Asian Option Pricing with Orthogonal Polynomials

29 Pages Posted: 6 Feb 2018 Last revised: 18 Sep 2018

See all articles by Sander Willems

Sander Willems

Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute

Date Written: January 29, 2018


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.

Keywords: Asian Option, Option Pricing, Orthogonal Polynomials

JEL Classification: C32, G13

Suggested Citation

Willems, Sander, Asian Option Pricing with Orthogonal Polynomials (January 29, 2018). Swiss Finance Institute Research Paper No. 18-09. Available at SSRN: or

Sander Willems (Contact Author)

Ecole Polytechnique Fédérale de Lausanne ( email )

Station 5
Odyssea 1.04
1015 Lausanne, CH-1015

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4

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