Market Pricing of Longevity-linked Securities

One way of mitigating longevity risk is constructing a hedge using longevity - or mortality - linked securities. A fundamental question is how to price these securities in an incomplete life market where liabilities are not liquidly traded. Although there are various pricing methods developed in the literature, there has been no consensus on which one is the best and the choice is often based on user's preference. This article investigates the potential impact of uncertainty arising from the choice of mortality models and pricing rules on the calculation of longevity - l inked security prices. Twelve premium principles based on risk - neutral and real - world measures are examined under the Lee - Carter model and a generalisation of the CBD model. The quotations of UK pension annuities are set as the calibration constraints to incorporate the market view of longevity risk. We compare the results between different pricing methods and model assumptions on the prices of S-forwards and longevity swaps with different maturities. Overall, w efind that the pricing rule uncertainty is less material than the mortality model uncertainty. Particularly, the relationships between the results from different premium principles tend to rely on the underlying mortality model assumption. Our results suggest that the Lee - Carter mode l tends to give higher implied risk premiums than the CBD model does for both S - forwards and longevity swaps. Besides, the risk premiums calculated by the risk - neutral pricing methods are often lower than those by methods with real - world probabilities, while the results are more comparable within each of the two families.