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Asian Option Pricing with Orthogonal Polynomials

Author

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  • Sander Willems

    (Ecole Polytechnique Fédérale de Lausanne and Swiss Finance Institute)

Abstract

In this paper we derive a series expansion for the price of a continuously sampled arithmetic Asian option in the Black-Scholes setting. The expansion is based on polynomials that are orthogonal with respect to the log-normal distribution. All terms in the series are fully explicit and no numerical integration nor any special functions are involved. We provide sufficient conditions to guarantee convergence of the series. We address the moment indeterminacy of the log-normal distribution and numerically investigate its impact on the asymptotic behavior of the series.

Suggested Citation

  • Sander Willems, 2018. "Asian Option Pricing with Orthogonal Polynomials," Swiss Finance Institute Research Paper Series 18-09, Swiss Finance Institute, revised Feb 2018.
    • Handle: RePEc:chf:rpseri:rp1809
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    Cited by:

    1. Damir Filipovi'c & Sander Willems, 2018. "A Term Structure Model for Dividends and Interest Rates," Papers 1803.02249, arXiv.org, revised May 2020.

    More about this item

    Keywords

    Asian Option; Option Pricing; Orthogonal Polynomials;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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