Abstract
We investigate the impact of model uncertainty on hedging longevity risk with index-based derivatives and assessing longevity basis risk, which arises from the mismatch between the hedging instruments and the portfolio being hedged. We apply the bivariate Lee–Carter model, the common factor model, and the M7-M5 model, with separate cohort effects between the two populations, and various time series processes and simulation methods, to build index-based longevity hedges and measure the hedge effectiveness. Based on our modeling and simulations on hypothetical scenarios, the estimated levels of hedge effectiveness are around 50% to 80% for a large pension plan, and the model selection, particularly in dealing with the computed time series, plays a very important role in the estimation. We also experiment with a modified bootstrapping approach to incorporate the uncertainty of model selection into the modeling of longevity basis risk. The hedging results under this approach may approximately be seen as a “weighted” average of those calculated from the different model candidates.
Highlights
Continual increase in longevity worldwide remains a serious concern for pension plan sponsors and annuity providers
Since demographic basis risk arises from possible deviations between the book and reference mortality movements, the behavior of these simulated ratios of death rates would have a significant implication on the calculated levels of hedge effectiveness, which will be discussed in the following numerical analysis
We study the impact of model uncertainty on hedging longevity risk via index-based derivatives and measuring longevity basis risk
Summary
Continual increase in longevity worldwide remains a serious concern for pension plan sponsors and annuity providers. We assess the hedge effectiveness based on three broad “families” of mortality projection models, a range of time series processes under each model, and several simulation methods for each combination. Many of these combinations have not been tested or studied in detail in the literature. We adopt the modified semi-parametric bootstrapping approach in Yang et al (2015) and incorporate all the three errors in an integrated manner From these two different perspectives, we attempt to obtain better insights into the potential impact of selecting an inappropriate model in hedging longevity risk with index-based solutions.
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