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Reserving, Pricing and Hedging For Policies with Guaranteed Annuity Options

Published online by Cambridge University Press:  10 June 2011

A. D. Wilkie ,
H. R. Waters  and
S. Yang
A. D. Wilkie
Affiliation:
Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, U.K. E-mail: A.D.Wilkie@ma.hw.ac.uk and InQA Limited, Dennington, Ridgeway, Horsell, Woking GU21 4QR, U.K. E-mail: david.wilkie@inqa.com
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Abstract

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

Keywords

Guaranteed Annuity OptionsContingency ReservesQuantile ReservesConditional Tail ExpectationsCharging for Contingency ReservesMortality ImprovementsQuanto OptionsOption PricesHedging ProportionsDynamic HedgingEmpirical HedgingHedging ErrorsTransaction CostsPracticability of HedgingFat-tailed InnovationsStochastic Mortality ModelsStochastic HypermodelsStochastic BridgesBrownian BridgesOrnstein-Uhlenbeck Bridges
Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 9 , Issue 2 , 01 June 2003 , pp. 263 - 391
Copyright
Copyright © Institute and Faculty of Actuaries 2003

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