SUBLEADING CORRECTION to the ASIAN OPTIONS VOLATILITY in the BLACK-SCHOLES MODEL

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.