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Geometric Asian options: valuation and calibration with stochastic volatility


  • Hoi Ying Wong
  • Ying Lok Cheung


This paper studies continuously sampled geometric Asian options (GAO) in a stochastic volatility economy. The underlying asset price is assumed to follow a geometric Brownian motion with stochastic volatility driven by a mean-reverting process. Semi-analytical pricing formulae for GAO are derived in a fast mean-reverting stochastic volatility economy by the means of a perturbation method. The effects of stochastic volatility on averaging type options are examined. A unified regression approach is proposed to capture smiles of some geometric Asian options and European options in one shot.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:quantf:v:4:y:2004:i:3:p:301-314
    DOI: 10.1088/1469-7688/4/3/006

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    References listed on IDEAS

    1. Min Dai, 2003. "One-state variable binomial models for European-/American-style geometric Asian options," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 288-295.
    2. Turnbull, Stuart M. & Wakeman, Lee Macdonald, 1991. "A Quick Algorithm for Pricing European Average Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(03), pages 377-389, September.
    3. Vorst, Ton, 1992. "Prices and hedge ratios of average exchange rate options," International Review of Financial Analysis, Elsevier, vol. 1(3), pages 179-193.
    4. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May.
    5. John E. Angus, 1999. "A note on pricing Asian derivatives with continuous geometric averaging," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 19(7), pages 845-858, October.
    6. 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 327-343.
    7. Jean-Pierre Fouque & Chuan-Hsiang Han, 2003. "Pricing Asian options with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 3(5), pages 353-362.
    8. Klaus Sandmann & J. Aase Nielsen, 2002. "Pricing of Asian exchange rate options under stochastic interest rates as a sum of options," Finance and Stochastics, Springer, vol. 6(3), pages 355-370.
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    Cited by:

    1. repec:wsi:rpbfmp:v:20:y:2017:i:01:n:s0219091517500059 is not listed on IDEAS
    2. repec:eee:phsmap:v:490:y:2018:i:c:p:402-418 is not listed on IDEAS
    3. repec:eee:phsmap:v:507:y:2018:i:c:p:175-191 is not listed on IDEAS
    4. Bara Kim & In-Suk Wee, 2014. "Pricing of geometric Asian options under Heston's stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 14(10), pages 1795-1809, October.
    5. Akira Yamazaki, 2014. "Pricing average options under time-changed Lévy processes," Review of Derivatives Research, Springer, vol. 17(1), pages 79-111, April.
    6. Kijima, Masaaki & Wong, Tony, 2007. "Pricing of Ratchet equity-indexed annuities under stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 41(3), pages 317-338, November.
    7. Kenichiro Shiraya & Akihiko Takahashi, 2010. "Pricing Average Options on Commodities," CIRJE F-Series CIRJE-F-747, CIRJE, Faculty of Economics, University of Tokyo.
    8. Hoi Ying Wong & Chun Man Chan, 2008. "Turbo warrants under stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 8(7), pages 739-751.
    9. Wong, Hoi Ying & Chan, Chun Man, 2007. "Lookback options and dynamic fund protection under multiscale stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 357-385, May.
    10. 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.

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