CHICAGO: A Fast and Accurate Method for Portfolio Risk Calculation

The estimation of multivariate GARCH models remains a challenging task, even in modern computer environments. This manuscript shows how Independent Component Analysiscan be used to estimate the Generalized Orthogonal GARCH model in a fraction of the time otherwise required. The proposed method is a two-step procedure, separating the estimation of the correlation structure from that of the univariate dynamics, thus facilitating the incorporation of non-Gaussian innovations distributions in a straightforward manner. Thegeneralized hyperbolic distribution provides an excellent parametric description of financial returns data and is used for the univariate fits, but its convolutions, necessary for portfoliorisk calculations, are intractable. This restriction is overcome by a saddlepoint approximation to the required distribution function, which is computationally cheap and extremely accurate — most notably in the tail, which is crucial for risk calculations. A simulation study and an application to stock returns demonstrate the validity of the procedure.