Mortality is a stochastic process. We have imprecise knowledge about the probability distribution of mortality rates in the future. Mortality risk, therefore, can be defined in a broader term of ambiguity. In this article, we investigate the effects of ambiguity and ambiguity aversion on prices of mortality-linked securities. Ambiguity may arise from parameter uncertainty due to a finite sample of data and inaccurate old-age mortality rates. We compare the price of a mortality bond in three scenarios: (1) no parameter uncertainty, (2) parameter uncertainty with Bayesian updates, and (3) parameter uncertainty with the smooth ambiguity preference. We use the indifference pricing approach to derive the minimum ask price and the maximum bid price, and adopt the economic pricing method to compute the equilibrium price that clears the market. We reveal the connection between the indifference pricing approach and the economic pricing approach and find that ambiguity aversion has a much smaller effect on prices of mortality-linked securities than risk aversion in our example.
Bibliographical noteHua Chen acknowledges the financial support from Temple University. Michael Sherris acknowledges the support of ARC Linkage Grant Project LP0883398 Managing Risk with Insurance and Superannuation as Individuals Age with industry partners PwC and APRA and the Australian Research Council Centre of Excellence in Population Ageing Research (project number CE110001029).
CHEN, H., SHERRIS, M., SUN, T., & ZHU, W. (2013). Living with ambiguity : pricing mortality-linked securities with smooth ambiguity preferences. Journal of Risk and Insurance, 80(3), 705-732. https://doi.org/10.1111/j.1539-6975.2013.12001.x