Value at Risk (VaR) Using Volatility Forecasting Models: EWMA, GARCH and Stochastic Volatility

Abstract

This paper explores three models to estimate volatility: exponential weighted moving average (EWMA), generalized autoregressive conditional heteroskedasticity (GARCH) and stochastic volatility (SV). The volatility estimated by these models can be used to measure the market risk of a portfolio of assets, called Value at Risk (VaR). VaR depends on the volatility, time horizon and confidence interval for the continuous returns under analysis. For empirical assessment of these models, we used a sample based on Petrobras stock prices to specify the GARCH and SV models. Additionally, we adjusted these models by violation backtesting for one-day VaR, to compare the efficiency of the SV, GARCH and EWMA volatility models (suggested by RiskMetrics). The results suggest that VaR calculated considering EWMA was less violated than when considering SV and GARCH for a 1500-observation window. Hence, for our sample, the model suggested by RiskMetrics (1999), which uses exponential smoothing and is easier to implement, did not produce inferior violation test results when compared to more sophisticated tests such as SV and GARCH.