Fair Valuation of Cliquet-Style Return Guarantees in (Homogeneous and) Heterogeneous Life Insurance Portfolios

Scandinavian Actuarial Journal, No. 6, pp. 478-507, 2019.

38 Pages Posted: 16 Jan 2016 Last revised: 25 Aug 2019

See all articles by Peter Hieber

Peter Hieber

University of Ulm - Department of Mathematics and Economics; Technische Universität München (TUM) - Department of Mathematics

Jan Natolski

University of Augsburg

Ralf Werner

Universität Augsburg

Date Written: January 23, 2019

Abstract

Participating life insurance contracts allow the policyholder to participate in the annual return of a reference portfolio. Additionally, they are often equipped with an annual (cliquet-style) return guarantee. The current low interest rate environment has again refreshed the discussion on risk management and fair valuation of such embedded options. While this problem is typically discussed from the viewpoint of a single contract or a homogeneous insurance portfolio, contracts are, in practice, managed within a heterogeneous insurance portfolio. Their valuation must then - unlike the case of asset portfolios - take account of portfolio effects: Their premiums are invested in the same reference portfolio; the contracts interact by a joint reserve, individual surrender options and joint default risk of the policy sponsor. Here, we discuss the impact of portfolio effects on the fair valuation of insurance contracts jointly managed in (homogeneous and) heterogeneous life insurance portfolios. First, in a rather general setting, including stochastic interest rates, we consider the case that otherwise homogeneous contracts interact due to the default risk of the policy sponsor. Second, and more importantly, we then also consider the case when policies are allowed to differ in further aspects like the guaranteed rate or time to maturity.
We also provide an extensive numerical example for further analysis.

Keywords: Life insurance, Fair valuation, Embedded options, Heterogeneous portfolios, Participating contracts, Return guarantee

JEL Classification: G13, G22

Suggested Citation

Hieber, Peter and Natolski, Jan and Werner, Ralf, Fair Valuation of Cliquet-Style Return Guarantees in (Homogeneous and) Heterogeneous Life Insurance Portfolios (January 23, 2019). Scandinavian Actuarial Journal, No. 6, pp. 478-507, 2019.. Available at SSRN: https://ssrn.com/abstract=2715571 or http://dx.doi.org/10.2139/ssrn.2715571

Peter Hieber (Contact Author)

University of Ulm - Department of Mathematics and Economics ( email )

Helmholzstrasse
Ulm, D-89081
Germany

Technische Universität München (TUM) - Department of Mathematics ( email )

Boltzmannstr. 3
Garching bei München, Bavaria 85748
Germany

Jan Natolski

University of Augsburg ( email )

Universitätsstr. 2
Augsburg, 86159
Germany

Ralf Werner

Universität Augsburg ( email )

Augsburg
Germany

Register to save articles to
your library

Register

Paper statistics

Downloads
224
Abstract Views
885
rank
137,351
PlumX Metrics