Extension of stochastic volatility equity models with the Hull-White interest rate process

We present an extension of stochastic volatility equity models by a stochastic Hull-White interest rate component while assuming non-zero correlations between the underlying processes. We place these systems of stochastic differential equations in the class of affine jump-diffusion-linear quadratic jump-diffusion processes so that the pricing of European products can be efficiently performed within the Fourier cosine expansion pricing framework. We compare the new stochastic volatility Schobel-Zhu-Hull-White hybrid model with a Heston-Hull-White model, and also apply the models to price hybrid structured derivatives that combine the equity and interest rate asset classes.