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Variance reduction for Monte Carlo simulation in a stochastic volatility environment

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  • Jean-Pierre Fouque
  • Tracey Andrew Tullie

Abstract

We propose a variance reduction method for Monte Carlo computation of option prices in the context of stochastic volatility. This method is based on importance sampling using an approximation of the option price obtained by a fast mean-reversion expansion introduced in Fouque et al (2000 Derivatives in Financial Markets with Stochastic Volatility (Cambridge: Cambridge University Press)). We compare this with the small noise expansion method proposed in Fournie et al (1997 Asymptotic Anal. 14 361-76) and demonstrate numerically the efficiency of our method, in particular in the presence of a skew.

Suggested Citation

  • Jean-Pierre Fouque & Tracey Andrew Tullie, 2002. "Variance reduction for Monte Carlo simulation in a stochastic volatility environment," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 24-30.
    • Handle: RePEc:taf:quantf:v:2:y:2002:i:1:p:24-30
    DOI: 10.1088/1469-7688/2/1/302
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    References listed on IDEAS

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    1. 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.
    2. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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    Cited by:

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    2. Cheng-Der Fuh & Yanwei Jia & Steven Kou, 2023. "A General Framework for Importance Sampling with Latent Markov Processes," Papers 2311.12330, arXiv.org.
    3. 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.
    4. Collan, Mikael, 2004. "Giga-Investments: Modelling the Valuation of Very Large Industrial Real Investments," MPRA Paper 4328, University Library of Munich, Germany.
    5. Song-Ping Zhu & Wen-Ting Chen, 2011. "Should An American Option Be Exercised Earlier Or Later If Volatility Is Not Assumed To Be A Constant?," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(08), pages 1279-1297.
    6. Yijuan Liang & Xiuchuan Xu, 2019. "Variance and Dimension Reduction Monte Carlo Method for Pricing European Multi-Asset Options with Stochastic Volatilities," Sustainability, MDPI, vol. 11(3), pages 1-21, February.
    7. Traian A. Pirvu & Gordan Zitkovic, 2007. "Maximizing the Growth Rate under Risk Constraints," Papers 0706.0480, arXiv.org.

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