WORKING PAPER Value-at-Risk Prediction Using Context Modeling

In financial market risk measurement, Value-at-Risk (VaR) techniques have proven to be a very useful and popular tool. Unfortunately, most VaR estimation models suffer from major drawbacks: the lognormal (Gaussian) modeling of the returns does not take into account the observed fat tail distribution and the non-stationarity of the financial instruments severely limits the efficiency of the VaR predictions. In this paper, we present a new approach to VaR estimation which is based on ideas from the field of information theory and lossless data compression. More specifically, the technique of context modeling is applied to estimate the VaR by conditioning the probability density function on the present context. Tree-structured vector quantization is applied to partition the multi-dimensional state space of both macroeconomic and microeconomic priors into an increasing but limited number of context classes. Each class can be interpreted as a state of aggregation with its own statistical and dynamic behavior, or as a random walk with its own drift and step size. Results on the US S&P500 index, obtained using several evaluation methods, show the strong potential of this approach and prove that it can be applied successfully for, amongst other useful applications, VaR and volatility prediction. The October 1997 crash is indicated in time.