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Pricing Average Options on Commodities

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  • Kenichiro Shiraya

    (Mizuho-DL Financial Technology Co., Ltd. and Graduate School of Economics, University of Tokyo)

  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)

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    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 lambda-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.

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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2010/2010cf747.pdf
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    Bibliographic Info

    Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-747.

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    Length: 30pages
    Date of creation: Jul 2010
    Date of revision:
    Handle: RePEc:tky:fseres:2010cf747

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    1. 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.
    2. Graeme West, 2005. "Calibration of the SABR Model in Illiquid Markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(4), pages 371-385.
    3. Akihiko Takahashi & Nakahiro Yoshida, 2005. "Monte Carlo Simulation with Asymptotic Method," CIRJE F-Series CIRJE-F-335, CIRJE, Faculty of Economics, University of Tokyo.
    4. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
    5. 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.
    6. Jean-Pierre Fouque & Chuan-Hsiang Han, 2003. "Pricing Asian options with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 3(5), pages 353-362.
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