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An FBSDE Approach to American Option Pricing with an Interacting Particle Method

Author

Listed:
  • Masaaki Fujii

    (Faculty of Economics, University of Tokyo)

  • Seisho Sato

    (Faculty of Economics, University of Tokyo)

  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)

Abstract

In the paper, we propose a new calculation scheme for American options in the framework of a forward backward stochastic di erential equation (FBSDE). The well-known decomposition of an American option price with that of a European option of the same maturity and the remaining early exercise premium can be cast into the form of a decoupled non-linear FBSDE. We numerically solve the FBSDE by applying an interacting particle method recently proposed by Fujii & Takahashi (2012c), which allows one to perform a Monte Carlo simulation in a fully forward-looking manner. We perform the fourth-order analysis for the Black-Scholes (BS) model and the third-order analysis for the Heston model. The comparison to those obtained from exising tree algorithms shows the effectiveness of the particle method.

Suggested Citation

  • Masaaki Fujii & Seisho Sato & Akihiko Takahashi, 2012. "An FBSDE Approach to American Option Pricing with an Interacting Particle Method," CIRJE F-Series CIRJE-F-871, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2012cf871
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    References listed on IDEAS

    as
    1. Masaaki Fujii & Akihiko Takahashi, 2012. "Perturbative Expansion of FBSDE in an Incomplete Market with Stochastic Volatility," CARF F-Series CARF-F-270, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jun 2012.
    2. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2011. "A General Computation Scheme for a High-Order Asymptotic Expansion Method," CARF F-Series CARF-F-242, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jul 2011.
    3. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2011. "A General Computation Scheme for a High-Order Asymptotic Expansion Method," CIRJE F-Series CIRJE-F-787, CIRJE, Faculty of Economics, University of Tokyo.
    4. Marek Rutkowski, 1994. "The Early Exercise Premium Representation Of Foreign Market American Options1," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 313-325, October.
    5. Masaaki Fujii & Akihiko Takahashi, 2012. "Perturbative Expansion of FBSDE in an Incomplete Market with Stochastic Volatility," CIRJE F-Series CIRJE-F-840, CIRJE, Faculty of Economics, University of Tokyo.
    6. Masaaki Fujii & Akihiko Takahashi, 2012. "Perturbative Expansion of FBSDE in an Incomplete Market with Stochastic Volatility," Papers 1202.0608, arXiv.org, revised Sep 2012.
    7. Duffie, Darrell & Huang, Ming, 1996. "Swap Rates and Credit Quality," Journal of Finance, American Finance Association, vol. 51(3), pages 921-949, July.
    8. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14, April.
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    Cited by:

    1. Akihiko Takahashi & Toshihiro Yamada, 2013. "On an Asymptotic Expansion of Forward-Backward SDEs with a Perturbed Driver," CARF F-Series CARF-F-326, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Oct 2013.
    2. Masaaki Fujii & Akihiko Takahashi, 2013. "Making Mean-Variance Hedging Implementable in a Partially Observable Market," Papers 1306.3359, arXiv.org, revised Nov 2013.
    3. Masaaki Fujii & Akihiko Takahashi, 2013. "Making Mean-Variance Hedging Implementable in a Partially Observable Market -with supplementary contents for stochastic interest rates-," CARF F-Series CARF-F-332, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    4. Kenichiro Shiraya & Akihiko Takahashi, 2013. "Pricing Basket Options under Local Stochastic Volatility with Jumps," CARF F-Series CARF-F-336, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised May 2014.
    5. Kenichiro Shiraya & Akihiko Takahashi, 2015. "An approximation formula for basket option prices under local stochastic volatility with jumps: an application to commodity markets," CARF F-Series CARF-F-361, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Aug 2015.
    6. Kenichiro Shiraya & Akihiko Takahashi, 2015. "An Approximation Formula for Basket Option Prices under Local Stochastic Volatility with Jumps: an Application to Commodity Markets," CIRJE F-Series CIRJE-F-973, CIRJE, Faculty of Economics, University of Tokyo.
    7. Akihiko Takahashi & Toshihiro Yamada, 2013. "On an Asymptotic Expansion of Forward-Backward SDEs with a Perturbed Driver," CIRJE F-Series CIRJE-F-902, CIRJE, Faculty of Economics, University of Tokyo.
    8. Kenichiro Shiraya & Akihiko Takahashi, 2014. "Pricing Basket Options under Local Stochastic Volatility with Jumps," CIRJE F-Series CIRJE-F-913, CIRJE, Faculty of Economics, University of Tokyo.
    9. Akihiko Takahashi, 2015. "Asymptotic Expansion Approach in Finance," CARF F-Series CARF-F-356, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Aug 2015.
    10. Masaaki Fujii & Akihiko Takahashi, 2013. "Making Mean-Variance Hedging Implementable in a Partially Observable Market -with supplementary contents for stochastic interest rates-," CIRJE F-Series CIRJE-F-891, CIRJE, Faculty of Economics, University of Tokyo.
    11. Masaaki Fujii & Akihiko Takahashi, 2013. "Making Mean-Variance Hedging Implementable in a Partially Observable Market," CARF F-Series CARF-F-321, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

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