IDEAS home Printed from https://ideas.repec.org/p/uts/rpaper/75.html
   My bibliography  Save this paper

A Variance Reduction Technique Based on Integral Representations

Author

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
    as

    Download full text from publisher

    File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp75.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    2. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    3. David Heath & Eckhard Platen & Martin Schweizer, 2001. "Numerical Comparison of Local Risk-Minimisation & Mean-Variance Hedging," Published Paper Series 2001-3, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    4. Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992. "Option Pricing Under Incompleteness and Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 153-187, July.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    6. Jouini,E. & Cvitanic,J. & Musiela,Marek (ed.), 2001. "Handbooks in Mathematical Finance," Cambridge Books, Cambridge University Press, number 9780521792370.
    7. Corwin Joy & Phelim P. Boyle & Ken Seng Tan, 1996. "Quasi-Monte Carlo Methods in Numerical Finance," Management Science, INFORMS, vol. 42(6), pages 926-938, June.
    8. Dwight Grant & Gautam Vora & David Weeks, 1997. "Path-Dependent Options: Extending the Monte Carlo Simulation Approach," Management Science, INFORMS, vol. 43(11), pages 1589-1602, November.
    9. Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
    10. Platen, Eckhard, 1995. "On weak implicit and predictor-corrector methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 38(1), pages 69-76.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ravi Kashyap, 2022. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Annals of Operations Research, Springer, vol. 315(2), pages 1175-1215, August.
    2. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    3. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    4. Ammann, Manuel & Kind, Axel & Wilde, Christian, 2008. "Simulation-based pricing of convertible bonds," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 310-331, March.
    5. Nelson Areal & Artur Rodrigues & Manuel Armada, 2008. "On improving the least squares Monte Carlo option valuation method," Review of Derivatives Research, Springer, vol. 11(1), pages 119-151, March.
    6. Zbigniew Palmowski & Tomasz Serafin, 2020. "Note on simulation pricing of $\pi$-options," Papers 2007.02076, arXiv.org, revised Aug 2020.
    7. Hatem Ben-Ameur & Michèle Breton & Pierre L'Ecuyer, 2002. "A Dynamic Programming Procedure for Pricing American-Style Asian Options," Management Science, INFORMS, vol. 48(5), pages 625-643, May.
    8. Christian Bayer & Ra'ul Tempone & Soren Wolfers, 2018. "Pricing American Options by Exercise Rate Optimization," Papers 1809.07300, arXiv.org, revised Aug 2019.
    9. Martin B. Haugh & Leonid Kogan, 2004. "Pricing American Options: A Duality Approach," Operations Research, INFORMS, vol. 52(2), pages 258-270, April.
    10. Zbigniew Palmowski & Tomasz Serafin, 2020. "A Note on Simulation Pricing of π -Options," Risks, MDPI, vol. 8(3), pages 1-19, August.
    11. O. Samimi & Z. Mardani & S. Sharafpour & F. Mehrdoust, 2017. "LSM Algorithm for Pricing American Option Under Heston–Hull–White’s Stochastic Volatility Model," Computational Economics, Springer;Society for Computational Economics, vol. 50(2), pages 173-187, August.
    12. Song-Ping Zhu & Xin-Jiang He, 2018. "A hybrid computational approach for option pricing," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-16, September.
    13. Augusto Castillo, 2004. "Firm and Corporate Bond Valuation: A Simulation Dynamic Programming Approach," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 41(124), pages 345-360.
    14. repec:hum:wpaper:sfb649dp2006-051 is not listed on IDEAS
    15. Denis Belomestny & Grigori Milstein & Vladimir Spokoiny, 2009. "Regression methods in pricing American and Bermudan options using consumption processes," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 315-327.
    16. Cosma, Antonio & Galluccio, Stefano & Pederzoli, Paola & Scaillet, Olivier, 2020. "Early Exercise Decision in American Options with Dividends, Stochastic Volatility, and Jumps," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(1), pages 331-356, February.
    17. Antonio Cosma & Stefano Galluccio & Paola Pederzoli & O. Scaillet, 2012. "Valuing American Options Using Fast Recursive Projections," Swiss Finance Institute Research Paper Series 12-26, Swiss Finance Institute.
    18. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    19. Ascione, Giacomo & Mehrdoust, Farshid & Orlando, Giuseppe & Samimi, Oldouz, 2023. "Foreign Exchange Options on Heston-CIR Model Under Lévy Process Framework," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    20. Berridge, S.J. & Schumacher, J.M., 2002. "An Irregular Grid Approach for Pricing High Dimensional American Options," Other publications TiSEM 416a6d43-3466-47e0-b656-d, Tilburg University, School of Economics and Management.
    21. John Board & Charles Sutcliffe & William T. Ziemba, 2003. "Applying Operations Research Techniques to Financial Markets," Interfaces, INFORMS, vol. 33(2), pages 12-24, April.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:uts:rpaper:75. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Duncan Ford (email available below). General contact details of provider: https://edirc.repec.org/data/qfutsau.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.