  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.
