Markov Processes and the Distribution of Volatility: A Comparison Of Discrete and Continuous Specifications

Abstract:     
Two mixtures of Normal distributions, created by persistent changes in volatility, are compared as models for asset returns. A Markov chain with two states for volatility is contrasted with an autoregressive Gaussian process for the logarithm of volatility. The conditional variances of asset returns are shown to have a bimodal distribution for the former process when volatility is persistent, that contrasts with a unimodal distribution for the latter process. A test procedure based upon this contrast shows that a lognormal distribution for Sterling/Dollar volatility is far more credible than only two volatility states.

JEL Classification: C22, C52, F31, G15

working papers series