Analyzing investment return of asset portfolios with multivariate Ornstein-Uhlenbeck processes

The investment return rates of an asset portfolio can be fitted and analyzed by one univariate Ornstein-Uhlenbeck (O-U) process (global model), several univariate O-U processes (univariate model) or one multivariate O-U process (multivariate model). The expected values, variances and covariance of the instantaneous and accumulated return rates of different asset portfolios are calculated from the three models and compared. Furthermore, we price for annuity products, optimize asset allocation strategy and compare the results. The multivariate model is the most comprehensive and complete of the three models in term of fully capturing the correlation among the assets in a single portfolio.