Realized Matrix Exponential Stochastic Volatility Model: Application to Market, Size, and Value Factor Realized Covariance

Abstract

A matrix exponential multivariate asymmetric stochastic volatility model with realized covariance matrix measurement is proposed. A Bayesian inference method using Markov chain Monte Carlo is developed. A new high-frequency quasi risk factors: market, size, and value factors are calculated using the Tokyo stock market index (TOPIX) size-based sub-indices and style indices.Daily factor series and their realized covariance are calculated and used in our analysis.Proposed three risk factors account for the variation of individual stock returns, and have time-varying volatilities and correlations, and volatility asymmetry.Proposed several models are fit to the proposed risk factors, and the model comparison based on the volatility prediction is conducted. For the latent volatility prediction, the results are consistent with preceding studies about univariate realized stochastic volatility models. The asymmetric covariance structure of the three factors can be shown by the news impact curves.