Time Series Models for Measuring Market Risk Technical Report

The task of measuring market risk requires to make use of a probabilistic model that captures the statistical properties of price variations in financial assets. The most important of these properties are autocorrelations, time-dependent volatility and extreme events. GARCH processes are financial models that can successfully account for the time-dependent volatility. However, they assume Gaussian errors whereas empirical studies generally lead to residuals which exhibit more extreme events than those implied by a Gaussian distribution. In this document we analyze the performance of different models which try to solve this deficiency of standard GARCH processes. The first group of models is based on mixtures of autoregressive experts which work together following three possible strategies: collaboration, soft competition or hard competition. Mixtures of soft competitive experts produce the best estimates of risk because their hypothesis space is a mixture of Gaussian distribution which can account for extreme events. Finally, we study a model which improves standard GARCH processes by means of modelling the innovations in a non-parametric way. The resulting model turns out to provide very precise measurements of market risk and outperforms soft competitive mixtures with 2 experts.