The Impact of Model Uncertainty on Index-Based Longevity Hedging and Measurement of Longevity Basis Risk

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.