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Analytical Pricing of the Unit-Linked Endowment with Guarantees and Periodic Premiums

Published online by Cambridge University Press:  09 August 2013

Werner Hürlimann
Werner Hürlimann*
Affiliation:
FRSGlobal Switzerland AG, c/o. Regus Business Center, Seefeldstrasse 69, CH-8008 Zürich, E-Mail: werner.huerlimann@frsglobal.com
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Abstract

We consider the unit-linked endowment with guarantee and periodic premiums, where at each premium payment date the insurance company invests a certain fraction of the premium into a risky reference portfolio. In the dual random environment of stochastic interest rates with deterministic volatilities and mortality risk, and for a fixed guarantee, simple analytical lower and upper bounds for the fair periodic premium are explicitly derived. We also consider contracts with guaranteed minimum benefits that vary over time and we obtain tight lower and upper bounds for both fair periodic premiums and guaranteed minimum benefits that increase over time. The numerical illustrations of our results reveal that the analytical bounds are very tight. Moreover, the simple, fast and very reliable analytical numerical calculations with controlled accuracy avoid time consuming Monte Carlo calculations and are almost always preferred by practitioners. Some analytical closed-form solutions for one- and two-year maturity dates are also stated.

Keywords

Unit-linked endowmentguaranteed minimum death and accumulation benefitsfair premiumconvex lower and upper bounds
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 2 , November 2010 , pp. 631 - 653
Copyright
Copyright © International Actuarial Association 2010

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