Mortality patterns in time
Summary
To estimate the mortality hazard by age, \(\hat\mu_x\), we would need to take first differences of a smoothed version of \(\hat{\Lambda}_x(t)\), and Anderson et al (1992, page 579) discuss using kernel smoothers for this. Equation (3) is a uniform kernel smoother and the results for varying values of the bandwidth parameter \(c\) are shown in Figure 2. Lower values of \(c\) apply less smoothing, and in Figure 2 this enables the identification of the winters of 1999/2000 and 2000/2001 as experiencing particularly heavy mortality. Unlike grouped counts of population data, the use of individual records underlying Figure 2 brings out the sharpness of the spike in deaths in the winters of 1999/2000 and 2000/2001. This spikiness brings us back to our opening premise, namely the COVID-19 mortality shock and how actuaries can detect it in their portfolio data.
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