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.

In this paper the ‘Wilkie investment model’ is discussed, updated and extended. The original model covered price inflation, share dividends, share dividend yields (and hence share prices) and long-term interest rates, and was based on data for the United Kingdom from 1919 to 1982, taken at annual intervals. The additional aspects now covered include: the extension of the data period to 1994 (with omission of the period from 1919 to 1923); the inclusion of models for a wages (earnings) index, short-term interest rates, property rentals and yields (and hence property prices) and yields on index-linked stock; consideration of data for observations more frequently than yearly, in particular monthly data; extension of the U.K. model to certain other countries; introduction of a model for currency exchange rates; extension of certain aspects of the model to a larger number of other countries; and consideration of more elaborate forms of time-series modelling, in particular cointegrated models and ARCH models.

This paper reviews the stochastic asset model described in Wilkie (1995) and previous work on refining this model. The paper then considers the application on non-linear modelling to investment series, considering both ARCH techniques and threshold modelling. The paper suggests a threshold autoregressive (TAR) system as a useful progression from the Wilkie (1995) model. The authors are making available (on compact disk) a collection of spreadsheets, which they have used to simulate the stochastic asset models which are considered in this paper.

This study aimed to compare systematically approaches to estimating influenza-attributable mortality in older Australians. Using monthly age-specific death data together with viral surveillance counts for influenza and respiratory syncytial virus, we explored two of the most frequently used methods of estimating excess influenza-attributable disease: Poisson and Serfling regression models. These approaches produced consistent age and temporal patterns in estimates of influenza-attributable mortality in older Australians but some variation in the magnitude of the disease burden. Of Australians aged >50 years, average annual estimated influenza-attributable deaths (all cause) ranged from 2314 to 3457 for the Serfling and Poisson regression models, respectively. The excess influenza-attributable disease burden was substantial under all approaches.

We present a class of stochastic regime-switching models. The time-series models may have periodic transition probabilities and the drifts may be seasonal. In the latter case, the model exhibits seasonal dummy variation that may change with the regime. The processes entail nontrivial interactions between so-called business and seasonal cycles. We discuss the stochastic properties as well as their relationship with periodic ARMA processes. Estimation and testing are also discussed in detail.