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.