Volatility Forecasting Comparison Between Implied Volatility and Model Based Forecasts

Abstract

The purpose of this study is to compare the forecasting performance between implied volatility and model based forecasts (MBFs) in the U.S. stock market. During recent thirty years, volatility forecasting has always been a hot and important issue in both practical and academic areas, but there is no final conclusion on the best forecasting method. This study aims to use the long enough and updated data from Jan 1990 to Dec 2009 to reexamine this significant topic. Moreover, by reviewing ample literatures, the author found that the efficiency of option markets developed by leaps and bounds after severe financial crisis. Therefore, this study also throws a light on testing whether the efficiency of the U.S. option market has been improved since 2007 financial crisis burst.

The empirical study consists of monthly volatility forecasting and the predictive power comparison. Model based forecasts are given by several econometrical models including: random walk,〖 Riskmetrics〗^TM, GARCH (1, 1) and GJR (1, 1) by using the daily closing prices of S&P 500 index. VIX index implied by options on S&P 500 is used as the representative of the implied volatility forecast. Forecasting performance is compared by three error measures-mean square error, mean absolute percentage error, QLIKE, and regression based evaluation.

Two hypotheses are tested here: firstly, implied volatility performs better on the volatility forecasting than MBFs do; secondly, the efficiency of option market improved after 2007 financial crisis. The empirical evidence rejects the first hypothesis and finds that GJR (1, 1) model dominates other methods as the best forecast. Implied volatility is even inferior to GARCH (1, 1) model. Meanwhile, more sophisticated models are superior to simple historical models on monthly forecasting. The second hypothesis is strongly supported. The U.S. option market realized an obvious improvement after 2007 financial crisis.