DELFT UNIVERSITY OF TECHNOLOGY REPORT 09-05 On The Heston Model with Stochastic Interest Rates

In this article we discuss the Heston [17] model with stochastic interest rates driven by Hull-White [18] (HW) or Cox-Ingersoll-Ross [8] (CIR) processes. We define a so-called volatility compensator which guarantees that the Heston hybrid model with a non-zero correlation between the equity and interest rate processes is properly defined. Moreover, we propose an approximation for the characteristic function, so that pricing of basic derivative products can be efficiently done using Fourier techniques [12; 7]. We also discuss the effect of the approximations on the instantaneous correlations, and check the influence of the correlation between stock and interest rate on the implied volatilities.