"CHICAGO: A Fast and Accurate Method for Portfolio Risk Calculation"

by Simon Broda and Marc Paolella

Abstract: The estimation of multivariate GARCH models remains a challenging task, even in modern 
computer environments. The present manuscript shows how Independent Component Analysis can 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 simple and efficient manner. The generalized hyperbolic distribution provides an 
excellent parametric description of financial returns data and is used for the univariate fits, but 
its convolutions, necessary for portfolio risk calculations, are intractable. In order to overcome 
this restriction, a saddlepoint approximation to the required distribution function is derived, 
which is both 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 data 
demonstrate the validity of the procedure.