Sensitivities of Asian options in the Black-Scholes model

TL;DR

This paper develops analytical approximations for the sensitivities of Asian options in the Black-Scholes model, using small maturity and volatility assumptions, and explores their qualitative properties including sign changes.

Contribution

It introduces new analytical formulas for Asian option Greeks based on large deviations theory and small maturity approximations, with insights into their qualitative behavior.

Findings

Good agreement with numerical simulations for practical cases

New results on Rho and Psi sensitivities, including sign changes

Analytical approximations valid for small maturity and volatility

Abstract

We propose analytical approximations for the sensitivities (Greeks) of the Asian options in the Black-Scholes model, following from a small maturity/volatility approximation for the option prices which has the exact short maturity limit, obtained using large deviations theory. Numerical tests demonstrate good agreement of the proposed approximation with alternative numerical simulation results for cases of practical interest. We also study the qualitative properties of Asian Greeks, including new results for Rho, the sensitivity with respect to changes in the risk-free rate, and Psi, the sensitivity with respect to the dividend yield. In particular we show that the Rho of a fixed-strike Asian option and the Psi of a floating-strike Asian option can change sign.