The Volatility of Mortality

Daniel Bauer, Matthias Börger, Jochen Ruß and Hans-Joachim Zwiesler
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Daniel Bauer: Georgia State University
Matthias Börger: Ulm University, Germany
Jochen Ruß: Institute of Finance and Actuarial Science at Ulm, Germany
Hans-Joachim Zwiesler: Ulm University, Germany

Asia-Pacific Journal of Risk and Insurance, 2008, vol. 3, issue 1, pages 10

Abstract:

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.

Date: 2008
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