Risk comparison of different bonus distribution approaches in participating life insurance

Abstract

a b s t r a c tThe fair pricing of explicit and implicit options in life insurance products has received broad attention in the academic literature over the past years. Participating life insurance (PLI) contracts have been the focus especially. These policies are typically characterized by a term life insurance, a minimum interest rate guarantee, and bonus participation rules with regard to the insurer's asset returns or reserve situation. Researchers replicate these bonus policies quite differently. We categorize and formally present the most common PLI bonus distribution mechanisms. These bonus models closely mirror the Danish, German, British, and Italian regulatory framework. Subsequently, we perform a comparative analysis of the different bonus models with regard to risk valuation. We calibrate contract parameters so that the compared contracts have a net present value of zero and the same safety level as the initial position, using risk-neutral valuation. Subsequently, we analyze the effect of changes in the asset volatility and in the initial reserve amount (per contract) on the value of the default put option (DPO), while keeping all other parameters constant. Our results show that DPO values obtained with the PLI bonus distribution model of Bacinello (2001), which replicates the Italian regulatory framework, are most sensitive to changes in volatility and initial reserves.

Main Determinants of Profit-Sharing Policy in the French Life Insurance Industry

“…Depending on the considered regulatory constraints, American or barrier options naturally appear, when policyholders are assumed to feature financial rationality. Zemp (2011) compares the estimations and models the risks faced by an insurer for different participation strategies.…”

Is Fair Pricing Possible? An Analysis of Participating Life Insurance Portfolios

“…Other authors, such as, Kling et al. (a,b), Graf, Richter, and Ruß (), Zemp (), and Bohnert and Gatzert (), have investigated different schemes for distributing surplus and the effects of such schemes on both the fair valuation of contracts and the insurer's risk exposure.…”

“…Many studies have also investigated the interactions between the contract parameters that define the insurer's and customers' risk situations (e.g., Gatzert and Kling, 2007;Kling, Richter, and Ruß, 2007b;Le Courtois and Quittard-Pinon, 2008;Schmeiser and Wagner, 2015). Other authors, such as Ruß (2007a,2007b), Graf, Richter, and Ruß (2011), Zemp (2011), and Bohnert and Gatzert (2012), have investigated different schemes for distributing surplus and the effects of such schemes on both the fair valuation of contracts and the insurer's risk exposure.…”

A Discussion of a Risk-Sharing Pension Plan

“…They find that their proposed plan increases the risk tolerance and the expected utility of the retirement benefits. Analyses of different surplus appropriation schemes in participating policies are provided by Bohnert and Gatzert [17] and Zemp [18].…”