Forecasting the Value-at-Risk of an Equity Portfolio: A Recurrent Mixture Density Network Approach

Abstract

   The value-at-risk is a useful metric employed by financial institutions to measure the risk of a portfolio. However, accurately forecasting the value-at-risk is difficult as it requires forecasting the returns of the portfolio’s assets. Forecasting assets returns is particularly difficult due to their stochastic nature and the presence of “stylized facts” such as heteroskedasticity, fat tail and skewness in stock returns series. This thesis considers modelling the assets returns using a recurrent mixture density network has been previously proposed to model In this thesis, we propose an improved recurrent mixture density network architecture, as well as a pretraining method for improving the numerical stability and convergence speed of the model. We also propose the copula-S-RMDNGARCH, which extends the current recurrent mixture density network architecture to multivariate settings. We compare the value-at-risk forecast obtained with the copula-S-RMDN-GARCH with the forecasts obtained from a copula-AR-GARCH.