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Modelling and Management of Longevity Risk: Approximations to Survivor Functions and Dynamic Hedging

Andrew J.G. Cairns

This paper looks at the development of dynamic hedging strategies for typical pension plan liabilities using longevity-linked hedging instruments. Progress in this area has been hindered by the lack of closed-form formulas for the valuation of mortality linked liabilities and assets, and the consequent requirement for simulations within simulations. We propose use of the probit function along with a Taylor expansion to approximate longevity-contingent values. This makes it possible to develop and
implement computationally efficient, discrete-time Delta hedging strategies using q-forwards as hedging instruments.

The methods are tested using the model proposed by Cairns, Blake and Dowd (2006a) (CBD). We find that the probit approximations are generally very accurate, and that the discrete-time hedging strategy is very effective at reducing risk.

Keywords: longevity risk, dynamic hedging, Delta hedging, probit-Taylor approximation, CBD model, q-forward, Solvency II.