Spatial natural hedging: a general framework with application to the mortality of U.S. states

Abstract

It is well known that coupling life and death benefits within an insurance portfolio may be a beneficial longevity risk reduction technique, especially when policies are underwritten in the same geographical region. However, though desirable, the lack of available capacity of life insurance instruments in terms of underlying cohorts or duration of products underwritten within a given region can substantially constrain the use of natural hedging strategies for life insurance companies. That is why the primary objective of this paper is to investigate the implementation and effectiveness of natural hedging strategies when considering the geographical or spatial dimension. Starting from a well-known multi-population mortality model, we evaluate the relevance of natural hedging strategies and their susceptibility to basis risk resulting from age, period, and spatial effects. Our novel theoretical findings provide direct insights into specific and often complex positions necessary for optimal real-world hedging. In a practical numerical application predicated on U.S. mortality data, we demonstrate the situation of a U.S.-based insurance company capable of selling policies across different states. Though often unable to curtail product sales, an insurance company using our analytical tool can effectively, through marketing strategies, stimulate or destimulate sales to approach an optimal hedging position of an overall portfolio.