In this paper we consider reserving and pricing methodologies for a pensions-type contract with a simple form of guaranteed annuity option. We consider only unit-linked contracts, but our methodologies and, to some extent, our numerical results would apply also to with-profits contracts.

The Report of the Annuity Guarantees Working Party (Bolton et al., 1997), presented the results of a very interesting survey, as at the end of 1996, of life assurance companies offering guaranteed annuity options. There was no consensus at that time among the companies on how to reserve for such options. The Report discussed several approaches to reserving, but concluded that it was unable to recommend a single approach. This paper is an attempt to fill that gap.

We investigate two approaches to reserving and pricing. In the first sections of the paper we consider quantile, and conditional tail expectation, reserves. The methodology we adopt here is very close to that proposed by the Maturity Guarantees Working Party in its Report to the profession (Ford et al., 1980). We show how these policies could have been reserved for in 1985, and what would have been the outcome of using the proposed method.

In a later section we consider the feasibility of using option pricing methodology to dynamically hedge a guaranteed annuity option. It is shown that this is possible within the context of the model we propose, but we submit that, in practical terms, dynamic hedging is not a complete solution to the problem since suitable tradeable assets do not in practice exist.

Finally, we describe several enhancements to our models and methodology, which would make them even more realistic, though generally they would have the effect of increasing the required contingency reserves

The paper introduces a setting in which each business in an economy faces considerable uncertainty about the cost of providing its service and therefore needs risk capital to give consumers confidence in its solvency. The paper then explores the operation of the capital market under conditions where businesses charge for this service dependability by setting an entity specific profit margin.

This entity specific profit margin is associated with an optimal, arbitrage-free investment portfolio for investors and, as they optimise their portfolios, generates a market equilibrium. Under these conditions it is shown that the entity specific risk premium for investors is the same as the premium for non-diversifiable risk relative to the market portfolio. This reconciles an entity specific approach with the capital asset pricing model, and in this setting would allow the use of the former without having to explicitly take the latter into consideration.

A consequence of this is that entity specific pricing and valuation are fair in such an setting and, for example, the fair value accounting of insurance liabilities can be performed on an entity specific basis.

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