Analytical Approximation of Pricing Average Options under the Heston Model
Recent Advances in Financial Engineering, 2011
17 Pages Posted: 1 Nov 2011 Last revised: 14 Mar 2012
Date Written: November 16, 2011
This 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.
Keywords: Heston model, average option, Gram-Charlier expansion, moment, Girsanov transform
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