Forecasting volatility of futures market: the S&P 500 and FTSE 100 futures using high frequency returns and implied volatility

Abstract

We show that historical volatility from high frequency returns outperforms implied volatility when standardized returns by historical volatility tends to be normally distributed. For the FTSE 100 futures, we find that historical volatility using high frequency returns outperforms implied volatility in forecasting future volatility. However, we find that implied volatility outperforms historical volatility in forecasting future volatility for the S&P 500 futures. The results also indicate that historical volatility using high frequency returns could be an unbiased forecast for the FTSE 100 futures.

¹ We thank Christopher Lowes for his excellent research assistance.

Notes

¹ We thank Christopher Lowes for his excellent research assistance.

² In their out-of-sample forecasting for future volatility, while GARCH volatility showed smaller root mean squared error (RMSE) than implied volatility, implied volatility had more coefficient weights in encompassing regression than GARCH volatility.

³ He did not compare the predictive power of implied volatility with historical volatility from high frequency returns. He used realized volatility from high frequency returns as a dependent variable.

⁴ When we used 5 trading days, we had to drop 85 days over the sample period because there were not enough intra-day price changes. We found 10 days were optimal with 53 days dropped out.

⁵ Minimum and maximum of trading days till expiration is 12 and 21 days, respectively.

⁶ We also used ARFIMA(1,d,1) model to estimate daily volatility and used it in forecasting as is shown is section IV.

⁷ The difference between the implied volatility and intra-day volatility could be smaller than the numbers of Table 1. For example, mean of intra-day volatilities sampled at 240 minutes is 14.91 and 16.53 for S&P 500 and FTSE, respectively.

⁸ We didn’t report the result of ARFIMA(1,d,1) model since its forecasting performance over the historical volatility becomes negligible in one month forecasting horizon. The results are available upon request.

⁹ For example, if we think that the regression, , is correctly specified. It can be rewritten as, , or as an Error-Correction Model (ECM). Hence, a regression of will be omitting a term, −(1−αg)g _t−1 , unless α _g =1. We also estimated an ECM model, , and the results are available upon request.

¹⁰ For the properties of different kernels, see also Andrews and Monahan (1992).