Valuing Options in Heston’s Stochastic Volatility Model: Another Analytical Approach

Abstract

We are concerned with the valuation of European options in Heston's stochastic volatility model with correlation. Based on Mellin transforms we present new closed-form 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 transforming the current stock price. Our solution has the nice feature that similar to the approach of Carr and Madan (1999) it requires only a single integration. We make numerical tests to compare our results to Heston's solution based on Fourier inversion and investigate the accuracy of the derived pricing formulae.