Title

A Class of Nonlinear Stochastic Volatility Models

Publication Type

Conference Paper

Publication Date

2006

Abstract

This paper proposes a class of nonlinear stochastic volatility models based on the Box-Cox transformation which offers an alternative to the one introduced in Andersen (1994). The proposed class encompasses many parametric stochastic volatility models that have appeared in the literature, including the well known lognormal stochastic volatility model, and has an advantage in the ease with which different specifications on stochastic volatility 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 stochastic volatility. The efficient method of moments approach is used to estimate model parameters. Empirical results reveal that the lognormal stochastic volatility model is rejected for daily index return data but not for daily individual stock return data. As a consequence, the stock volatility can be well described by the lognormal distribution as its marginal distribution, consistent with the result found in a recent literature (cf Andersen et al (2001a)). However, the index volatility does not follow the lognormal distribution as its marginal distribution.

Keywords

Box-Cox Transformation, GARCH, EMM, Stochastic Volatility

Discipline

Applied Statistics | Econometrics

Research Areas

Econometrics

Publication

Proceedings of the 5th International Conference on Computational Intelligence in Economics and Finance, Atlantis Press.

Identifier

10.2991/jcis.2006.87