A multivariate FGD technique to improve VaR computation in equity markets

We present a multivariate, non-parametric technique for constructing reliable daily VaR predictions for individual assets belonging to a common equity market segment, which takes also into account the possible dependence structure between the assets and is still computationally feasible in large dimensions. The procedure is based on functional gradient descent (FGD) estimation for the volatility matrix (Audrino and Buhlmann, 2002) in connection with asset historical simulation and can also be seen as a multivariate extension of the filtered historical simulation method proposed by Barone-Adesi et al. (1999). Our FGD algorithm is very general and can be further adapted to other multivariate problems dealing with (volatility) function estimation. We concentrate our empirical investigations on the Swiss pharmaceutical and the US biotechnological equity market and we collect, using statistical and economical backtests, strong empirical evidence of the better predictive poten-tial of our multivariate strategy over other univariate techniques, with a resulting significant improvement in the measurement of risk.