A Comparative Performance of Conventional Methods for Estimating Market Risk Using Value at Risk

Abstract

This paper presents a comparative evaluation of the predictive performance of conventional univariate VaR models including unconditional normal distribution model, exponentially weighted moving average (EWMA/RiskMetrics), Historical Simulation, Filtered Historical Simulation, GARCH-normal and GARCH Students t models in terms of their forecasting accuracy. The paper empirically determines the extent to which the aforementioned methods are reliable in estimating one-day ahead Value at Risk (VaR). The analysis is based on daily closing prices of the USD/KES exchange rates over the period starting January 03, 2003 to December 31, 2016. In order to assess the performance of the models, the rolling window of approximately four years (n=1000 days) is used for backtesting purposes. The backtesting analysis covers the sub-period from November 2008 to December 2016, consequently including the most volatile periods of the Kenyan shilling and the historical all-time high in September 2015. The empirical results demonstrate that GJR-GARCH-t approach and Filtered Historical Simulation method with GARCH volatility specification perform competitively accurate in estimating VaR forecasts for both standard and more extreme quantiles thereby generally out-performing all the other models under consideration.