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Markov processes and the distribution of volatility: a comparison of discrete and continuous specifications

Research output: Contribution to Journal/MagazineJournal articlepeer-review

<mark>Journal publication date</mark>1/08/1999
<mark>Journal</mark>Philosophical Transactions A: Mathematical, Physical and Engineering Sciences
Issue number1758
Number of pages12
Pages (from-to)2059-2070
Publication StatusPublished
<mark>Original language</mark>English


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 log–normal distribution for sterling/dollar volatility is far more credible than only two volatility states.