**DISCUSSION PAPER PI-1206**

Robust Hedging of Longevity Risk

Andrew J.G. Cairns

We consider situations where a pension plan has opted to hedge its longevity
risk using an index-based longevity hedging instrument such as a q-forward
or deferred longevity swap. The use of index-based hedges gives rise to basis
risk, but benefits, potentially, from lower costs to the hedger and greater
liquidity. We focus on quantification of optimal hedge ratios and hedge effectiveness
and investigate how robust these quantities are relative to inclusion of recalibration
risk, parameter uncertainty and Poisson risk. We find that strategies are
robust relative to the inclusion of parameter uncertainty and Poisson risk.
In contrast, single-instrument hedging strategies are found to lack robustness
relative to the inclusion of recalibration risk at the future valuation date,
although we also demonstrate that some hedging instruments are more robust
than others. To address this problem, we develop multi-instrument hedging
strategies that are robust relative to recalibration risk.

Key words: Robust hedging, recalibration risk, hedge ratios, hedge effectiveness,
Delta hedging, Nuga hedging.