An article published in the British Medical Journal in 2018 reveals that a number of developed countries have experienced a decline in life expectancy in recent years. Within the classical framework of stochastic mortality modeling, the observed decline in life expectancy may be attributed to noises around the fitted log-linear trends in age-specific death rates. However, the patterns of the mortality heat maps for these countries suggest that it is likely a result of a fading of waves of high mortality improvement, which previously contributed to a linear rise in life expectancy in the developed world. In this paper, we introduce an improved version of the heat wave mortality model, which has the potential to capture the cessation of the waves of high mortality improvement. The proposed model is then used to examine the impact of declines in life expectancy on index-based longevity hedges. It is found that if life expectancy declines, a simple delta hedge still performs reasonably well in the sense that the over-hedging problem is only modest.

一篇发表在《英国医学杂志》上的文章2018年的数据显示，近年来一些发达国家的预期寿命有所下降。在随机死亡率建模的经典框架内，观察到的预期寿命下降可能归因于特定年龄死亡率的拟合对数线性趋势周围的噪声。但是，这些国家的死亡率热图的模式表明，这很可能是高死亡率改善浪潮逐渐消退的结果，以前，这些浪潮促使发达国家的预期寿命呈线性增长。在本文中，我们介绍了热浪死亡率模型的改进版本，该模型具有捕获高死亡率改进浪潮停止的潜力。然后，将所提出的模型用于检验预期寿命下降对基于指数的长寿套期保值的影响。