The Affine Heston Model with Correlated Gaussian Interest Rates for Pricing Hybrid Derivatives

In this article we define a multi-factor equity-interest rate hybrid model with non-zero correlation between the stock and interest rate. The equity part is modeled by the Heston model [Heston-1993] and we use a Gaussian multi-factor short rate process [Brigo,Mercurio-2007; Hull-2006]. By construction, the model fits in the framework of affine diffusion processes [Duffie, et al.-2000] allowing fast calibration to plain vanilla options. We also provide an efficient Monte Carlo simulation scheme and investigate hedging in the presence of non-zero correlation between the processes from different asset classes