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Adaptive Monte Carlo Variance Reduction for Lévy Processes with Two-Time-Scale Stochastic Approximation

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  • Reiichiro Kawai

    (Osaka University)

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.

Suggested Citation

  • Reiichiro Kawai, 2008. "Adaptive Monte Carlo Variance Reduction for Lévy Processes with Two-Time-Scale Stochastic Approximation," Methodology and Computing in Applied Probability, Springer, vol. 10(2), pages 199-223, June.
    • Handle: RePEc:spr:metcap:v:10:y:2008:i:2:d:10.1007_s11009-007-9043-5
    DOI: 10.1007/s11009-007-9043-5
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    References listed on IDEAS

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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Kallsen, Jan & Tankov, Peter, 2006. "Characterization of dependence of multidimensional Lévy processes using Lévy copulas," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1551-1572, August.
    3. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 1999. "Asymptotically Optimal Importance Sampling and Stratification for Pricing Path‐Dependent Options," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 117-152, April.
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    Cited by:

    1. Youngjun Choe & Henry Lam & Eunshin Byon, 2018. "Uncertainty Quantification of Stochastic Simulation for Black-box Computer Experiments," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1155-1172, December.

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