TY - JOUR
T1 - Fair valuation of cliquet-style return guarantees in (homogeneous and) heterogeneous life insurance portfolios
AU - Hieber, Peter
AU - Natolski, Jan
AU - Werner, Ralf
N1 - Publisher Copyright:
© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2019/7/3
Y1 - 2019/7/3
N2 - 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.
AB - 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.
KW - G13
KW - G22
KW - Life insurance
KW - embedded options
KW - fair valuation
KW - heterogeneous portfolios
KW - participating contracts
KW - return guarantee
UR - http://www.scopus.com/inward/record.url?scp=85062338487&partnerID=8YFLogxK
U2 - 10.1080/03461238.2019.1574889
DO - 10.1080/03461238.2019.1574889
M3 - Article
AN - SCOPUS:85062338487
SN - 0346-1238
VL - 2019
SP - 478
EP - 507
JO - Scandinavian Actuarial Journal
JF - Scandinavian Actuarial Journal
IS - 6
ER -