Implied Volatility and Historical Volatility : An Empirical Evidence About The Content of Information And Forecasting Power

Abstract: This study examines whether the implied volatility index can provide further information in forecasting volatility than historical volatility using GARCHfamily models. For this purpose, this researchhas been conducted to forecast volatility in two main markets the United States of America through its wildly used Standard and Poor’s 500 index and its correspondingvolatility index VIX and in Europe through its Euro Stoxx 50 and its correspondingvolatility index VSTOXX. To evaluate the in-sample content of information, the conditional variance equations of GARCH(1,1) and EGARCH (1,1) are supplemented by integrating implied volatility as an explanatory variable. The realized volatility has been generated from daily squared returns and was employed as a proxy for true volatility. To examine the out-of-sample forecast performance, one-day-ahead rolling forecasts have been generated, and Mincer–Zarnowitz regression and encompassing regression has been utilized. The predictive power of implied volatility has been assessed based on Mean Square Error (MSE). Findings suggest that the integration of implied volatility as an exogenous variable in the conditional variance of GARCHmodels enhancesthe fitness of modelsand decreasesvolatility persistency. Furthermore, the significance of the implied volatility coefficient suggests that implied volatility includes pertinent information in illuminating the variation of the conditional variance. Implied volatility is found to be a biased forecast of realized volatility. Empirical findings of encompassingregression testsimply that the implied volatility index does not surpass historical volatility in terms of forecasting future realized volatility.