Testing for One-Factor Models versus Stochastic Volatility Models

Economics

Further details

In the finance literature, short term interest rates have been often modeled as a one-factor diffusion process, in which volatility is a continuous function of the level of the observable state variable. Hence, several specification tests for the appropriate functional form within this class of models have been proposed. Recently, in order to capture some features observed in the dynamic behaviour of the implied volatilities, the use of multi factor models has been suggested. In this paper we propose a testing procedure in order to distinguish between the cases in which the volatility of an asset is a function of the asset itself (and therefore the volatility process is Markov and predictable in terms of its own past), and the case in which it is a diffusion process driven by one or more Brownian motions. The proposed test is based on the difference between two different nonparametric estimators of the integrated volatility process. Building on some recent work by Bandi and Philipps (2003) and Barndorff-Nielsen and Shephard (2004b), we show that the test statistics converge to a mixed normal distributions under the null hypothesis of a one factor diffusion process, while diverge in the case of multifactor models. The findings from a small Monte Carlo study indicate that the tests statistic has reasonably good finite sample properties.