COMPUTATION OF THE GREEKS DELTA AND GAMMA OF ASIAN OPTION: A MALLIAVIN CALCULUS APPROACH

COMPUTATION OF THE GREEKS DELTA AND GAMMA OF ASIAN OPTION

Abstract

The challenges of pricing and hedging in financial market arise due to market uncertainties, quantified by sensitivities of underlying asseys, often represented using Greeks. Effective pricing and Hedging strategies are crucial for risk management, portfolio optimization and overall decision making in financial markets. These sensitivities which are represented by the Greeks are obtained with Malliavin calculus. The Malliavin integral calculus given by the Skorohod integral and the integration by part technique for stochastic variation were used to derive weight functions of the Greeks for Asian Option (AO). The weight functions were used to derive expressions for the Greeks which represent the sensitivities of the Asian option with respect to the parameters; price of the underlying asset at initial time $S_{0}$, and the volatility $\sigma$, respectively.
These sensitivities are important in financial market because it helps to monitor investment trajectory, it guide investor in decision making about the right time to cash in on their investment and to minimize risk.