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Efficient and accurate quadratic approximation methods for pricing Asian strike options

  • Chuang-Chang Chang
  • Chueh-Yung Tsao
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    This study is on valuing Asian strike options and presents efficient and accurate quadratic approximation methods that work extremely well, both with regard to the volatility of a wide range of underlying assets, and longer average time windows. We demonstrate that most of the well-known quadratic approximation methods used in the literature for pricing Asian strike options are special cases of our model, with the numerical results demonstrating that our method significantly outperforms the other quadratic approximation methods examined here. Using our method for the calculation of hundreds of Asian strike options, the pricing errors (in terms of the root mean square errors) are reasonably small. Compared with the Monte Carlo benchmark method, our method is shown to be rapid and accurate. We further extend our method to the valuing of quanto forward-starting Asian strike options, with the pricing accuracy of these options being largely the same as the pricing of plain vanilla Asian strike options.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/14697680903369492
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    Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

    Volume (Year): 11 (2011)
    Issue (Month): 5 ()
    Pages: 729-748

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    Handle: RePEc:taf:quantf:v:11:y:2011:i:5:p:729-748
    DOI: 10.1080/14697680903369492
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    1. Chueh‐Yung Tsao & Chuang‐Chang Chang & Chung‐Gee Lin, 2003. "Analytic approximation formulae for pricing forward‐starting Asian options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 23(5), pages 487-516, 05.
    2. Vicky Henderson & David Hobson & William Shaw & Rafal Wojakowski, 2007. "Bounds for in-progress floating-strike Asian options using symmetry," Annals of Operations Research, Springer, vol. 151(1), pages 81-98, April.
    3. Jin E. Zhang, 2003. "Pricing continuously sampled Asian options with perturbation method," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 23(6), pages 535-560, 06.
    4. 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.
    5. Nielsen, J. Aase & Sandmann, Klaus, 2003. "Pricing Bounds on Asian Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(02), pages 449-473, June.
    6. Barraquand, Jérôme & Martineau, Didier, 1995. "Numerical Valuation of High Dimensional Multivariate American Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(03), pages 383-405, September.
    7. Levy, Edmond, 1992. "Pricing European average rate currency options," Journal of International Money and Finance, Elsevier, vol. 11(5), pages 474-491, October.
    8. Boyle, Phelim & Potapchik, Alexander, 2008. "Prices and sensitivities of Asian options: A survey," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 189-211, February.
    9. Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
    10. Jèôme Barraquand, 1995. "Numerical Valuation of High Dimensional Multivariate European Securities," Management Science, INFORMS, vol. 41(12), pages 1882-1891, December.
    11. Milevsky, Moshe Arye & Posner, Steven E., 1998. "Asian Options, the Sum of Lognormals, and the Reciprocal Gamma Distribution," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(03), pages 409-422, September.
    12. Jin-Chuan Duan & Jean-Guy Simonato, 1998. "Empirical Martingale Simulation for Asset Prices," Management Science, INFORMS, vol. 44(9), pages 1218-1233, September.
    13. Bouaziz, Laurent & Briys, Eric & Crouhy, Michel, 1994. "The pricing of forward-starting asian options," Journal of Banking & Finance, Elsevier, vol. 18(5), pages 823-839, October.
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