In finance, it is often of interest to study market volatility for portfolios that may consist of a large number of assets usingmultivariate stochastic volatility models. However, such models, though useful, do not usually incorporate investor viewsthat might be available. In this paper we introduce a novel hierarchical Bayesian methodology of modeling volatility fora large portfolio of assets that incorporates investor’s personal views of the market via the Black-Litterman (BL) model.We extend the scope and use of BL models by using it within a multivariate stochastic volatility model based on latentfactors for dimensionality reduction but allows for time varying correlations. Detailed derivations of MCMC algorithm areprovided with an illustration with S &P500 asset returns. Moreover, sensitivity analysis for the confidence levels that theinvestor has in their personal views is also explored. Numerical results show that the proposed method provides flexibleinterpretation based on the investor’s uncertainty in personal beliefs, and converges to the empirical sample estimate whentheir confidence level of the market becomes weak.
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