Article2006

A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty

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Insurance, Mortality, Demography, Risk Management Insurance and Financial Risk Management Stochastic processes and financial applications

Abstract

In this paper we consider the evolution of the post-60 mortality curve in the UK and its impact on the pricing of the risk associated with 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 paper then examines the pricing of longevity bonds with different terms to maturity referenced to different cohorts. We find that longevity risk over relativelyshort time horizons is very low, but at horizons in excess of 10 years it begins to pick up very rapidly. We propose a method for risk-adjusting the market price of a longevity bond which includes an allowance for parameter risk in the stochastic mortality model. We utilise 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.

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References

1992Modeling and Forecasting U. S. Mortality 2002A Poisson log-bilinear regression approach to the construction of projected lifetables 2003Lee–Carter mortality forecasting with age-specific enhancement 2001Survivor Bonds: Helping to Hedge Mortality Risk 2006Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk 2005Securitization of Mortality Risks in Life Annuities 1932On Some Experiments in the Graduation of Mortality Statistics 2006Living with Mortality: Longevity Bonds and Other Mortality-Linked Securities

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2006Life is Cheap: Using Mortality Bonds to Hedge Aggregate Mortality Risk 2011Longevity Risk, Retirement Savings and Financial Innovation 2008Valuation of mortality risk via the instantaneous Sharpe ratio: Applications to life annuities 2012Optimal retirement consumption with a stochastic force of mortality 2010The impact of aggregate mortality risk on defined benefit pension plans 2006

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