## Forecasting Stock Market Volatility : The Predictive Power of Implied Volatility and GARCH

##### Holopainen, Miro (2018-04-09)

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Holopainen, Miro

Turun yliopisto

09.04.2018

##### Tiivistelmä

Modern institutions from multinationals to nation states use the global derivatives market in order to manage risk. The value of most derivatives is influenced by future volatility, and for the purposes of valuing them, volatility forecasts that are as accurate as possible are needed. Numerous models have been developed in order to forecast stock volatility. This paper adds to a well-established body of econometric research in which the predictive power of two forecasters—option implied volatility and GARCH—is being compared. According to financial theory, in an efficient option market implied volatility subsumes all the information contained in GARCH, and is therefore a superior predictor of future realized volatility. Consequently, the efficient market hypothesis is tested simultaneously when implied volatility is compared empirically to GARCH.

Time series samples of daily price observations from four stock indices are used. These indices include the Euro Stoxx 50, the OMX Helsinki 25, the Nikkei 225 and the S&P 500, while the lengths of the samples range from c.a. six to fourteen years. Additionally, three of the four indices are examined during a subsample period beginning in September 15th 2008 and ending in June 30th 2009 to see whether differences in predictive power remain constant during the financial crisis of 2008. Altogether four GARCH specifications are formed. These include GARCH (1,1) and IGARCH (1,1), which simply attempt to model volatility clustering with a conditional mean, as well as the asymmetric EGARCH (1,1) and GJR–GARCH (1,1), which take into account the leverage effect. The implied volatility and GARCH forecasts are evaluated by studying regression parameters, and they are compared to each other by using the Diebold–Mariano test statistic.

The results suggest that implied volatility generally outperforms GARCH. The index option market is not, however, completely weakly efficient: all relevant price information contained in GARCH is not embedded in implied volatility. During the 2008 financial crisis all forecasts become substantially less accurate and no model is the best across the board. Interestingly, implied volatility does contain all relevant price information contained in GARCH during the crisis. The asymmetric GARCH models forecast realized volatility significantly better than the simple GARCH models, which is evidence for the inclusion of the leverage effect in GARCH modeling. The results are robust to extra-GARCH nonlinearity but not necessarily to the long memory effect. Future research should focus on whether the difference in predictive power is large enough to result in a significant difference in terms of risk-adjusted portfolio returns.

Time series samples of daily price observations from four stock indices are used. These indices include the Euro Stoxx 50, the OMX Helsinki 25, the Nikkei 225 and the S&P 500, while the lengths of the samples range from c.a. six to fourteen years. Additionally, three of the four indices are examined during a subsample period beginning in September 15th 2008 and ending in June 30th 2009 to see whether differences in predictive power remain constant during the financial crisis of 2008. Altogether four GARCH specifications are formed. These include GARCH (1,1) and IGARCH (1,1), which simply attempt to model volatility clustering with a conditional mean, as well as the asymmetric EGARCH (1,1) and GJR–GARCH (1,1), which take into account the leverage effect. The implied volatility and GARCH forecasts are evaluated by studying regression parameters, and they are compared to each other by using the Diebold–Mariano test statistic.

The results suggest that implied volatility generally outperforms GARCH. The index option market is not, however, completely weakly efficient: all relevant price information contained in GARCH is not embedded in implied volatility. During the 2008 financial crisis all forecasts become substantially less accurate and no model is the best across the board. Interestingly, implied volatility does contain all relevant price information contained in GARCH during the crisis. The asymmetric GARCH models forecast realized volatility significantly better than the simple GARCH models, which is evidence for the inclusion of the leverage effect in GARCH modeling. The results are robust to extra-GARCH nonlinearity but not necessarily to the long memory effect. Future research should focus on whether the difference in predictive power is large enough to result in a significant difference in terms of risk-adjusted portfolio returns.