Subleading correction to the Asian options volatility in the Black-Scholes model

Dan Pirjol

Papers from arXiv.org

Abstract: The short maturity limit $T\to 0$ 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.

Date: 2024-07, Revised 2024-12
New Economics Papers: this item is included in nep-rmg and nep-sea
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Published in IJTAF vol 26, no. 2-3, 2350005, 2023

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2407.05142

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