IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v289y2001i3p517-525.html
   My bibliography  Save this article

Hedged Monte-Carlo: low variance derivative pricing with objective probabilities

Author

Listed:
  • Potters, Marc
  • Bouchaud, Jean-Philippe
  • Sestovic, Dragan

Abstract

We propose a new ‘hedged’ Monte-Carlo (HMC) method to price financial derivatives, which allows to determine simultaneously the optimal hedge. The inclusion of the optimal hedging strategy allows one to reduce the financial risk associated with option trading, and for the very same reason reduces considerably the variance of our HMC scheme as compared to previous methods. The explicit accounting of the hedging cost naturally converts the objective probability into the ‘risk-neutral’ one. This allows a consistent use of purely historical time series to price derivatives and obtain their residual risk. The method can be used to price a large class of exotic options, including those with path dependent and early exercise features.

Suggested Citation

  • Potters, Marc & Bouchaud, Jean-Philippe & Sestovic, Dragan, 2001. "Hedged Monte-Carlo: low variance derivative pricing with objective probabilities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 289(3), pages 517-525.
    • Handle: RePEc:eee:phsmap:v:289:y:2001:i:3:p:517-525
    DOI: 10.1016/S0378-4371(00)00554-9
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437100005549
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/S0378-4371(00)00554-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Andrew Matacz & Jean-Philippe Bouchaud, 2000. "An Empirical Investigation Of The Forward Interest Rate Term Structure," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 703-729.
    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. William Lefebvre & Gr'egoire Loeper & Huy^en Pham, 2022. "Differential learning methods for solving fully nonlinear PDEs," Papers 2205.09815, arXiv.org.
    2. Igor Halperin, 2017. "QLBS: Q-Learner in the Black-Scholes(-Merton) Worlds," Papers 1712.04609, arXiv.org, revised Sep 2019.
    3. Lisa Borland & Jean-Philippe Bouchaud & Jean-Francois Muzy & Gilles Zumbach, 2005. "The Dynamics of Financial Markets -- Mandelbrot's multifractal cascades, and beyond," Science & Finance (CFM) working paper archive 500061, Science & Finance, Capital Fund Management.
    4. Wang, Xiao-Tian, 2010. "Scaling and long range dependence in option pricing, IV: Pricing European options with transaction costs under the multifractional Black–Scholes model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(4), pages 789-796.
    5. Wang, Xiao-Tian & Wu, Min & Zhou, Ze-Min & Jing, Wei-Shu, 2012. "Pricing European option with transaction costs under the fractional long memory stochastic volatility model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1469-1480.
    6. Ankirchner, Stefan & Schneider, Judith C. & Schweizer, Nikolaus, 2014. "Cross-hedging minimum return guarantees: Basis and liquidity risks," Journal of Economic Dynamics and Control, Elsevier, vol. 41(C), pages 93-109.
    7. Wang, Xiao-Tian & Li, Zhe & Zhuang, Le, 2017. "Risk preference, option pricing and portfolio hedging with proportional transaction costs," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 111-130.
    8. Wang, Xiao-Tian, 2011. "Scaling and long-range dependence in option pricing V: Multiscaling hedging and implied volatility smiles under the fractional Black–Scholes model with transaction costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1623-1634.
    9. Emmanuel Gobet & Isaque Pimentel & Xavier Warin, 2018. "Option valuation and hedging using asymmetric risk function: asymptotic optimality through fully nonlinear Partial Differential Equations," Working Papers hal-01761234, HAL.
    10. Christa Cuchiero & Wahid Khosrawi & Josef Teichmann, 2020. "A Generative Adversarial Network Approach to Calibration of Local Stochastic Volatility Models," Risks, MDPI, vol. 8(4), pages 1-31, September.
    11. Ludovic Gouden`ege & Andrea Molent & Antonino Zanette, 2023. "Backward Hedging for American Options with Transaction Costs," Papers 2305.06805, arXiv.org, revised Jun 2023.
    12. Emmanuel Gobet & Isaque Pimentel & Xavier Warin, 2020. "Option valuation and hedging using an asymmetric risk function: asymptotic optimality through fully nonlinear partial differential equations," Finance and Stochastics, Springer, vol. 24(3), pages 633-675, July.
    13. Wang, Xiao-Tian, 2010. "Scaling and long-range dependence in option pricing I: Pricing European option with transaction costs under the fractional Black–Scholes model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 438-444.
    14. Benoit Pochard & Jean-Philippe Bouchaud, 2003. "Option pricing and hedging with minimum expected shortfall," Science & Finance (CFM) working paper archive 500029, Science & Finance, Capital Fund Management.
    15. Wang, Xiao-Tian & Zhao, Zhong-Feng & Fang, Xiao-Fen, 2015. "Option pricing and portfolio hedging under the mixed hedging strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 424(C), pages 194-206.
    16. Ajay Khanna & Dilip Madan, 2004. "Understanding option prices," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 55-63.
    17. William Lefebvre & Grégoire Loeper & Huyên Pham, 2023. "Differential learning methods for solving fully nonlinear PDEs," Digital Finance, Springer, vol. 5(1), pages 183-229, March.

