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A general control variate method for Lévy models in finance

Author

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  • Shiraya, Kenichiro
  • Uenishi, Hiroki
  • Yamazaki, Akira
Abstract
This study proposes a new control variate method for Lévy models in finance. Our method generates a process of the control variate whose initial and terminal values coincide with those of the target Lévy model process, with both processes being driven by the same Brownian motion in the simulation. These features efficiently reduce the variance of the Monte Carlo simulation. As a typical application of this method, we provide the calculation scheme for pricing path-dependent exotic options.

Suggested Citation

  • Shiraya, Kenichiro & Uenishi, Hiroki & Yamazaki, Akira, 2020. "A general control variate method for Lévy models in finance," European Journal of Operational Research, Elsevier, vol. 284(3), pages 1190-1200.
    • Handle: RePEc:eee:ejores:v:284:y:2020:i:3:p:1190-1200
    DOI: 10.1016/j.ejor.2020.01.043
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    References listed on IDEAS

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    1. Shiraya, Kenichiro & Takahashi, Akihiko, 2017. "A general control variate method for multi-dimensional SDEs: An application to multi-asset options under local stochastic volatility with jumps models in finance," European Journal of Operational Research, Elsevier, vol. 258(1), pages 358-371.
    2. Caldana, Ruggero & Fusai, Gianluca, 2013. "A general closed-form spread option pricing formula," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4893-4906.
    3. Fusai, Gianluca & Germano, Guido & Marazzina, Daniele, 2016. "Spitzer identity, Wiener-Hopf factorization and pricing of discretely monitored exotic options," European Journal of Operational Research, Elsevier, vol. 251(1), pages 124-134.
    4. Athanassios N. Avramidis & Pierre L'Ecuyer, 2006. "Efficient Monte Carlo and Quasi-Monte Carlo Option Pricing Under the Variance Gamma Model," Management Science, INFORMS, vol. 52(12), pages 1930-1944, December.
    5. Ruggero Caldana & Gianluca Fusai & Alessandro Gnoatto & Martino Grasselli, 2016. "General closed-form basket option pricing bounds," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 535-554, April.
    6. Fusai, Gianluca & Meucci, Attilio, 2008. "Pricing discretely monitored Asian options under Levy processes," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2076-2088, October.
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    9. Xie, Fei & He, Zhijian & Wang, Xiaoqun, 2019. "An importance sampling-based smoothing approach for quasi-Monte Carlo simulation of discrete barrier options," European Journal of Operational Research, Elsevier, vol. 274(2), pages 759-772.
    10. Liming Feng & Vadim Linetsky, 2008. "Pricing Discretely Monitored Barrier Options And Defaultable Bonds In Lévy Process Models: A Fast Hilbert Transform Approach," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 337-384, July.
    11. Akira Yamazaki, 2016. "Generalized Barndorff-Nielsen And Shephard Model And Discretely Monitored Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-34, June.
    12. Yuji Umezawa & Akira Yamazaki, 2015. "Pricing Path-Dependent Options with Discrete Monitoring under Time-Changed Lévy Processes," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(2), pages 133-161, April.
    13. Gianluca Fusai & Ioannis Kyriakou, 2016. "General Optimized Lower and Upper Bounds for Discrete and Continuous Arithmetic Asian Options," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 531-559, May.
    14. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    15. Claudia Ribeiro & Nick Webber, 2006. "Correcting for Simulation Bias in Monte Carlo Methods to Value Exotic Options in Models Driven by Levy Processes," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(4), pages 333-352.
    16. Yuan Li & Kaimon Miyachi & Kenichiro Shiraya & Akira Yamazaki, 2019. "Approximation Method Using Black-Scholes Formula for Barrier Option Pricing under Lévy Models," CARF F-Series CARF-F-454, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jun 2021.
    17. Mark Broadie & Paul Glasserman & Steven Kou, 1997. "A Continuity Correction for Discrete Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 325-349, October.
    18. Dingeç, Kemal Dinçer & Hörmann, Wolfgang, 2012. "A general control variate method for option pricing under Lévy processes," European Journal of Operational Research, Elsevier, vol. 221(2), pages 368-377.
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    Cited by:

    1. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2021. "Efficient simulation of generalized SABR and stochastic local volatility models based on Markov chain approximations," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1046-1062.
    2. P. D. Hinds & M. V. Tretyakov, 2022. "Neural variance reduction for stochastic differential equations," Papers 2209.12885, arXiv.org, revised May 2023.
    3. Kenichiro Shiraya & Cong Wang & Akira Yamazaki, 2021. "A general control variate method for time-changed Lévy processes: An application to options pricing," CARF F-Series CARF-F-499, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

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