Pricing of geometric Asian options under Heston's stochastic volatility model

Abstract

In this work, it is assumed that the underlying asset price follows Heston's stochastic volatility model and explicit solutions for the prices of geometric Asian options with fixed and floating strikes are derived. This approach has to deal with the derivation of the generalized joint Fourier transform of a square-root process and of three different weighted integrals of the square-root process with constant, linear and quadratic weights. Numerical implementation results for the complicated expressions are presented, together with the computational stability and efficiency of the method.

Keywords:

• Stochastic volatility
• Asian options
• Options pricing
• Quantitative finance techniques
• Methodology of pricing derivatives

JEL Classification:

• C6
• C63
• C65

Acknowledgements

We would like to thank the anonymous referees for valuable comments which significantly improved the original version. This work was supported by the Seoul R & BD Program (10551).