A Comparative Analysis of Correlation Approaches in Finance (Digest Summary)

In this highly technical survey article, the authors systematically analyze the most widely used correlation approaches in finance. They initially investigate bottom-up approaches, which include the Pearson correlation coefficient, ordinal correlation measures, correlating Brownian motions, the binomial correlation measure, copula correlations, dynamic copulas, conditionally independent models, and the contagion correlation approach. They also discuss several properties of the Gaussian copula that relate to its use in risk management during the financial crisis. Finally, they discuss such top-down approaches as Vasicek’s large homogeneous portfolio, Markov chain models, and the top-down contagion model developed by Giesecke, Goldberg, and Ding (Operations Research 2009).

Financial correlations play a key role with regard to diversification and risk management. The lower the correlation, the higher the benefit of diversification and the lower the risk, according to the measures routinely applied in risk management. The limitations of the available correlation models became evident during the financial crisis of 2007–2008, and as a consequence, such richer correlation models as dynamic copulas and contagion default models were developed. The authors provide a summary of these modeling approaches. Although they treat technical aspects rigorously, the authors also provide the necessary intuition behind the models and summarize and compare major advantages and weaknesses of the various modeling categories.

With regard to the Gaussian copula, for example, the authors point to several limitations—namely, the lack of tail dependence, the difficulty of calibrating it to market prices, and its static nature. But they argue that in the period leading up to the global financial crisis, many risk models were fed with such benign input data as low-default intensities and low-default correlations. Obviously, the risk output will also be benign in these cases. In the opinion of the authors, the 2007–08 crisis was, therefore, less the result of faulty models and more the result of widespread complacency with regard to risk.

Two main questions remain with respect to the modeling of financial correlations. First, should bottom-up or top-down models be applied? The answer to this question depends on the nature of the portfolio that needs to be monitored. Heterogeneous portfolios with highly different default probabilities will benefit from dynamic and multifaceted bottom-up models. In contrast, parsimonious top-down models appear to be most suitable for portfolios with homogeneous default intensities and default correlations. Second, will we see the emergence of a dominant correlation model? Here, the authors are skeptical because the nature of the underlying portfolio tends to vary widely, and different correlation models have different characteristics and capabilities.

In their survey of correlation approaches, the authors cover a wide range of methodologies used to measure some form of dependency between variables. They start with the most familiar concept, the Pearson coefficient, which is termed a correlation coefficient. Ordinal dependence measures are referred to as rank correlation measures. Parameters derived by other methodologies are categorized as dependence coefficients.

The authors have a strong focus on theoretical modeling issues but also include intuitive explanations of the various methodologies. A clear logical progression is evident: The advances in modeling attempt to remedy flaws discovered in more seasoned approaches.

The field of financial risk management is evolving at a rapid pace, and increasingly sophisticated and computationally challenging methods are being used to assess financial market correlations and their implications for risk management. The authors’ timely survey helps to categorize and compare various strands of the literature and to develop a stringent approach to correlation modeling.