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An option pricing approach to bonus policy. In memoriam Anthony P. Limb

  • A. D. Wilkie


In this paper I discuss a simple application of option pricing theory to bonuses on with-profits life assurance policies. The approach is a new one and I have been able to make only an introductory exploration of its possible applications. Nevertheless it seems to me to give actuaries some sort of a handle for gripping the rather intractable problem of the relationship between reversionary bonus, terminal bonus and the proceeds of comparable unit-linked policies. I look at the problem very much from the policyholder's side, and I am not concerned here with aspects of valuation or solvency. These require further investigation.



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Beenstock, M. & Brasse, V. (1986) Using Options to Price Maturity Guarantees. J.I.A., 113, 151.
Black, F. & Scholes, M. (1973) The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81, 637.
Boyle, P.P. & Schwartz, E.S. (1977) Equilibrium Prices of Guarantees under Equity-linked Contracts. The Journal of Risk and Insurance, 44, 639.
Brennan, M.J. & Schwartz, E.S. (1976) The Pricing of Equity-linked Life Insurance Policies with an Asset Value Guarantee. Journal of Financial Economics, 3, 195.
Brennan, M.J. & Schwartz, E.S. (1979) Alternative Investment Strategies for the Issuers of Equity-linked Life Insurance with an Asset Value Guarantee. Journal of Business, 52, 63.
Brenner, M. Editor, (1983) Option Pricing, Theory and Applications. Lexington Books, D.C. Heath and Company, Lexington, Mass.
Chamberlin, G. (1983) Trading in Options, Second Edition. Woodhead-Faulkner, Cambridge.
Collins, T.P. (1977) Brownian Motion. Unpublished note.
Collins, T.P. (1982) An Exploration of the Immunization Approach to Provision for Unit-linked Policies with Guarantees. J.I.A., 109, 241.
Cox, J.C. & Rubinstein, M. (1983) A Survey of Alternative Option-pricing Models. In Brenner (1983).
Fagan, J.C. (1977) Maturity Guarantees under Investment-linked Contracts. Presented to the Society of Actuaries in Ireland, 10 November 1977.
Jarrow, R.A. & Rudd, A. (1983) Option Pricing. Richard D. Irwin, Homewood, 111.
Malliaris, A.G. & Brock, W.A. (1982) Stochastic Methods in Economics and Finance. North-Holland, Amsterdam.
Maturity Guarantees Working Party (1980) Report. J.I.A., 107, 101.
Merton, R. (1973) Theory of Rational Option Pricing. Bell Journal of Economics and Management Science, Spring 1973, 141.
Muckart, R.D. & Smith, W.J. (1984) Investment Options and Traded Trusts. Presented to the Faculty of Actuaries Students' Society, 6 February 1984.
Wilkie, A.D. (1985) Steps Towards a Stochastic Investment Model for Actuarial Use. O.A.R.D., 36, Institute of Actuaries.
Wilkie, A.D. (1986a) A Stochastic Investment Model for Actuarial Use. T.F.A., 39, 341.
Wilkie, A.D. (1986b) Some Applications of Stochastic Investment Models. J.S.S., 29, 25.
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Journal of the Institute of Actuaries
  • ISSN: 0020-2681
  • EISSN: 2058-1009
  • URL: /core/journals/journal-of-the-institute-of-actuaries
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