Dynamic rank correlation computing for financial risk analysis

A critical challenge in quantitative financial risk analysis is the effective computation of volatility and correlation. However, the dynamic nature of financial data environments create the challenges for robust correlation computing, particularly when the number of financial instruments and the volume of transactions grow dramatically. To this end, in this paper, we present an organized study of rank correlation computing for financial risk analysis in dynamic environments. Specifically, we focus on Kendall's τ, which is widely recognized as a robust correlation measure for evaluating financial risk. Kendall's τ is not widely used in practice partially because its computation complexity is O(n ²), making it difficult to frequently recompute in dynamic environments. After carefully studying the computational properties of Kendall's τ, we reveal that Kendall's τ is very computation-friendly for incremental computing of correlations, since the relativity of existing observations will not change as new observations come in. Based on this finding, we develop a τGrow algorithm for dynamically computing Kendall's τ. Also, even for one-time static Kendall's τ computation, we observe that the Kendall's τ correlations on smaller time pieces can provide concise summaries of how Kendall's τ evolves over the whole period. Finally, the effectiveness and the efficiency of the proposed methods have been demonstrated through the experiments on real-world financial data.