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A General Control Variate Method for Lévy Models in Finance (Published in European Journal of Operational Research.)

Author

Listed:
  • Kenichiro Shiraya

    (Graduate School of Economics, The University of Tokyo)

  • Hiroki Uenishi

    (Graduate School of Economics, The University of Tokyo)

  • Akira Yamazaki

    (Graduate School of Business Administration, Hosei University)

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. We use numerical experiments to examine the validity of our method for both continuously and discretely monitored path-dependent options under variance gamma and normal inverse Gaussian models.

Suggested Citation

  • Kenichiro Shiraya & Hiroki Uenishi & Akira Yamazaki, 2019. "A General Control Variate Method for Lévy Models in Finance (Published in European Journal of Operational Research.)," CARF F-Series CARF-F-455, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jan 2020.
    • Handle: RePEc:cfi:fseres:cf455
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Caldana, Ruggero & Fusai, Gianluca, 2013. "A general closed-form spread option pricing formula," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4893-4906.
    9. 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.
    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. 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.
    12. 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.
    13. 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.
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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. Yuan Li & Kenichiro Shiraya & Yuji Umezawa & Akira Yamazaki, 2022. "Moments of Maximum of Lévy Processes: Application to Barrier and Lookback Option Pricing," CARF F-Series CARF-F-536, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

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