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An approximation method for pricing continuous barrier options under multi-asset local stochastic volatility models (Forthcoming in International Journal of Theoretical and Applied Finance.)

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  • Kenichiro Shiraya

    (The University of Tokyo)

Abstract

This paper presents a new approximation method for pricing multi-asset continuous single barrier options under general local stochastic volatility models. The formula applies an asymptotic expansion technique and an approximation for the hitting probability. This method focuses on local stochastic volatility models with unknown characteristic function and transition density function. To the best of our knowledge, our approximation formula is the first to achieve analytic approximations for continuous barrier options prices in this environment. In numerical experiments, we examine the validity of the formula.

Suggested Citation

  • Kenichiro Shiraya, 2016. "An approximation method for pricing continuous barrier options under multi-asset local stochastic volatility models (Forthcoming in International Journal of Theoretical and Applied Finance.)," CARF F-Series CARF-F-397, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Nov 2018.
    • Handle: RePEc:cfi:fseres:cf397
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    References listed on IDEAS

    as
    1. Kenichiro Shiraya & Akihiko Takahashi & Toshihiro Yamada, 2012. "Pricing Discrete Barrier Options Under Stochastic Volatility," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 19(3), pages 205-232, September.
    2. Takashi Kato & Akihiko Takahashi & Toshihiro Yamada, 2013. "An Asymptotic Expansion Formula for Up-and-Out Barrier Option Price under Stochastic Volatility Model," Papers 1302.3306, arXiv.org.
    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. Yukihiro Tsuzuki, 2014. "Pricing Bounds on Barrier Options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(12), pages 1170-1184, December.
    5. Peter Carr & Katrina Ellis & Vishal Gupta, 1998. "Static Hedging of Exotic Options," Journal of Finance, American Finance Association, vol. 53(3), pages 1165-1190, June.
    6. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2009. "Computation in an Asymptotic Expansion Method," CIRJE F-Series CIRJE-F-621, CIRJE, Faculty of Economics, University of Tokyo.
    7. Takashi Kato & Akihiko Takahashi & Toshihiro Yamada, 2014. "A Semi-group Expansion for Pricing Barrier Options," CARF F-Series CARF-F-349, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    8. Haydyn Brown & David Hobson & L. C. G. Rogers, 2001. "Robust Hedging of Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 11(3), pages 285-314, July.
    9. Kenichiro Shiraya & Akihiko Takahashi & Toshihiro Yamada, 2010. "Pricing Discrete Barrier Options under Stochastic Volatility," CARF F-Series CARF-F-210, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Aug 2011.
    10. Takashi Kato & Akihiko Takahashi & Toshihiro Yamada, 2013. "An Asymptotic Expansion Formula for Up-and-Out Barrier Option Price under Stochastic Volatility Model," CIRJE F-Series CIRJE-F-873, CIRJE, Faculty of Economics, University of Tokyo.
    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. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2009. "Computation in an Asymptotic Expansion Method," CARF F-Series CARF-F-149, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
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