High Dimensionality in Finance: A Graph-Theory Analysis

Abstract

In this chapter, we propose a nonconventional methodology, the graph theory, which is especially relevant for the study of high-dimensional financial data. We illustrate the advantages of this method in the context of systemic risk in derivative markets, a main subject nowadays in finance. A key issue is that this methodology can be used in various areas. Numerous applications have now to face the challenge of analyzing gigantic financial data sets, which are more and more frequent. We offer a pedagogical introduction to the use of the graph theory in finance and to some tools provided by this method. As we focus on systemic risk, we first examine correlation-based graphs in order to investigate markets integration and inter/cross-market linkages. We then restrain the analysis to a subset of these graphs, the so-called “minimum spanning trees.” We study their topological and dynamic properties and discuss the relevance of these tools as well as the robustness of the empirical results relying on them.

Citation

Lautier, D. and Raynaud, F. (2012), "High Dimensionality in Finance: A Graph-Theory Analysis", Batten, J.A. and Wagner, N. (Ed.) Derivative Securities Pricing and Modelling (Contemporary Studies in Economic and Financial Analysis, Vol. 94), Emerald Group Publishing Limited, Leeds, pp. 93-119. https://doi.org/10.1108/S1569-3759(2012)0000094007