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Variance reduction for Monte Carlo methods to evaluate option prices under multi-factor stochastic volatility models

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  • Jean-Pierre Fouque
  • Chuan-Hsiang Han

Abstract

We present variance reduction methods for Monte Carlo simulations to evaluate European and Asian options in the context of multiscale stochastic volatility models. European option price approximations, obtained from singular and regular perturbation analysis [Fouque J P, Papanicolaou G, Sircar R and Solna K 2003 Multiscale stochastic volatility asymptotics SIAM J. Multiscale Modeling and Simulation 2], are used in importance sampling techniques, and their efficiencies are compared. Then we investigate the problem of pricing arithmetic average Asian options (AAOs) by Monte Carlo simulations. A two-step strategy is proposed to reduce the variance where geometric average Asian options (GAOs) are used as control variates. Due to the lack of analytical formulas for GAOs under stochastic volatility models, it is then necessary to consider efficient Monte Carlo methods to estimate the unbiased means of GAOs. The second step consists in deriving formulas for approximate prices based on perturbation techniques, and in computing GAOs by using importance sampling. Numerical results illustrate the efficiency of our method.

Suggested Citation

  • Jean-Pierre Fouque & Chuan-Hsiang Han, 2004. "Variance reduction for Monte Carlo methods to evaluate option prices under multi-factor stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 4(5), pages 597-606.
    • Handle: RePEc:taf:quantf:v:4:y:2004:i:5:p:597-606
    DOI: 10.1080/14697680400000041
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    Citations

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    Cited by:

    1. 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.
    2. Ioannis Kyriakou & Panos K. Pouliasis & Nikos C. Papapostolou, 2016. "Jumps and stochastic volatility in crude oil prices and advances in average option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 16(12), pages 1859-1873, December.
    3. Susana Alvarez Diez & Samuel Baixauli & Luis Eduardo Girón, 2019. "Valoración de Opciones Call Asiáticas Promedio Aritmético bajo Movimiento Browniano Logístico," Working Papers 46, Faculty of Economics and Management, Pontificia Universidad Javeriana Cali.
    4. Susana Alvarez Diez & Samuel Baixauli & Luis Eduardo Girón, 2019. "Valoración de opciones call asiáticas Promedio Aritmético usando Taylor Estocástico 1.5," Working Papers 44, Faculty of Economics and Management, Pontificia Universidad Javeriana Cali.
    5. Wong, Hoi Ying & Chan, Chun Man, 2007. "Lookback options and dynamic fund protection under multiscale stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 357-385, May.
    6. Kenichiro Shiraya & Akihiko Takahashi, 2009. "Pricing Average Options on Commodities," CARF F-Series CARF-F-177, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Feb 2012.
    7. Jeonggyu Huh & Jaegi Jeon & Yong-Ki Ma, 2020. "Static Hedges of Barrier Options Under Fast Mean-Reverting Stochastic Volatility," Computational Economics, Springer;Society for Computational Economics, vol. 55(1), pages 185-210, January.
    8. 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.
    9. Han, Chuan-Hsiang & Lai, Yongzeng, 2010. "A smooth estimator for MC/QMC methods in finance," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(3), pages 536-550.
    10. 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.
    11. Deng, Guohe, 2020. "Pricing perpetual American floating strike lookback option under multiscale stochastic volatility model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    12. Ballestra, Luca Vincenzo & Pacelli, Graziella & Zirilli, Francesco, 2007. "A numerical method to price exotic path-dependent options on an underlying described by the Heston stochastic volatility model," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3420-3437, November.
    13. Kenichiro Shiraya & Akihiko Takahashi, 2010. "Pricing Average Options on Commodities," CIRJE F-Series CIRJE-F-747, CIRJE, Faculty of Economics, University of Tokyo.
    14. Zhang, Sumei & Gao, Xiong, 2019. "An asymptotic expansion method for geometric Asian options pricing under the double Heston model," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 1-9.
    15. Slim, Skander, 2016. "On the source of stochastic volatility: Evidence from CAC40 index options during the subprime crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 63-76.

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