SUBLEADING CORRECTION TO THE ASIAN OPTIONS VOLATILITY IN THE BLACK–SCHOLES MODEL

Abstract

The short maturity limit [Formula: see text] 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 [Formula: see text] 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.