Basis Risk in Index-Based Longevity Hedges: A Guide for Longevity Hedgers

Abstract

This article considers the assessment of longevity basis risk in the context of a general index-based hedge. We develop a detailed framework for measuring the impact of a hedge on regulatory or economic capital that takes population basis risk explicitly into account. The framework is set up in a way that accommodates a variety of regulatory regimes such as Solvency II as well as local actuarial practice, attempting, therefore, to bridge the gap between academia and practice. This is followed by a detailed analysis of the capital relief resulting from a hedge that uses a call spread as the hedging instrument. We find that the impact of population basis risk on capital relief (expressed in terms of a “haircut” relative to the case with no population basis risk) depends strongly on the exhaustion point of the hedge instrument. In particular, in a Solvency II setting, if the exhaustion point lies well below the 99.5% Value-at-Risk, population basis risk has a negligible impact and the haircut is zero.