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

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Abstract

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.

Original languageEnglish
Article number2350005
JournalInternational Journal of Theoretical and Applied Finance
Volume26
Issue number2-3
DOIs
StatePublished - 1 May 2023

Keywords

  • Asian options
  • Asymptotic expansions
  • time integral of the geometric Brownian motion

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