The cost of capital is a key element of the embedded value methodology for the valuation of a life business. In this paper we refer to a portfolio of immediate life annuities and we focus on longevity risk. Our purpose is to design a framework for a valuation of the portfolio which is market-consistent, and therefore based on a risk-neutral argument, while involving some of the basic items of a traditional valuation, viz best estimate future flows and allocated capital. This way, we try to reconcile the traditional with a market-consistent (or risk-neutral) approach. This allows us, in particular, to translate the results obtained under the risk-neutral approach in terms of a properly redefined embedded value.
