On the optimal hedge ratio in index-based longevity risk hedging
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In an index-based longevity hedge, the so-called longevity basis risk arises from the potential mismatch between the hedging instrument and the annuity portfolio being hedged, due to the differences in the underlying populations and payoff structures. To reduce the impact of this longevity basis risk and increase the hedge effectiveness, an optimal position in the hedging instrument should be determined appropriately with regard to the nature of the two populations and also the timing of the payments. In this paper, we examine some analytical results on the optimal hedge ratio in hedging the longevity exposure of an annuity portfolio with index-based longevity- or mortality-linked securities. This optimal hedge ratio may serve as a convenient starting point for constructing an index-based hedge. We also conduct a cost–benefit analysis using different financial objectives. Our results are based on data of Australian public sector pensioners.
KeywordsIndex-based longevity hedge Longevity swap S-forward q-forward Longevity basis risk
The authors thank Mercer Australia for providing the mortality datasets to the Longevity Basis Risk research project (Phase 2), which contributes to some parts of this paper. The Phase 2 project was sponsored jointly by the Institute and Faculty of Actuaries (IFoA) and the Life and Longevity Markets Association (LLMA).
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