Analytical Approximation of Pricing Average Options under the Heston Model

Abstract

AbstractThis paper proposes a new approximation formula for pricing average options under Heston's stochastic volatility model. When using the formula based on the Gram-Charlier expansion, it is necessary to know any moments of an averaged underlying asset price. We try to derive an analytical solution of the moments under the Heston model. There are two key points of the derivation: One of them is to repeatedly apply change of a certain measure. Another is to sequentially solve a system of ordinary differential equations. Moreover, numerical examples support the accuracy of the proposed average option pricing formula.