Disentangling Trend Risk and Basis Risk with Functional Time Series

Abstract

In recent multi-population stochastic mortality models, one critical scientific issue is the vague distinction between trend risk and population basis risk. In particular, the cross- and auto-correlations between the innovations of the latent factors representing the common trend and the population-specific trends are often assumed to be non-existent, although they are possibly statistically significant. While it is theoretically possible to capture such correlations by treating the latent factors as a vector time series, the resulting model would contain a large number of parameters, which may in turn lead to robustness problems. In this paper, we address these issues by the use of the product–ratio model. Contrary to the prevalent assumption of non-existent correlations, the latent factors under the product–ratio model are approximately uncorrelated. This permits us to disentangle trend risk and population basis risk, thereby sparing us from the need to use a heavily parameterized vector time-series process. Compared to the augmented common factor model, our approach demonstrates improved robustness in terms of correlation structures and hedging performance, offering a new perspective on treating cross- and auto-correlations between latent factors in mortality modeling.