7 CPD Points
Summit 2026: Beyond pairwise correlation: capturing nonlinear and higher-order dependence with distance statistics
Measuring and modelling dependence between risks is crucial in many actuarial applica
tions, such as when assessing diversification benefits or setting capital requirements. Current
industry practice relies heavily on Pearson’s correlation coefficient, despite well-known limita
tions. In particular, it captures only linear association, is restricted to pairwise relationships, and
does not naturally extend to multivariate settings involving multiple random variables or random
vectors (such as when one-hot encoding categorical variables). Sole reliance on Pearson’s lin
ear correlation may fail to detect important nonlinear, higher-order, and mutual dependence
structures.
In this paper, we discuss and illustrate several distance-based dependence statistics which
do not suffer from the same limitations as correlation, and discuss how they can be used in
actuarial applications. In the bivariate setting, we consider the Hellinger correlation (Geenens
&LafayedeMicheaux, 2022)asatoolfor measuring dependencebetweentwocontinuousuni
variate random variables, and distance covariance (Székely et al., 2007) as a tool for detecting
andtesting dependence, especially when randomvectorsareinvolved. Wethendiscussexten
sions to higher-dimensional settings, including joint distance covariance for assessing mutual
dependence across multiple random variables (or vectors), and the auto-distance correlation
function for time series applications such as forecasting mortality rates over time.
Throughout the paper, we illustrate the use of these tools in actuarial contexts and we direct
the reader to available software implementations. Overall, the paper aims to provide actuaries
with a practical introduction to distance-based dependence statistics and to show how they can
complement classical correlation-based tools in actuarial workflows.
Benjamin Avanzi, Guillaume Boglioni Beaulieu, Pierre Lafaye de Micheaux, Ho Ming Lee, Bernard Wong and Rui Zhou
17 April 2026