Search Results (5)

Human mortality has been improving faster than expected over the past few decades. This unprecedented improvement has caused significant financial stress to pension plan sponsors and annuity providers. The widely recognized Lee–Carter model often assumes linearity in its period effect as an integral part of the model. Nevertheless, deviation from linearity has been observed in historical mortality data. In this paper, we investigate the applicability of four nonlinear time-series models: threshold autoregressive model, Markov switching model, structural change model, and generalized autoregressive conditional heteroskedasticity model for mortality data. By analyzing the mortality data from England and Wales and Italy spanning the years 1900 to 2019, we compare the goodness of fit and forecasting performance of the four nonlinear models. We then demonstrate the implications of nonlinearity in mortality modeling on the pricing of longevity bonds as a practical illustration of our findings. Full article

For annuity providers, a higher life expectancy is not always positive news, as it potentially implies increased future costs, since benefits must be provided over a longer period of time. The underlying risk behind the unexpected improvement in life expectancy is called longevity risk. One way to hedge this risk can be attained with the process of securitization through mortality risk securities. This process requires an accurate prediction of the future mortality dynamics with an appropriate mortality model. However, a major issue in mortality modeling is the limited number of available data for a given population. The purpose of this paper is to present a mortality model under the credibility regression framework, aiming to capture the future mortality trends, especially for population datasets of limited available observations. Then, we show how this approach can be incorporated into pricing longevity bonds with the Wang transform. To ensure transparency and applicability in our illustration, the longevity bond pricing is based on the mortality data of Greece. Full article

Protecting against unexpected yield curve, inflation, and longevity shifts are some of the most critical issues institutional and private investors must solve when managing post-retirement income benefits. This paper empirically investigates the performance of alternative immunization strategies for funding targeted multiple liabilities that are fixed in timing but random in size (inflation-linked), i.e., that change stochastically according to consumer price or wage level indexes. The immunization procedure is based on a targeted minimax strategy considering the M-Absolute as the interest rate risk measure. We investigate to what extent the inflation-hedging properties of ILBs in asset liability management strategies targeted to immunize multiple liabilities of random size are superior to that of nominal bonds. We use two alternative datasets comprising daily closing prices for U.S. Treasuries and U.S. inflation-linked bonds from 2000 to 2018. The immunization performance is tested over 3-year and 5-year investment horizons, uses real and not simulated bond data and takes into consideration the impact of transaction costs in the performance of immunization strategies and in the selection of optimal investment strategies. The results show that the multiple liability immunization strategy using inflation-linked bonds outperforms the equivalent strategy using nominal bonds and is robust even in a nearly zero interest rate scenario. These results have important implications in the design and structuring of ALM liability-driven investment strategies, particularly for retirement income providers such as pension schemes or life insurance companies. Full article

Annuities providers become more and more exposed to longevity risk due to the increase in life expectancy. To hedge this risk, new longevity derivatives have been proposed (longevity bonds, q-forwards, S-swaps…). Although academic researchers, policy makers and practitioners have talked about it for years, longevity-linked securities are not widely traded in financial markets, due in particular to the pricing difficulty. In this paper, we compare different existing pricing methods and propose a Cost of Capital approach. Our method is designed to be more consistent with Solvency II requirement (longevity risk assessment is based on a one year time horizon). The price of longevity risk is determined for a S-forward and a S-swap but can be used to price other longevity-linked securities. We also compare this Cost of capital method with some classical pricing approaches. The Hull and White and CIR extended models are used to represent the evolution of mortality over time. We use data for Belgian population to derive prices for the proposed longevity linked securities based on the different methods. Full article

Standardized longevity risk transfers often involve modeling mortality rates of multiple populations. Some researchers have found that mortality indexes of selected countries are cointegrated, meaning that a linear relationship exists between the indexes. Vector error correction model (VECM) was used to incorporate this relation, thereby forcing the mortality rates of multiple populations to revert to a long-run equilibrium. However, the long-run equilibrium may change over time. It is crucial to incorporate these changes such that mortality dependence is adequately modeled. In this paper, we develop a framework to examine the presence of equilibrium changes and to incorporate these changes into the mortality model. In particular, we focus on equilibrium changes caused by threshold effect, the phenomenon that mortality indexes alternate between different VECMs depending on the value of a threshold variable. Our framework comprises two steps. In the first step, a statistical test is performed to examine the presence of threshold effect in the VECM for multiple mortality indexes. In the second step, threshold vector error correction model (TVECM) is fitted to the mortality indexes and model adequacy is evaluated. We illustrate this framework with the mortality data of England and Wales (EW) and Canadian populations. We further apply the TVECM to forecast future mortalities and price an illustrative longevity bond with multivariate Wang transform. Our numerical results show that TVECM predicted much faster mortality improvement for EW and Canada than single-regime VECM and thus the incorporation of threshold effect significant increases longevity bond price. Full article