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Asian Option Pricing with Orthogonal Polynomials

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  • Sander Willems

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. The moment indeterminacy of the log-normal distribution introduces an asymptotic bias in the series, however we show numerically that the bias can safely be ignored in practice.

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  • Sander Willems, 2018. "Asian Option Pricing with Orthogonal Polynomials," Papers 1802.01307, arXiv.org, revised Sep 2018.
    • Handle: RePEc:arx:papers:1802.01307
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    References listed on IDEAS

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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.

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