    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. Eckhard Platen, 2005. "An Alternative Interest Rate Term Structure Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(06), pages 717-735.
    2. 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.
    3. Tiziana Di Matteo & Tomaso Aste, 2002. "How Does The Eurodollar Interest Rate Behave?," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 107-122.
    4. repec:uts:finphd:40 is not listed on IDEAS
    5. Belal Baaquie & Jean-Philippe Bouchaud, 2004. ""Stiff" Field Theory of Interest Rates and Psychological Future Time," Papers cond-mat/0403713, arXiv.org.
    6. Shane Miller, 2007. "Pricing of Contingent Claims Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2007.
    7. Kevin John Fergusson, 2018. "Less-Expensive Pricing and Hedging of Extreme-Maturity Interest Rate Derivatives and Equity Index Options Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2018.
    8. Shane Miller, 2007. "Pricing of Contingent Claims Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 25, July-Dece.
    9. Baaquie, Belal E. & Liang, Cui & Warachka, Mitch C., 2007. "Hedging LIBOR derivatives in a field theory model of interest rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 730-748.
    10. Zhou, Wei-Xing & Sornette, Didier, 2004. "Causal slaving of the US treasury bond yield antibubble by the stock market antibubble of August 2000," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 337(3), pages 586-608.
    11. Belal E. Baaquie & Marakani Srikant & Mitch Warachka, 2002. "A Quantum Field Theory Term Structure Model Applied to Hedging," Papers cond-mat/0206457, arXiv.org.
    12. Belal Baaquie & Jean-Philippe Bouchaud, 2004. ""Stiff" Field Theory of Interest Rates and Psychological Future Time," Science & Finance (CFM) working paper archive 500064, Science & Finance, Capital Fund Management.
    13. Fergusson, Kevin, 2020. "Less-Expensive Valuation And Reserving Of Long-Dated Variable Annuities When Interest Rates And Mortality Rates Are Stochastic," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 381-417, May.
    14. Marc Potters & Jean-Philippe Bouchaud & Dragan Sestovic, 2000. "Hedged Monte-Carlo: low variance derivative pricing with objective probabilities," Science & Finance (CFM) working paper archive 500031, Science & Finance, Capital Fund Management.
    15. Belal E. Baaquie & Marakani Srikant & Mitch C. Warachka, 2003. "A Quantum Field Theory Term Structure Model Applied to Hedging," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(05), pages 443-467.
    16. Kevin Fergusson & Eckhard Platen, 2014. "Stylised Properties of the Interest Rate Term Structure Under The Benchmark Approach," Research Paper Series 351, Quantitative Finance Research Centre, University of Technology, Sydney.

    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:eee:phsmap:v:289:y:2001:i:3:p:517-525. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.