numerical examples of the CDO tranche pricing with the Gamma copula model and the intensity Gamma model are provided to illustrate the effectiveness of our method.
DOI Link: 10.1007/s11009-007-9043-5
ISSN: 1387-5841
Type: Article
Rights: This is the author's final draft of the paper published as Methodology and Computing in Applied Probability, 2008, 10 (2), pp. 199-223. The original publication is available at Doi: 10.1007/s11009-007-9043-5
Appears in Collections:Published Articles, Dept. of Mathematics

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