A Quick Tool to Forecast VaR Using Implied and Realized Volatilities

Abstract

We propose here a naive model to forecast ex-ante Value-at-Risk (VaR) using a shrinkage estimator between realized volatility estimated on past return time series, and implied volatility extracted from option pricing data. Implied volatility is often indicated as the operators expectation about future risk, while the historical volatility straightforwardly represents the realized risk prior to the estimation point, which by definition is backward looking. In a nutshell, our prediction strategy for VaR uses information both on the expected future risk and on the past estimated risk.We examine our model, called Shrinked Volatility VaR, both in the univariate and in the multivariate cases, empirically comparing its forecasting power with that of two benchmark VaR estimation models based on the Historical Filtered Bootstrap and on the RiskMetrics approaches.The performance of all VaR models analyzed is evaluated using both statistical accuracy tests and efficiency evaluation tests, according to the Basel II and ESMA regulatory frameworks, on several major markets around the world over an out-of-sample period that covers different financial crises.Our results confirm the efficacy of the implied volatility indexes as inputs for a VaR model, but combined together with realized volatilities. Furthermore, due to its ease of implementation, our prediction strategy to forecast VaR could be used as a tool for portfolio managers to quickly monitor investment decisions before employing more sophisticated risk management systems.