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

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  • 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
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    References listed on IDEAS

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    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.
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. repec:hal:wpaper:hal-01761234 is not listed on IDEAS
    4. 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.
    5. Emmanuel Gobet & Isaque Pimentel & Xavier Warin, 2020. "Option valuation and hedging using asymmetric risk function: asymptotic optimality through fully nonlinear Partial Differential Equations," Post-Print hal-01761234, HAL.
    6. Ludovic Gouden`ege & Andrea Molent & Antonino Zanette, 2023. "Backward Hedging for American Options with Transaction Costs," Papers 2305.06805, arXiv.org, revised Jun 2023.
    7. William Lefebvre & Gr'egoire Loeper & Huy^en Pham, 2022. "Differential learning methods for solving fully nonlinear PDEs," Papers 2205.09815, arXiv.org.
    8. 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.
    9. Igor Halperin, 2017. "QLBS: Q-Learner in the Black-Scholes(-Merton) Worlds," Papers 1712.04609, arXiv.org, revised Sep 2019.
    10. 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.
    11. 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.
    12. 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.
    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.
    18. 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.

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