Copyright © 2011 Robert Frontczak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We are concerned with the valuation of European options in the Heston stochastic volatility model with correlation. Based on Mellin transforms, we present new solutions for the price of European options and hedging parameters. In contrast to Fourier-based approaches, where the transformation variable is usually the log-stock price at maturity, our framework focuses on directly transforming the current stock price. Our solution has the nice feature that it requires only a single integration. We make numerical tests to compare our results with Heston's solution based on Fourier inversion and investigate the accuracy of the derived pricing formulae.