Modeling and predicting the CBOE market volatility index

Abstract

This paper performs a thorough statistical examination of the time-series properties of the daily market volatility index (VIX) from the Chicago Board Options Exchange (CBOE). The motivation lies not only on the widespread consensus that the VIX is a barometer of the overall market sentiment as to what concerns investors' risk appetite, but also on the fact that there are many trading strategies that rely on the VIX index for hedging and speculative purposes. Preliminary analysis suggests that the VIX index displays long-range dependence. This is well in line with the strong empirical evidence in the literature supporting long memory in both options-implied and realized variances. We thus resort to both parametric and semiparametric heterogeneous autoregressive (HAR) processes for modeling and forecasting purposes. Our main findings are as follows. First, we confirm the evidence in the literature that there is a negative relationship between the VIX index and the S&P 500 index return as well as a positive contemporaneous link with the volume of the S&P 500 index. Second, the term spread has a slightly negative long-run impact in the VIX index, when possible multicollinearity and endogeneity are controlled for. Finally, we cannot reject the linearity of the above relationships, neither in sample nor out of sample. As for the latter, we actually show that it is pretty hard to beat the pure HAR process because of the very persistent nature of the VIX index.

Effects of the US Stock Market Return and Volatility on the VKOSPI

“…However, unlike the findings of Fernandes et al (2014) for the US market, we find that incorporating domestic macroeconomic variables into the HAR model framework improves both insample fitting and out-of-sample forecasting performance. More importantly, we find that the S&P 500 spot returns and VIX of the US market play a dominant role in explaining the VKOSPI dynamics and predicting its future volatility.…”

“…Given the above considerations, our study is inspired by two recent influential studies: Corsi (2009) and Fernandes et al (2014). Corsi (2009) suggests a new way to analyze volatilities based on their persistence and long memory properties, while Fernandes et al (2014) examine the time-series properties of the VIX using new advances in econometrics and report that the pure heterogeneous autoregressive (HAR) model outperforms the extended HAR models, which incorporate exogenous macro-finance variables in forecasting, particularly shortterm ahead forecasting.…”

“…Corsi (2009) suggests a new way to analyze volatilities based on their persistence and long memory properties, while Fernandes et al (2014) examine the time-series properties of the VIX using new advances in econometrics and report that the pure heterogeneous autoregressive (HAR) model outperforms the extended HAR models, which incorporate exogenous macro-finance variables in forecasting, particularly shortterm ahead forecasting. Extending their studies, we analyze the statistical properties of the VKOSPI, which is the model-free implied volatility index of the South Korean market, under the elaborate HAR model framework.…”

“…Another motivation of this study is some weakness of Corsi (2009) andFernandes et al (2014). To mitigate endogeneity problems and measure the forecasting performance of the models, we modify the HAR model framework used in their studies.…”

Dynamics of the Relationship between Implied Volatility Indices and Stock Prices Indices: The Case of European Stock Markets

“…Thus, these differences could be attributed to the specific characteristics and behaviour of the Korean options market. Fernandes et al (2014) also showed that the relationship between daily changes in the VIX volatility index and contemporary performance of the market index S & P 500 is strongly negative during the period from 2 January 1992 to 15 January 2013. However, controlling asymmetric effects, they stated that there is no significant influence of the S & P 500 variations on the evolution of the VIX index for all time horizons considered in their study.…”