Option Pricing in Affine Generalized Merton Models

In this article we consider affine generalizations of theMerton jump diffusion model Merton (J Finan Econ 3:125-144, 1976 [8]) and the respective pricing of European options. On the one hand, the Brownian motion part in the Merton model may be generalized to a log-Heston model, and on the other hand, the jump part may be generalized to an affine process with possibly state dependent jumps. While the characteristic function of the log-Heston component is known in closed form, the characteristic function of the second component may be unknown explicitly. For the latter component we propose an approximation procedure based on the method introduced in Belomestny et al. (J Funct Anal 257(4):1222-1250, 2009 [1]). We conclude with some numerical examples.