A comprehensive review of Value at Risk methodologies

Abstract In this article we present a theoretical review of the existing literature on Value at Risk (VaR) specifically focussing on the development of new approaches for its estimation. We effect a deep analysis of the State of the Art, from standard approaches for measuring VaR to the more evolved, while highlighting their relative strengths and weaknesses. We will also review the backtesting procedures used to evaluate VaR approach performance. From a practical perspective, empirical literature shows that approaches based on the Extreme Value Theory and the Filtered Historical Simulation are the best methods for forecasting VaR. The Parametric method under skewed and fat-tail distributions also provides promising results especially when the assumption that standardised returns are independent and identically distributed is set aside and when time variations are considered in conditional high-order moments. Lastly, it appears that some asymmetric extensions of the CaViaR method provide results that are also promising.