Value at Risk (VaR) in uncertainty: Analysis with parametric method and Black & Scholes simulations

Abstract

VaR is the most accepted risk measure worldwide and the leading reference in any risk management assessment. However, its methodology has important limitations which makes it unreliable in contexts of crisis or high uncertainty. For this reason, the aim of this work is to test the VaR accuracy when is employed in contexts of volatility, for which we compare the VaR outcomes in scenarios of both stability and uncertainty, using the parametric method and a historical simulation based on data generated with the Black & Scholes model. VaR main objective is the prediction of the highest expected loss for any given portfolio, but even when it is considered a useful tool for risk management under conditions of markets stability, we found that it is substantially inaccurate in contexts of crisis or high uncertainty. In addition, we found that the Black & Scholes simulations lead to underestimate the expected losses, in comparison with the parametric method and we also found that those disparities increase substantially in times of crisis. In the first section of this work we present a brief context of risk management in finance. In section II we present the existent literature relative to the VaR concept, its methods and applications. In section III we describe the methodology and assumptions used in this work. Section IV is dedicated to expose the findings. And finally, in Section V we present our conclusions.