Analyzing Mortality Bond Indexes Via Hierarchical Forecast Reconciliation

In recent decades, there has been significant growth in the capital market for mortality- and longevity-linked bonds. Therefore, modeling and forecasting the mortality indexes underlying these bonds have crucial implications for risk management in life insurance companies. In this paper, we propose a hierarchical reconciliation approach to constructing probabilistic forecasts for mortality bond indexes. We apply this approach to analyzing the Swiss Re Kortis bond, which is the first “longevity trend bond†introduced in the market. We express the longevity divergence index associated with the bond’s principal reduction factor (PRF) in a hierarchical setting. We first adopt time-series models to obtain forecasts on each hierarchical level, and then apply a minimum trace reconciliation approach to ensure coherence of forecasts across all levels. Based on the reconciled probabilistic forecasts of the longevity divergence index, we estimate the probability distribution of the PRF of the Kortis bond, and compare our results with those stated in Standard and Poor’s report on pre-sale information. We also illustrate the strong performance of the approach by comparing the reconciled forecasts with unreconciled forecasts as well as those from the bottom-up approach and the optimal combination approach. Finally, we provide first insights on the interest spread of the Kortis bond throughout its risk period 2010–2016.