Testing for one-factor models versus stochastic volatility models

Abstract

This paper proposes a testing procedure in order to distinguish between the case where the volatility of an asset price is a deterministic function of the price itself and the one where it is a function of one or more (possibly unobservable) factors, driven by not perfectly correlated Brownian motions. Broadly speaking, the objective of the paper is to distinguish between a generic one-factor model and a generic stochastic volatility model. In fact, no specific assumption on the functional form of the drift and variance terms is required. The proposed tests are based on the difference between two different nonparametric estimators of the integrated volatility process. Building on some recent work by Bandi and Phillips (2003) and Barndorff-Nielsen and Shephard (2004a), it is shown that the test statistics converge to a mixed normal distribution under the null hypothesis of a one factor diffusion process, while diverge in the case of multifactor models. The findings from a Monte Carlo experiment indicate that the suggested testing procedure has good finite sample properties