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Pricing Average Options on Commodities

Author

Listed:
  • Kenichiro Shiraya

    (Mizuho-DL Financial Technology Co.,Ltd.)

  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)

Abstract

This paper proposes a new approximation formula for pricing average options on commodities under a stochastic volatility environment. In particular, it derives an option pricing formula under Heston and an extended λ-SABR stochastic volatility models (which includes an extended SABR model as a special case). Moreover, numerical examples support the accuracy of the proposed average option pricing formula.

Suggested Citation

  • 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.
    • Handle: RePEc:cfi:fseres:cf177
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    References listed on IDEAS

    as
    1. Anders B. Trolle & Eduardo S. Schwartz, 2009. "Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives," The Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4423-4461, November.
    2. Akihiko Takahashi & Nakahiro Yoshida, 2005. "Monte Carlo Simulation with Asymptotic Method," CIRJE F-Series CIRJE-F-335, CIRJE, Faculty of Economics, University of Tokyo.
    3. 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.
    4. Akihiko Takahashi & Nakahiro Yoshida, 2004. "An Asymptotic Expansion Scheme for Optimal Investment Problems," Statistical Inference for Stochastic Processes, Springer, vol. 7(2), pages 153-188, May.
    5. Kenichiro Shiraya & Akihiko Takahashi & Masashi Toda, 2009. "Pricing Barrier and Average Options under Stochastic Volatility Environment," CIRJE F-Series CIRJE-F-682, CIRJE, Faculty of Economics, University of Tokyo.
    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    7. Kenichiro Shiraya & Akihiko Takahashi & Masashi Toda, 2009. "Pricing Average Options under Stochastic Volatility Models," CARF J-Series CARF-J-059, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    8. Jean-Pierre Fouque & Chuan-Hsiang Han, 2003. "Pricing Asian options with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 3(5), pages 353-362.
    9. 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.
    10. 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.
    11. Hoi Ying Wong & Ying Lok Cheung, 2004. "Geometric Asian options: valuation and calibration with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 301-314.
    12. Graeme West, 2005. "Calibration of the SABR Model in Illiquid Markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(4), pages 371-385.
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    Cited by:

    1. Louis-Pierre Arguin & Nien-Lin Liu & Tai-Ho Wang, 2018. "Most-Likely-Path In Asian Option Pricing Under Local Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(05), pages 1-32, August.
    2. Louis-Pierre Arguin & Nien-Lin Liu & Tai-Ho Wang, 2017. "Most-likely-path in Asian option pricing under local volatility models," Papers 1706.02408, arXiv.org, revised Aug 2018.

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