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A P.D.E. approach to Asian options: analytical and numerical evidence


  • Alziary, Benedicte
  • Decamps, Jean-Paul
  • Koehl, Pierre-Francois


We first derive a one state variable partial differential equation, easy to emplement, which characterizes the price of a European type Asian option. This result is explained and related to previous literature. When we derive new results on the hedging of an Asian option and propose analytical and numerical analysis on the comparison between Asian and European options. Our methodology which applies to "fixed-strike" Asian options as well to "floating-strike" Asian options completes and clarifies various results in the literature. In this paper we focus on "backward-starting" Asian options. Our approach is quite general however, and we explain how to adapt our main results to the case of "forward-starting" Asian options.
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Suggested Citation

  • Alziary, Benedicte & Decamps, Jean-Paul & Koehl, Pierre-Francois, 1997. "A P.D.E. approach to Asian options: analytical and numerical evidence," Journal of Banking & Finance, Elsevier, vol. 21(5), pages 613-640, May.
  • Handle: RePEc:eee:jbfina:v:21:y:1997:i:5:p:613-640

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    References listed on IDEAS

    1. Isabelle Bajeux-Besnainou & Jean-Charles Rochet, 1996. "Dynamic Spanning: Are Options An Appropriate Instrument?," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 1-16.
    2. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375.
    3. 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.
    4. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    5. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    6. 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.
    7. 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.
    8. Hull, John & White, Alan, 1990. "Valuing Derivative Securities Using the Explicit Finite Difference Method," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(01), pages 87-100, March.
    9. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
    10. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    11. Levy, Edmond, 1992. "Pricing European average rate currency options," Journal of International Money and Finance, Elsevier, vol. 11(5), pages 474-491, October.
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    13. Courtadon, Georges, 1982. "The Pricing of Options on Default-Free Bonds," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(01), pages 75-100, March.
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    Cited by:

    1. Boyle, Phelim & Draviam, Thangaraj, 2007. "Pricing exotic options under regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 267-282, March.
    2. Eric Benhamou & Alexandre Duguet, 2000. "A 2 Dimensional Pde For Discrete Asian Options," Computing in Economics and Finance 2000 33, Society for Computational Economics.
    3. repec:eee:phsmap:v:490:y:2018:i:c:p:402-418 is not listed on IDEAS
    4. Chad E. Hart & Bruce A. Babcock & Dermot J. Hayes, 2001. "Livestock Revenue Insurance," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 21(6), pages 553-580, June.
    5. Manuel Moreno & Javier F. Navas, 2003. "Australian Asian Options," Working Papers 28, Barcelona Graduate School of Economics.
    6. repec:dau:papers:123456789/5374 is not listed on IDEAS
    7. 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.
    8. Renyuan Shao & Brian Roe, 2003. "The design and pricing of fixed‐ and moving‐window contracts: An application of Asian‐Basket option pricing methods to the hog‐finishing sector," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 23(11), pages 1047-1073, November.
    9. Dan Pirjol & Lingjiong Zhu, 2017. "Asymptotics for the Discrete-Time Average of the Geometric Brownian Motion and Asian Options," Papers 1706.09659,
    10. Keng‐Hsin Lo & Kehluh Wang & Ming‐Feng Hsu, 2008. "Pricing European Asian options with skewness and kurtosis in the underlying distribution," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 28(6), pages 598-616, June.
    11. Koekebakker, Steen & Adland, Roar & Sødal, Sigbjørn, 2007. "Pricing freight rate options," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 43(5), pages 535-548, September.
    12. Dan Pirjol & Lingjiong Zhu, 2016. "Short Maturity Asian Options in Local Volatility Models," Papers 1609.07559,
    13. Manuel Moreno & Javier F. Navas, 2008. "Australian Options," Australian Journal of Management, Australian School of Business, vol. 33(1), pages 69-93, June.
    14. Dan Pirjol & Lingjiong Zhu, 2017. "Short Maturity Asian Options for the CEV Model," Papers 1702.03382,
    15. Nielsen, J.A. & Sandmann, K., 1998. "Asian Exchange Rate Options under Stochastic Interest Rates: Pricing as a Sum of Delayed Payment Options," Discussion Paper Serie B 431, University of Bonn, Germany.
    16. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.

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    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing


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