Disentangling trend risk and basis risk with functional time series

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.