A cluster driven log-volatility factor model: a deepening on the source of the volatility clustering

Abstract

We introduce a new factor model for log volatilities that considers contributions, and performs dimensionality reduction, at a global level through the market, and at a local level through clusters and their interactions. We do not assume a-priori the number of clusters in the data, instead using the Directed Bubble Hierarchical Tree algorithm to fix the number of factors. We use the factor model to study how the log volatility contributes to volatility clustering, quantifying the strength of the volatility clustering using a new nonparametric integrated proxy. Indeed finding a link between volatility and volatility clustering, we find that a global analysis reveals that only the market contributes to the volatility clustering. A local analysis reveals that for some clusters, the cluster itself contributes statistically to the volatility clustering effect. This is significantly advantageous over other factor models, since it offers a way of selecting factors in a statistical way, whilst also keeping economically relevant factors. Finally, we show that the log volatility factor model explains a similar amount of memory to a principal components analysis factor model and an exploratory factor model.

Keywords:

• Econophysics
• Empirical finance
• Volatility clustering
• Clustering
• Multi factor models
• Dimensionality reduction

Acknowledgments

We thank Bloomberg for providing the data. We also thank Dr Pierpaolo Vivo and Dr Alessia Annibale for their valuable comments and suggestions. Anshul Verma wishes to thank EPSRC for providing funding. We also thank the anonymous referee whose comments have greatly improved our contribution.

Disclosure statement

No potential conflict of interest was reported by the authors.