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A Variance Reduction Technique Based on Integral Representations

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Abstract

Standard Monte Carlo methods can often be significantly improved with the addition of appropriate variance reduction techniques. In this paper a new and powerful variance reduction technique is presented. The method is based directly on the Ito calculus and is used to find unbiased variance reduced estimators for the expectation of functionals of Ito diffusion processes. The approach considered has wide applicability, for instance, it can be used as a means of approximating solutions of parabolic partial differential equations or applied to valuation problems that arise in mathematical finance. We illustrate how the method can be applied by considering the pricing of European style derivative securities for a class of stochastic volatility models, including the Heston model.

Suggested Citation

  • David Heath & Eckhard Platen, 2002. "A Variance Reduction Technique Based on Integral Representations," Research Paper Series 75, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:75
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    File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp75.pdf
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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
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    11. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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    Cited by:

    1. Kailin Ding & Zhenyu Cui & Xiaoguang Yang, 2023. "Pricing arithmetic Asian and Amerasian options: A diffusion operator integral expansion approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(2), pages 217-241, February.
    2. David Heath & Eckhard Platen, 2014. "A Monte Carlo Method using PDE Expansions for a Diversifed Equity Index Model," Research Paper Series 350, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Chuan-Hsiang Han & Wei-Han Liu & Tzu-Ying Chen, 2014. "VaR/CVaR ESTIMATION UNDER STOCHASTIC VOLATILITY MODELS," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(02), pages 1-35.
    4. Gao, Jiti, 2002. "Modeling long-range dependent Gaussian processes with application in continuous-time financial models," MPRA Paper 11973, University Library of Munich, Germany, revised 18 Sep 2003.
    5. Nicola Bruti-Liberati & Christina Nikitopoulos-Sklibosios & Eckhard Platen & Erik Schlögl, 2009. "Alternative Defaultable Term Structure Models," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 16(1), pages 1-31, March.
    6. Belomestny, D. & Häfner, S. & Urusov, M., 2018. "Stratified regression-based variance reduction approach for weak approximation schemes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 143(C), pages 125-137.
    7. David Heath & Eckhard Platen, 2006. "Local volatility function models under a benchmark approach," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 197-206.
    8. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, November.
    9. Okano Yusuke & Yamada Toshihiro, 2019. "A control variate method for weak approximation of SDEs via discretization of numerical error of asymptotic expansion," Monte Carlo Methods and Applications, De Gruyter, vol. 25(3), pages 239-252, September.
    10. Mark Broadie & Özgür Kaya, 2006. "Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes," Operations Research, INFORMS, vol. 54(2), pages 217-231, April.
    11. Johan Auster & Ludovic Mathys & Fabio Maeder, 2021. "JDOI Variance Reduction Method and the Pricing of American-Style Options," Papers 2104.01365, arXiv.org, revised May 2021.
    12. Coskun Sema & Korn Ralf, 2018. "Pricing barrier options in the Heston model using the Heath–Platen estimator," Monte Carlo Methods and Applications, De Gruyter, vol. 24(1), pages 29-41, March.
    13. Denis Belomestny & Stefan Hafner & Mikhail Urusov, 2016. "Stratified regression-based variance reduction approach for weak approximation schemes," Papers 1612.05255, arXiv.org, revised Mar 2017.

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    More about this item

    Keywords

    monte carlo method; variance reduction; stochastic volatility; heston model;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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