Using Clustering Method to Understand Indian Stock Market Volatility

Abstract

In this paper we use Clustering Method to understand whether stock market volatility can be predicted at all, and if so, when it can be predicted. The exercise has been performed for the Indian stock market on daily data for two years. For our analysis we map number of clusters against number of variables. We then test for efficiency of clustering. Our contention is that, given a fixed number of variables, one of them being historic volatility of NIFTY returns, if increase in the number of clusters improves clustering efficiency, then volatility cannot be predicted. Volatility then becomes random as, for a given time period, it gets classified in various clusters. On the other hand, if efficiency falls with increase in the number of clusters, then volatility can be predicted as there is some homogeneity in the data. If we fix the number of clusters and then increase the number of variables, this should have some impact on clustering efficiency. Indeed if we can hit upon, in a sense, an optimum number of variables, then if the number of clusters is reasonably small, we can use these variables to predict volatility. The variables that we consider for our study are volatility of NIFTY returns, volatility of gold returns, India VIX, CBOE VIX, volatility of crude oil returns, volatility of DJIA returns, volatility of DAX returns, volatility of Hang Seng returns and volatility of Nikkei returns. We use three clustering algorithms namely Kernel K-Means, Self Organizing Maps and Mixture of Gaussian models and two internal clustering validity measures, Silhouette Index and Dunn Index, to assess the quality of generated clusters.