Human being’s moods tend to change in a discrete fashion, rather than continuously. The same can be said of the financial markets. Investment advisors usually give their recommendations to buy/sell/hold, representing their view on the market as bull/bear/neutral respectively. However, it takes time for these opinions to show in stock prices. It is instead a more immediate echo in the option market, which is a more comprehensive representation of future market performance.
The following is a plot of ATMVol/Skew/Smile of STOXX50E implied volatility over the last 5 years. Except for the huge jump in Mar 2020 in the ATMVol, which was due to the covid outbreak, we don’t actually see the obvious shift in states over time. However, if we change the way we look at the same data, we see a different story. As below, we can use a scatter plot for these 3 market variables. From different angles, we are able to see the data tends to cluster at different regimes, which is labelled by different colours. Each of the regimes has distinct differences from others, indicating a different view of investors.
By applying the labelled regime back to the time series of ATMVol, we are now able to see how the regime changes over time as shown below.
It does not only identify the turning point where the market was hit by the covid but also highlights the point when investors were in an optimistic mood in April 2017, the market went through the longest bull streak since 60 years ago. Also, the short term turmoil in the market at the end of 2019 is also highlighted, the spike is due to the trading war between the US and China. The uncertainty vanished quickly as the conflict was contained quickly.
The mathematical tool we used here is called Gaussian Mixture model, which assumes that the objectives, which are the tuples of ATMVol/Skew/Smile, are randomly distributed in N numbers of mixed multivariate Gaussian distribution. By applying maximum likelihood, we are able to estimate the mean/variance matrix of those N distributions, as well as the number of distributions, N. The challenging part is to evaluate the robustness of the estimation so that we are able to achieve better performance in the out of sample dataset. A more interesting question is how it would be different if we are running a filtering based on a hidden Markov chain model, which is able to predict the conditional transition probability matrix between different regimes.
Based on this classification result, it would be much easier for trading to adjust their trading positions and strategies in different regimes.