An exploration of the immunization approach to provision for unit-linked policies with guarantees

1.1. This paper explores the possibility that a company which sells unit-linked policies with death and maturity benefit guarantees may follow an investment strategy which reduces the risks associated with them. It originated when the author was requested by the Institute to study papers on the subject by P. P. Boyle, M. J. Brennan and E. S. Schwartz1 2 of the University of British Columbia in Canada and also a paper presented to the Society of Actuaries in Ireland by J. C. Fagan.3 1.2. The approach to provision for guarantees suggested by these authors is very different from that advocated by the main contributors to the subject, from S. Benjamin4 through to the Maturity Guarantees Working Party.5 Boyle, Brennan and Schwartz based their work on some results on options derived by F. Black and M. Scholes6 and developed further by R. C. Merton.7 Fagan devised his approach independently using methods similar to those employed by F. M. Reddington8 for immunization of fixed-benefit policies. The author has deposited a longer paper,9 which includes a review of existing work on the subject, in the Institute library and has confined this version as far as possible to his own ideas and investigations. 1.3. Although a negative conclusion is reached here about the practicability of the approach which is investigated the author hopes that the paper may still be of interest because it sheds new light on the risks inherent in financial guarantees and the shortcomings of the conventional method of providing for them. It is also possible that the author's endeavours may prompt others to develop the theory further or to find other areas in which it may be applied more successfully. 1.4. In order to make this paper as short and readable as possible many theoretical results whose derivation involves complex mathematics are stated without proof, some of the assumptions and arguments are presented without the qualifications and provisos which should strictly accompany them and the results of many of the investigations which were performed are summarized or omitted entirely. The interested reader may refer to the author's longer paper for a more thorough treatment.