Volatility Forecasting Models

Comparison of Three Volatility Forecasting Models

• Forecasting volatility is important in assessing financial risks for investors.

• Two time-series models, GARCH (1,1) and EWMA, can be used by investors with basic training.

• Implied volatility indexes provide a direct assessment of market volatility and can be used by investors.

• This research compares the predictive ability of 11 implied volatility indexes with that of GARCH (1,1) and EWMA for underlying stock indexes.

• The root mean-square error (RMSE) is used to examine the predictive ability of the three volatility forecasting methods.

• Results show that implied volatility indexes perform better than GARCH (1,1) and EWMA models for stock indexes in most situations.

• GARCH (1,1) has stronger forecasting powers than EWMA for stock indexes.

• Most implied volatility indexes can be regarded as good forecasts of future volatility to be used by investors in the markets.

• If an implied volatility index is unavailable or not suitable, averaging the forecasts from GARCH (1,1) and EWMA would be a good way to ensure investors get relatively accurate forecasts.

• The research focuses on finding accessible and relatively accurate volatility forecasting methods that could be used by individual investors.

• The Black-Scholes model and GARCH-type models have been compared in past research.

• Volatility indexes were created to solve the mismatch problem and can provide more accurate forecasts than some GARCH-type models in most situations.Comparing GARCH (1,1) and EWMA Models for Volatility Forecasting

• The study aims to provide practical recommendations for individual investors to estimate volatilities using GARCH (1,1) and EWMA models.

• The study compares eight volatility indexes on U.S. stock indexes and three foreign volatility indexes.

• GARCH (1,1) and EWMA models were chosen because they are easier for individual investors to use than complex models.

• The GARCH (1,1) model estimates variance based on a linear combination of previous rates of returns and long-running average variance.

• The EWMA model estimates volatility by assigning exponentially decreasing weights to previous data.

• Implied volatility indexes represent the implied volatility of underlying assets and are a more straightforward method for estimating future volatility.

• The study uses out-of-sample forecasting for GARCH (1,1) and EWMA models.

• The study uses rolling estimation method to choose data for constructing GARCH (1,1) models.

• The study compares the predictive abilities of GARCH (1,1) and EWMA models for eight stock indexes.

• The study aims to provide generalized methods for individual investors to estimate volatilities for most assets.

• The study discusses whether averaging the forecasts from GARCH (1,1) and EWMA could be a generalized method for individual investors to use.

• The data for implied volatility indexes and stock prices were obtained from various sources and cover the period from 8.21.2008 to 7.7.2017.Comparing Forecasting Models for Volatility: GARCH (1,1), EWMA, and Implied Volatility Indexes

• The study compares the accuracy of three forecasting models for volatility: GARCH (1,1), EWMA, and implied volatility indexes.

• The data used for the study covers eight stock indexes and their corresponding options trading volumes from 2011 to 2017.

• The GARCH (1,1) model estimates volatility based on historical data and has a long-run variance rate factor.

• The EWMA model estimates volatility based on a weighted average of past observations, with more recent observations having higher weights.

• Implied volatility indexes are calculated from option prices and represent people's expectations for future markets.

• The RMSE (root mean square error) is used to evaluate the accuracy of the forecasts, with smaller values indicating better performance.

• Implied volatility indexes generally perform better than the GARCH (1,1) and EWMA models in most cases, especially for short-term forecasts.

• However, when options on underlying assets have low liquidity, the volatility indexes can be biased and underperform compared to time-series models.

• The GARCH (1,1) model generally outperforms the EWMA model, except for a few cases where the EWMA model has lower RMSEs.

• The long-run variance rate factor in the GARCH (1,1) model contributes to its better predictive power in most cases, but does not guarantee accuracy in every case.

• The study's results are specific to stock indexes and may not generalize to other types of assets, which require further research.

• Individual investors should consider using the GARCH (1,1) model for stock indexes when options have low liquidity, and implied volatility indexes for most cases when options have relatively high liquidity.

• Overall, implied volatility indexes are likely to provide more accurate forecasts than GARCH (1,1) and EWMA models, as they incorporate people's expectations for future markets.Comparing Volatility Forecasting Models for Individual Investors

• Averaging GARCH (1,1) and EWMA forecasts can be used as a generalized method for individual investors to get volatilities for most assets if volatility indexes are unavailable or biased.

• The RMSEs for average forecasts of GARCH (1,1) and EWMA are smaller than the RMSEs for the single GARCH (1,1) and EWMA forecasts, indicating that the average forecasts could be more accurate than the single forecasts.

• Implied volatility indexes are likely to be a better guide than the GARCH (1,1) and EWMA models for individual investors who want to know the volatility of stock indexes.

• Individual investors need to be cautious when they face volatility indexes for which the corresponding options have relatively low trading volumes, because this can bias calculations and result in less reliable estimations.

• If no implied volatility index is available or the implied volatility index is not good to use, then the GARCH (1,1) model is likely to provide more accurate forecasts for stock indexes because the GARCH (1,1) model tended to have smaller RMSEs than the EWMA in most cases.

• Averaging forecasts from EWMA and GARCH (1,1) could improve the accuracy of forecasts for stock indexes compared to the forecasts from GARCH (1,1).

• For other assets that do not have implied volatility indexes or do not have unbiased volatility indexes, averaging forecasts from EWMA and GARCH (1,1) is a possible good solution for individual investors to get good forecasts.

• It would be worth checking whether the results are consistent for other volatility indexes with different underlying assets, such as the volatility indexes for non-U.S. stock ETFs, interest rates, and individual stocks.

• High-frequency data could be used in further research to see whether the outcomes change.

• Armstrong found that averaging improved the accuracy of forecasts in 30 different examples of forecasting research.

• Some forecasts from different forecasting models could have inverse prediction errors that could be offset through averaging.

• The work of Blair, Poon, and Taylor (2001) indicated that low-frequency data (daily-based stock prices) might cause biases in evaluation results and that high-frequency data (taken every 5 minutes) can give a more precise evaluation.