DISCUSSION PAPER PI-1105
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.