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

Andrew J.G. Cairns, David Blake, Kevin Dowd

In this paper we consider the evolution of the post-age-60 mortality curve
in the UK 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 a®ects 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
relatively short time horizons is very low, but at horizons in excess of 10 years
it begins to pick up very rapidly.

A key component of the paper 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 utilise the pricing information
con- tained 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 di®erent characteristics.

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