The Locally Linear Cairns–Blake–Dowd Model: A Note On Delta–Nuga Hedging Of Longevity Risk

Although longevity risk arises from both the variation surrounding the trend in future mortality and the uncertainty about the trend itself, the latter is often left unmodeled. In this paper, we address this problem by introducing the locally linear CBD model, in which the drifts that govern the expected mortality trend are allowed to follow a stochastic process. This specification results in median forecasts that are more consistent with the recent trends and more robust relative to changes in the data sample period. It also yields wider prediction intervals that may better reflect the possibilities of future trend changes. The treatment of the drifts as a stochastic process naturally calls for nuga hedging, a method proposed by Cairns (2013) to hedge the risk associated with changes in drifts. To improve the existing nuga-hedging method, we propose a new hedging method which demands less stringent assumptions. The proposed method allows hedgers to extract more hedge effectiveness out of a hedging instrument, and is therefore useful when there are only a few traded longevity securities in the market.