A multivariate functional gradient descent technique to improve Value-at-Risk computation in equity markets

It is difficult to compute Value-at-Risk (VaR) using multivariate models able to take into account the dependence structure between large numbers of assets and being still computationally feasible. A possible procedure is based on functional gradient descent (FGD) estimation for the volatility matrix in connection with asset historical simulation. Backtest analysis on simulated and real data provides strong empirical evidence of the better predictive ability of the proposed procedure over classical filtered historical simulation, with a resulting significant improvement in the measurement of risk.