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Longevity risk, that is, the uncertainty of the demographic survival rate, is an important risk for insurance companies and pension funds, which have large, and long‐term, exposures to survivorship. The purpose of this paper is to propose a new model to describe this demographic survival risk.

The model proposed in this paper satisfies all the desired properties of a survival rate and has an explicit distribution for both single years and accumulative years.

The results show that it is important to consider the expected shift and risk premium of life table uncertainty and the stochastic behaviour of survival rates when pricing the survivor derivatives.

This model can be applied to the rapidly growing market for survivor derivatives.