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 Schöbel--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.