TY - JOUR
T1 - SUBLEADING CORRECTION to the ASIAN OPTIONS VOLATILITY in the BLACK-SCHOLES MODEL
AU - Pirjol, D. A.N.
N1 - Publisher Copyright:
© 2023 World Scientific Publishing Company.
PY - 2023/5/1
Y1 - 2023/5/1
N2 - 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.
AB - 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.
KW - Asian options
KW - Asymptotic expansions
KW - time integral of the geometric Brownian motion
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U2 - 10.1142/S021902492350005X
DO - 10.1142/S021902492350005X
M3 - Article
AN - SCOPUS:85151855445
SN - 0219-0249
VL - 26
JO - International Journal of Theoretical and Applied Finance
JF - International Journal of Theoretical and Applied Finance
IS - 2-3
M1 - 2350005
ER -