  The CBOE Volatility Index, known by its ticker symbol VIX, is a popular
measure of the market's expected volatility on the SP 500 Index, calculated and
published by the Chicago Board Options Exchange (CBOE). It is also often
referred to as the fear index or the fear gauge. The current VIX index value
quotes the expected annualized change in the SP 500 index over the following 30
days, based on options-based theory and current options-market data. Despite
its theoretical foundation in option price theory, CBOE's Volatility Index is
prone to inadvertent and deliberate errors because it is weighted average of
out-of-the-money calls and puts which could be illiquid. Many claims of market
manipulation have been brought up against VIX in recent years.
  This paper discusses several approaches to replicate the VIX index as well as
VIX futures by using a subset of relevant options as well as neural networks
that are trained to automatically learn the underlying formula. Using subset
selection approaches on top of the original CBOE methodology, as well as
building machine learning and neural network models including Random Forests,
Support Vector Machines, feed-forward neural networks, and long short-term
memory (LSTM) models, we will show that a small number of options is sufficient
to replicate the VIX index. Once we are able to actually replicate the VIX
using a small number of SP options we will be able to exploit potential
arbitrage opportunities between the VIX index and its underlying derivatives.
The results are supposed to help investors to better understand the options
market, and more importantly, to give guidance to the US regulators and CBOE
that have been investigating those manipulation claims for several years.
