Guaranteed Rate-setting Behavior, Life Insurance Premium, and Policyholder Protection

ABSTRACT

This study explores the determinants of an insurer’s guaranteed rate based on a contingent claim model. According to the model development, we structure and estimate the guaranteed rate setting and policyholder protection equations. A time-series approach explains the guaranteed rate-setting behavior and insurance stability captured by policyholder protection from 1990 to 2018. The evidence suggests that derivatives, life insurance premiums, administrative costs, and federal income tax affect the insurer’s guaranteed rate-setting behavior. Increasing life insurance premiums and administrative costs in asset-liability matching management significantly enhance policyholder protection, contributing to insurance stability.

KEYWORDS:

• Guaranteed rate-setting
• life insurance premium
• policyholder protection

JEL:

• G21
• G28

Acknowledgments

The authors would like to thank Prof. Paresh Kumar Narayan (Editor) and the anonymous referees for their helpful comments and suggestions. The usual disclaimer applies.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1. See https://www.iii.org/fact-statistic/facts-statistics-life-insurance. Accessed Oct 10, 2021.

2. $\phi (.)$ is probability density function of standard normal distribution. $\frac{\mathrm{\partial }S(V_A,X)}{\mathrm{\partial }R}=(X+V_B)\{[V_A\phi (d_1)(\frac{-1}{\sigma +\kappa })\frac{1}{X}-e^{-R_B}N(d_2)+e^{-R_B}\phi (d_2)(\frac{1}{\sigma +\kappa })]$$-(h/V_A{)}^{2\eta -2}{X}^{2\eta -2}[V_{A}2\eta X(h/V_A{)}^{2}N(d_3)+V_{A}X(h/V_A{)}^2\phi (d_3)(\frac{1}{\sigma +\kappa })-(2\eta -1)e^{-R_B}N(d_4)$$-e^{-R_B}\phi (d_4)(\frac{1}{\sigma +\kappa })]\}-\delta (X+V_B)\{[(1-\theta )V_A\phi (d_5)(\frac{-1}{\sigma +\kappa })\frac{1}{X}-e^{-R_B}N(d_6)+e^{-R_B}\phi (d_6)(\frac{1}{\sigma +\kappa })]$$-(h/(1-\theta )V_A{)}^{2\eta -2}{X}^{2\eta -2}[(1-\theta )V_{A}2\eta X(h/V_A{)}^{2}N(d_7)+V_{A}X(h/(1-\theta )V_A{)}^2\phi (d_7)(\frac{1}{\sigma +\kappa })$$-(2\eta -1)e^{-R_B}N(d_8)-e^{-R_B}\phi (d_8)(\frac{1}{\sigma +\kappa })]\}$

So $\mathrm{\partial }S(V_A,X)/\mathrm{\partial }R=0$ is a transcendental equation with no analytical solution.

We can not obtained specific functional form of $R$. We apply Slovin and Sushka (1983) to express the guaranteed rate function based on our developed model for the empirical study.

3. See Bartosz (2015) for detecting structural breaks in financial volatility.

4. See Life Insurers Fact Book, Available at http://www.acli.com/Industry-Facts/Life-Insurers-Fact-Book. Accessed Oct 10, 2021. Our model is a firm-level one. However, those data are industry-level. The industry-level data might be applicable to a monopolistic representative firm-level analysis, which is a limit of our empirical study.

5. According to the reviewer’s suggestion, we defined the a ratio of ($x_i,i=1\text{~}15$) relative to ($x_1+x_2+x_3+x_4+x_5$). The estimation result is very similar to the regression results shown in Table 2. The regression coefficient of life insurance premiums’ratio is significantly positive, the regression coefficients of general and administrative expenses’ratio and federal income tax’s ratio are significantly negative.

Additional information

Funding

This paper was supported by Ministry of Education Humanities and Social Sciences Fund [No. 21YJA790031], Project 2021 of the 14th Five Year Plan for Social Science Research of Sichuan Province [SC21B141] and Fundamental Research Funds for the Central Universities [JBK1805006].