Neural Networks and Arbitrage in the VIX – A Deep Learning Approach for the VIX

The Chicago Board Options Exchange (CBOE) Volatility Index, often referred to as VIX Volatility Index (VIX), is considered by many market participants as a common measure of market risk and investors' sentiment. It is also sometimes called the fear index. In general, the VIX represents the market's expectation of the 30-day-ahead looking implied volatility obtained from real-time prices of options on the S&P 500 index.Over the last few years, many claims about possible VIX manipulations have been brought up by market participants. The increased attention on the VIX has been revived again by unusual trading patterns, which were observed on the market, on February 5 and April 18, 2018.While smaller deviations between implied and realized volatility are a well-known stylized fact of financial markets, large, time-varying differences are also frequently observed throughout the day. In theory, such large deviations might lead to arbitrage opportunities on the VIX market. However, it is hard to exploit as the potential replication strategy requires buying several hundred out-of-the-money (put and call) options on the S&P 500 index. In addition, the potential list of options used for building the replication strategy constantly changes due to underlying price movements, making it difficult to implement it in real-time. Finally, in most cases, the theoretical replication strategy involves high transaction costs which are driven by illiquid options. This paper discusses a novel approach to replicating and predicting the VIX by using just a subset of the most liquid options. The presented approach is based on a recurrent neural network, more precisely on a long short-term model (LSTM) and it uses intraday data of S&P 500 options and the VIX. The results can be used to find a much more cost-efficient way of replicating the VIX and exploiting any arbitrage opportunities. To the best of the authors' knowledge, this the first paper, that describes a new methodology on how to replicate the VIX (to potentially exploit arbitrage opportunities using VIX futures) and applies most recently developed machine learning models to intraday data of S&P 500 options and the VIX. The presented results are supposed to shed more light on the ongoing discussions about possible market manipulations, help other investors to better understand the market and support regulators to investigate market inefficiencies