The Forecast Performance of Model-Free Implied Volatility: Evidence from DAX Index Options

Abstract

Volatility has a central role in various theoretical and practical applications in financial markets. These include the applications related to portfolio theory, derivatives pricing and financial risk management. Both theoretical and practical applications require good estimates and forecasts for the asset return volatility. The goal of this study is to examine the forecast performance of one of the more recent volatility measures, model-free implied volatility.

Model-free implied volatility is extracted from the prices in the option markets, and it aims to provide an unbiased estimate for the market’s expectation on the future level of volatility. Since it is extracted from the option prices, model-free implied volatility should contain all the relevant information that the market participants have. Moreover, model-free implied volatility requires less restrictive assumptions than the commonly used Black-Scholes implied volatility, which means that it should be less biased estimate for the market’s expectations. Therefore, it should also be a better forecast for the future volatility.

The forecast performance of model-free implied volatility is evaluated by comparing it to the forecast performance of Black-Scholes implied volatility and GARCH(1,1) forecast. Weekly forecasts for six years period were calculated for the forecasted variable, German stock market index DAX. The data consisted of price observations for DAX index options. The forecast performance was measured using econometric methods, which aimed to capture the biasedness, accuracy and the information content of the forecasts.

The results of the study suggest that the forecast performance of model-free implied volatility is superior to forecast performance of GARCH(1,1) forecast. However, the results also suggest that the forecast performance of model-free implied volatility is not as good as the forecast performance of Black-Scholes implied volatility, which is against the hypotheses based on theory. The results of this study are consistent with the majority of prior research on the subject.