Intelligent Probabilistic Forecasts of VIX and its Volatility using Machine Learning Methods

Abstract

The market focuses on the Cboe Volatility Index (VIX) or Fear Index, an option-implied forecast of 30 calendar-day realized volatility of S&P 500 returns derived from a cross-section of vanilla options. The VIX is determined using a formula that derives the market’s expectation of realized one-month standard deviation of returns backed out from the near-term call and put options on the S&P 500 index. Market participants such as traders, asset managers, and risk managers, keenly watch the VIX index, and are interested in achieving accurate intelligent probabilistic forecasts of the VIX, and also of the realized volatility of individual stocks. These volatility forecasts are useful to options traders placing bets on the future volatility of individual stocks. This paper examines models that only utilize past values of the VIX and document improvements in forecasting the VIX (and its volatility) over different horizons. The approaches include long short-term memory (LSTM) models, simple moving average methods, data-driven neuro volatility techniques, and industry models like Prophet. Uniquely, we propose a novel VIX price interval forecasting model. The driving idea, unlike the existing VIX price forecasting models, is that the proposed novel LSTM interval forecasting method trains two LSTMs to obtain price forecasts and the forecast error volatility forecasts. All the proposed forecasting methods also avoid model identification and estimation issues, especially for a series like the VIX which is non-stationary. We compare models and document which ones perform best for varied horizons.