Scalable inference for a full multivariate stochastic volatility model
This addresses the challenge of scalable volatility modeling for financial data, particularly for large portfolios, though it is incremental in improving computational efficiency.
The authors tackled the problem of modeling multivariate stochastic volatility for asset returns without restrictions on the volatility matrix, proposing a factor model for large datasets and achieving inference via a scalable MCMC algorithm with quadratic computational complexity. They applied this to 571 stock daily returns over 10 years, demonstrating feasibility.
We introduce a multivariate stochastic volatility model for asset returns that imposes no restrictions to the structure of the volatility matrix and treats all its elements as functions of latent stochastic processes. When the number of assets is prohibitively large, we propose a factor multivariate stochastic volatility model in which the variances and correlations of the factors evolve stochastically over time. Inference is achieved via a carefully designed feasible and scalable Markov chain Monte Carlo algorithm that combines two computationally important ingredients: it utilizes invariant to the prior Metropolis proposal densities for simultaneously updating all latent paths and has quadratic, rather than cubic, computational complexity when evaluating the multivariate normal densities required. We apply our modelling and computational methodology to $571$ stock daily returns of Euro STOXX index for data over a period of $10$ years. MATLAB software for this paper is available at http://www.aueb.gr/users/mtitsias/code/msv.zip.