The Volatility of Mortality

Daniel Bauer, Matthias Borger, Jochen Rub and Hans-Joachim Zwiesler

The use of forward models for the future development of mortality has been
proposed by several authors. In this article, we specify adequate volatility
structures for such models. We derive a Heath-Jarrow-Morton drift condition
under different measures. Based on demographic and epidemiological insights,
we then propose two different models with a Gaussian and a non-Gaussian
volatility structure, respectively. We present a Maximum Likelihood approach
for the calibration of the Gaussian model and develop a Monte Carlo Pseudo
Maximum Likelihood approach that can be used in the non-Gaussian case.
We calibrate our models to historic mortality data and analyze and value certain
longevity-dependent payoffs within the models.

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