Living with Ambiguity: Pricing Mortality-Linked Securities with Smooth Ambiguity Preferences

Journal of Risk and Insurance, Forthcoming

40 Pages Posted: 18 Feb 2012 Last revised: 1 Apr 2014

See all articles by Hua Chen

Hua Chen

University of Hawaiʻi at Mānoa

Michael Sherris

University of New South Wales - ARC Centre of Excellence in Population Ageing Research and School of Risk and Actuarial Studies; UNSW Australia Business School

Tao Sun

Independent

Wenge Zhu

Shanghai University of Finance and Economics

Multiple version iconThere are 2 versions of this paper

Date Written: February 22, 2013

Abstract

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 broad term of ambiguity. In this paper, we investigate the effects of ambiguity and ambiguity aversion on prices of mortality-linked securities. We adopt an asymmetric mortality jump model proposed by Chen et al. (2011) for mortality modeling and forecasting. 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 four scenarios: no parameter uncertainty, parameter uncertainty with a given prior distribution, parameter uncertainty with Bayesian updates, and 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 employ 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.

Keywords: ambiguity, ambiguity aversion, mortality-linked securities

JEL Classification: C11, G13, G22, I12

Suggested Citation

Chen, Hua and Sherris, Michael and Sun, Tao and Zhu, Wenge, Living with Ambiguity: Pricing Mortality-Linked Securities with Smooth Ambiguity Preferences (February 22, 2013). Journal of Risk and Insurance, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2007342 or http://dx.doi.org/10.2139/ssrn.2007342

Hua Chen (Contact Author)

University of Hawaiʻi at Mānoa ( email )

2404 Maile Way, E-602e
Honolulu, HI 96822
United States
(808) 956-8063 (Phone)
(808) 956-9887 (Fax)

Michael Sherris

University of New South Wales - ARC Centre of Excellence in Population Ageing Research and School of Risk and Actuarial Studies ( email )

UNSW Business School
Risk and Actuarial Studies
Sydney, NSW 2052
Australia
+61 2 9385 2333 (Phone)
+61 2 9385 1883 (Fax)

HOME PAGE: http://www.asb.unsw.edu.au/schools/Pages/MichaelSherris.aspx

UNSW Australia Business School ( email )

Sydney, NSW 2052
Australia

Tao Sun

Independent

No Address Available

Wenge Zhu

Shanghai University of Finance and Economics ( email )

AK Shanghai

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