A Note on the Wang Transform for Stochastic Volatility Pricing Models

Abstract

In this paper we study a conditional version of the Wang transform in the context of discrete GARCH models and their diffusion limits. Our first contribution shows that the conditional Wang transform and Duan’s generalized local risk-neutral valuation relationship based on equilibrium considerations, lead to the same GARCH option pricing model. We derive the weak limit of an asymmetric GARCH model risk-neutralized via Wang's transform. The connection with stochastic volatility limits constructed using other standard pricing kernels, such as the conditional Esscher transform or the extended Girsanov principle, is further investigated by comparing the corresponding market prices of variance risk.

Keywords: distortion function, stochastic discount factor, generalized local risk-neutral valuation relationship, GARCH models, weak convergence, stochastic volatility

JEL Classification: C22, C32, C5