A class of nonlinear stochastic volatility models

Abstract

This paper proposes a class of nonlinear stochastic volatility (SV) models based on the Box-Cox transformation. The proposed class encompasses many parametric SV models that have appeared in the literature, including the well known lognormal SV model, and has an advantage in the ease with which different specifications on SV can be tested. In addition, the functional form of transformation which induces marginal normality of volatility is obtained as a byproduct of this general way of modeling SV. Efficient method of moments is used to estimate the model. Empirical results reveal that the lognormal SV model is rejected.