Subleading correction to the Asian options volatility 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.

17 pages, 5 figures. Expanded version of the published paper, including also the convexity of the subleading Asian volatility. v2: fixed a typo in the convexity result. v3: fixed typos in several equations and corrected one numerical value in Table 1

References in corpus (2)

• Asymptotic expansion for the Hartman-Watson distribution
• On the distribution of the time-integral of the geometric Brownian motion