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A Two-Factor Model for Stochastic Mortality With Parameter Uncertainty: Theory and Calibration

32 Pages Posted: 29 Nov 2006  

Andrew J. G. Cairns

Heriot-Watt University - Department of Actuarial Science & Statistics

David P. Blake

City University London - Cass Business School - The Pensions Institute

Kevin Dowd

Nottingham University Business School (NUBS)

Abstract

A key component of the article is the proposal and development of a method for calculating the market risk-adjusted price of a longevity bond. The proposed adjustment includes not just an allowance for the underlying stochastic mortality, but also makes an allowance for parameter risk. We utilize the pricing information contained in the November 2004 European Investment Bank longevity bond to make inferences about the likely market prices of the risks in the model. Based on these, we investigate how future issues might be priced to ensure an absence of arbitrage between bonds with different characteristics. In this article, we consider the evolution of the post-age-60 mortality curve in the United Kingdom and its impact on the pricing of the risk associated with aggregate mortality improvements over time: so-called longevity risk. We introduce a two-factor stochastic model for the development of this curve through time. The first factor affects mortality-rate dynamics at all ages in the same way, whereas the second factor affects mortality-rate dynamics at higher ages much more than at lower ages. The article then examines the pricing of longevity bonds with different terms to maturity referenced to different cohorts. We find that longevity risk over relatively short time horizons is very low, but at horizons in excess of ten years it begins to pick up very rapidly. A key component of the article is the proposal and development of a method for calculating the market risk-adjusted price of a longevity bond. The proposed adjustment includes not just an allowance for the underlying stochastic mortality, but also makes an allowance for parameter risk. We utilize the pricing information contained in the November 2004 European Investment Bank longevity bond to make inferences about the likely market prices of the risks in the model. Based on these, we investigate how future issues might be priced to ensure an absence of arbitrage between bonds with different characteristics.

Suggested Citation

Cairns, Andrew J. G. and Blake, David P. and Dowd, Kevin, A Two-Factor Model for Stochastic Mortality With Parameter Uncertainty: Theory and Calibration. Journal of Risk & Insurance, Vol. 73, No. 4, pp. 687-718, December 2006. Available at SSRN: https://ssrn.com/abstract=947962 or http://dx.doi.org/10.1111/j.1539-6975.2006.00195.x

Andrew Cairns (Contact Author)

Heriot-Watt University - Department of Actuarial Science & Statistics ( email )

Edinburgh EH14 4AS Scotland
United Kingdom

David Blake

City University London - Cass Business School - The Pensions Institute ( email )

London, EC2Y 8HB
Great Britain
+44 (0) 20-7040-5143 (Phone)
+44 (0) 20-7040-8881 (Fax)

Kevin Dowd

Nottingham University Business School (NUBS) ( email )

Jubilee Campus
Wollaton Road
Nottingham, NG8 1BB
United Kingdom

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