Star Vars: Finding the optimal Value-at-Risk approach for the banking industry

Abstract: This paper explores the concept of Value-at-Risk (VaR) through a comparative study of nonparametric and parametric models in order to find the best risk model for banks’ trading portfolios. The non-parametric methods consist of three different approaches: Simple Historical Simulation, Age Weighted Historical Simulation and Volatility Weighted Historical Simulation by means of the EWMA and GARCH models for forecasting volatility. The parametric methods comprise six different approaches: VaR based on the normal distribution, VaR with Student’s t-distribution, RiskMetrics, VaR with implied volatility and VaR with GARCH volatility dynamics (both assuming normality and t-distribution). The models are estimated and tested on the S&P500 and a hypothetical bank trading portfolio. The evaluation of the models follows the Christoffersen framework of testing for correct conditional coverage together with assessment of model performance according to the regulatory requirements of the Basel Accord. The general finding is that models with leptokurtic features and time-varying volatility perform the best, while naïve models assuming normality and/or without volatility dynamics in general display poor performance. The GARCH(1,1)-t model by far outperforms its competitors as it can correctly account for both correct unconditional coverage and volatility clustering. The implications of market risk regulation are explored and it is argued that the current regulatory environment might provide incentives for low-quality risk management practices with significant room for regulatory improvements.