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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.

Suggested Citation

  • Sander Willems, 2019. "Asian option pricing with orthogonal polynomials," Quantitative Finance, Taylor & Francis Journals, vol. 19(4), pages 605-618, April.
    • Handle: RePEc:taf:quantf:v:19:y:2019:i:4:p:605-618
    DOI: 10.1080/14697688.2018.1526396
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    Cited by:

    1. Alghalith, Moawia, 2019. "The distribution of the average of log-normal variables and exact Pricing of the Arithmetic Asian Options: A Simple, closed-form Formula," MPRA Paper 105588, University Library of Munich, Germany.
    2. Peter Carr & Sander Willems, 2019. "A lognormal type stochastic volatility model with quadratic drift," Papers 1908.07417, arXiv.org.
    3. Alghalith, Moawia, 2019. "A New Price of the Arithmetic Asian Option: A Simple Formula," MPRA Paper 117047, University Library of Munich, Germany.
    4. Chih-Chen Hsu & Chung-Gee Lin & Tsung-Jung Kuo, 2020. "Pricing of Arithmetic Asian Options under Stochastic Volatility Dynamics: Overcoming the Risks of High-Frequency Trading," Mathematics, MDPI, vol. 8(12), pages 1-16, December.
    5. Damir Filipović & Sander Willems, 2020. "A term structure model for dividends and interest rates," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1461-1496, October.
    6. Brignone, Riccardo & Kyriakou, Ioannis & Fusai, Gianluca, 2021. "Moment-matching approximations for stochastic sums in non-Gaussian Ornstein–Uhlenbeck models," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 232-247.
    7. Yue Qi & Yue Wang, 2023. "Innovating and Pricing Carbon-Offset Options of Asian Styles on the Basis of Jump Diffusions and Fractal Brownian Motions," Mathematics, MDPI, vol. 11(16), pages 1-22, August.
    8. Silvia Lavagnini, 2021. "Pricing Asian Options with Correlators," Papers 2104.11684, arXiv.org.
    9. Alghalith, Moawia, 2019. "The distribution of the average of log-normal variables and Exact Pricing of the Arithmetic Asian Options: A Simple, closed-form Formula," MPRA Paper 97324, University Library of Munich, Germany.

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