An asset return model capturing stylized facts

In this paper, we seek a model for asset returns which reproduces several well-documented stylized facts: 1. log returns are not Gaussian; 2. absolute log returns are serially correlated, but the log returns are not; 3. the Taylor effect. There are many attempts to deal with the first, using various log-Levy models for the asset; some of these are successful in fitting the unconditional distribution of log returns, but cannot of course reproduce the second stylized fact. We propose to model the returns with a hidden two-state Markovian regime (as in J Appl Econ 13:217-244, 1998), conditional on the value of which the returns have different distributions. A key observation is that if the means of the returns in the different regimes are the same, then the log returns are automatically uncorrelated, so we fit to index data under this restriction. By choosing symmetric hyperbolic distributions for the conditional returns, we are able to fit well the unconditional distributions, the autocovariances of absolute returns and the Taylor effect. Moreover, we find that a common regime model explains simultaneously these statistics for the S&P500, FTSE, DAX, Nikkei and CAC40. Implications for investment and option pricing are discussed.