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

TL;DR

This paper derives the subleading correction to the implied volatility of Asian options in the Black-Scholes model for short maturities, improving accuracy over leading order large deviations estimates.

Contribution

It introduces an asymptotic expansion for the Hartman-Watson distribution to compute subleading corrections to Asian options implied volatility in the short maturity limit.

Findings

Derived the $O(T)$ correction to implied volatility for Asian options.

Validated the correction with numerical benchmarks.

Enhanced the precision of Asian options pricing in the Black-Scholes model.

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.