Pricing q-forward contracts: an evaluation of estimation window and pricing method under different mortality models

The aim of this paper is to study the impact of various sources of uncertainty on the pricing of a special longevity–based instrument: a q-forward contract. At the expiry of a q-forward contract, the realized mortality rate for a given population is exchanged in return for a fixed (mortality) rate that is agreed at the initiation of the contract. Pricing a q-forward involves determining this fixed rate. In our study, we disentangle three main sources of uncertainty and consider their impact on pricing: model choice for the underlying mortality rate, time-window used for estimation and the pricing method itself.