Reserving for maturity guarantees: Two approaches. (English) Zbl 0894.90044

Summary: This is paper examines the pricing of and reserving for certain guarantees that are associated with some insurance contracts. Specifically, we deal with maturity guarantees, which provide a minimum level of benefits at contract maturity. Under these contracts the policyholders’ premiums are invested in a specified portfolio. When the contract matures the value of the benefit is guaranteed not to fall below a certain level. We examine and contrast two approaches to the pricing and reserving for these guarantees. The first approach is based on stochastic simulation of future investment returns. The second approach is based on modern option pricing theory. The reserving procedures under the two approaches differ dramatically. We provide numerical estimates of the reserves required under each approach using realistic assumptions. We find that the conventional option hedging strategies in the presence of transaction costs become relatively expensive.


91B30 Risk theory, insurance (MSC2010)
91B28 Finance etc. (MSC2000)
Full Text: DOI


[1] Bacinello, A.R.; Ortu, F., Pricing equity-linked life insurance with endogenous minimum guarantees, Insurance mathematics and economics, 12, 245-257, (1993) · Zbl 0778.62093
[2] Bacinello, A.R.; Ortu, F., Pricing equity-linked life insurance with endogenous minimum guarantees: A corrigendum, Insurance mathematics and economics, 13, 303-304, (1993) · Zbl 0778.62093
[3] Bates, D.S., Testing option pricing models, (), Chap. 20
[4] Boyle, P.P., Options and the management of financial risk, (1994), Society of Actuaries Schaumburg, IL, USA
[5] Boyle, P.P.; Emanuel, D., Discretely adjusted option hedges, Journal of financial economics, 8, 259-282, (1980)
[6] Boyle, P.P.; Hardy, M.R., Reserving for maturity guarantees, (1996), Institute for Insurance and Pension Research, Research Report 96-18, University of Waterloo Waterloo, Ont., Canada N2L 3G1 · Zbl 0894.90044
[7] Boyle, P.P.; Schwartz, E.S., Equilibrium prices of equity linked insurance policies with an asset value guarantee, Journal of risk and insurance, 44, 639-660, (1977)
[8] Brennan, M.J.; Schwartz, E.S., The pricing of equity-linked life insurance policies with an asset value guarantee, Journal of financial economics, 3, 195-213, (1976)
[9] Brennan, M.J.; Schwartz, E.S., Pricing and investment strategies for guaranteed equity-linked life insurance, ()
[10] Canadian Institute of Actuaries (CIA), ()
[11] Delbaen, F., Equity-linked policies, Bulletin association royal actuaries belges, 33-52, (1990)
[12] Hardy, M.R., Stochastic simulation in life office solvency assessment, Journal of the institute of actuaries, 120, 131-151, (1993)
[13] Hardy, M.R., Reserving for segregated fund contracts, () · Zbl 1083.91518
[14] Harris, P., Statistical data analysis and stochastic asset model validation, (), 311-331
[15] Henrotte, P., Transactions cost and duplication strategies, ()
[16] Huber, P., A review of Wilkie’s stochastic investment model, (), 333-364
[17] Hull, J.C., Options, futures and other derivative securities, (1997), Prentice-Hall Englewood Cliffs, NJ, USA
[18] Maturity Guarantees Working Party (MGWP), Journal of the institute of actuaries, 107, 103-209, (1980)
[19] Neilsen, J.; Aase, K.; Sandmann, K., Uniqueness of the fair premium for equity-linked life insurance contracts, Geneva papers on risk and insurance theory, 21, 65-102, (1996)
[20] Toft, K.B., On the Mean-variance tradeoff in option replication with transaction costs, Journal of financial and quantitative analysis, 31, 2, 233-263, (1996)
[21] Wilkie, A.D., A stochastic investment model for actuarial use, Transactions of the faculty of actuaries, 39, 341-381, (1986)
[22] Wilkie, A.D., More on a stochastic asset model for actuarial use, British actuarial journal, 1, 777-964, (1995)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.