A Time Series Analysis of the Chicago Board Options Exchange Volatility Index (VIX) Thomas Koundakjian Ryan Liebert December 6, 2014
Background Purpose of Study Chicago Board Options Exchange (CBOE) Volatility Index (VIX) The VIX An index that measures the market s perceived future volatility. More specifically, the VIX measures the market s expectation of future volatility implied by the S&P 500 stock index (SPX) option prices. Volatility has emerged as a new asset class that may be traded using a variety of trading vehicles, such as futures, that are based on the level of the VIX index. The VIX is updated continuously throughout the trading day. End-of-day historical data is freely available on the CBOE website.
Background Purpose of Study Appeal of modeling the VIX Theoretical Non stationary No clear trend Time-varying volatility Commercial Futures and Options on the VIX are actively traded Nicknamed the fear index so can be used to gauge market sentiment Useful for investors and policy makers
Background Purpose of Study The VIX Time Series
Background Purpose of Study Purpose of Study Research Questions Can the VIX be transformed into a stationary time series and robustly modeled as an ARIMA process? Can future values of the VIX be effectively forecasted based on an ARIMA model? What alternatives to an ARIMA modeling approach are appropriate for modeling the VIX?
ARIMA Modeling Forecasting ARMA Model for the Differenced Natural Logged VIX W t = 0.7075W t 1 + Z t 0.8276Z t 1 where W t = X t where X t is the natural logged VIX.
ARIMA Modeling Forecasting 1-step Ahead Forecast
Fractional Differencing GARCH Modeling Fractional Differencing of the VIX
Fractional Differencing GARCH Modeling GARCH Modeling for the VIX W t = 0.7075W t 1 + ε t 0.8276ε t 1 ε t = Z t ht h t = 0.0586 + 0.1520ε 2 t 1 + 0.8234h t 1
Conclusions Conclusions The VIX presented several modeling challenges, and the forecasts of an ARMA(1,1) for the natural logged differenced VIX were disappointing. Additional modeling techniques were shown to be appropriate. Forecasts of the ARMA(1,1) + GARCH(1,1) may better capture volatility in the VIX, but were not performed in this study.
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