Pricing and Inference with Mixtures of Conditionally Normal Processes

Abstract

We consider the problems of derivative pricing and inference when the stochastic discount factor has an exponential-affine form and the geometric return of the underlying asset has a dynamics characterized by a mixture of conditionally Normal processes. We consider both the static case in which the underlying process is a white noise distributed as a mixture of Gaussian distributions (including extreme risks and jump diffusions) and the dynamic case in which the underlying process is conditionally distributed as a mixture of Gaussian laws. Semi-parametric, non parametric and Switching Regime situations are also considered. In all cases, the risk-neutral processes and explicit pricing formulas are obtained.

Keywords: Derivative Pricing, Stochastic Discount Factor, Implied Volatility, Mixture of Normal Distributions, Mixture of Conditionally Normal Processes, Nonparametric Kernel Estimation, Mixed-Normal GARCH Processes, Switching Regime Models

JEL Classification: C1, C5, G1