The paper develops the structure of parsimonious portfolio single index (PSI) multivariate conditional and stochastic constant correlation volatility models, and methods for estimating the underlying parameters. These multivariate estimates of volatility can be used for more accurate portfolio risk management, to enable efficient forecasting of value-at-risk (VaR) thresholds, and to determine optimal Basel Accord capital charges. A parsimonious portfolio single index approach for modelling the conditional and stochastic covariance matrices of a portfolio of assets is developed, and estimation methods for the conditional and stochastic volatility models are discussed. (C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.