Non-affine GARCH option pricing models, variance-dependent kernels, and diffusion limits

Abstract

This paper investigates the pricing and weak convergence of an asymmetric nonaffine, non-Gaussian GARCH model when the risk neutralization is based on a variance-dependent exponential linear pricing kernel with stochastic risk aversion parameters. The risk-neutral dynamics are obtained for a general setting and its weak limit is derived. We show how several GARCH diffusions, martingalized via well-known pricing kernels, are obtained as special cases and we derive necessary and sufficient conditions for the presence of financial bubbles. An extensive empirical analysis using both historical returns and options data illustrates the advantage of coupling this pricing kernel with non-Gaussian innovations.