Journal of Risk Model Validation

A quick tool to forecast value-at-risk using implied and realized volatilities

Francesco Cesarone and Stefano Colucci

  • We present a simple prediction strategy to model VaR with performance comparable to that of sophisticated simulation models. 
  • We observe that the use of the shrinkage estimator between realized and implied volatilities works well both in the univariate and in the multivariate contexts. 
  • The performance of the models is treated using both statistical accuracy and efficiency evaluation tests according to the Basel II and ESMA regulatory frameworks. 
  • We examine the VaR forecasts performance on several markets over an out-of-sample period that covers different financial crises.


We propose a naive model to forecast ex ante value-at-risk (VaR), using a shrinkage estimator between realized volatility estimated on past return time series as well as implied volatility quoted in the market. Implied volatility is often indicated as the operator's expectation about future risk, while historical volatility straightforwardly represents the realized risk prior to the estimation point, which by definition is backward looking. Therefore, our VaR prediction strategy uses information both on expected future risk and past estimated risk. We examine our model, called shrun volatility VaR, in both the univariate and multivariate cases, empirically comparing its forecasting power with that of four benchmark VaR models. The performance of all VaR models is evaluated using both statistical accuracy and efficiency evaluation tests; this is done according to the Basel II and European Securities and Markets Authority regulatory frameworks, on several major markets, over an out-of-sample period that covers different financial crises. Our results confirm the efficacy of implied volatility indexes as inputs for a VaR model, but only when combined with realized volatilities. Further, due to its ease of implementation, our VaR prediction strategy could be used as a tool for portfolio managers to quickly monitor investment decisions before employing more sophisticated risk management systems.

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