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Subleading Correction To The Asian Options Volatility In The Black–Scholes Model

Author

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  • DAN PIRJOL

    (School of Business, Stevens Institute of Technology, Hoboken, NJ 07030, USA)

Abstract

The short maturity limit T → 0 for the implied volatility of an Asian option in the Black–Scholes model is determined by the large deviations property for the time-average of the geometric Brownian motion. In this note, we derive the subleading O(T) correction to this implied volatility, using an asymptotic expansion for the Hartman–Watson distribution. The result is used to compute subleading corrections to Asian options prices in a small maturity expansion, sharpening the leading order result obtained using large deviations theory. We demonstrate good numerical agreement with precise benchmarks for Asian options pricing in the Black–Scholes model.

Suggested Citation

  • Dan Pirjol, 2023. "Subleading Correction To The Asian Options Volatility In The Black–Scholes Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 26(02n03), pages 1-19, May.
    • Handle: RePEc:wsi:ijtafx:v:26:y:2023:i:02n03:n:s021902492350005x
    DOI: 10.1142/S021902492350005X
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