Risk analysis and valuation of life insurance contracts: Combining actuarial and financial approaches

Self Cite

Traditional participating life insurance contracts with year-to-year (cliquet-style) guarantees have come under pressure in the current situation of low interest rates and volatile capital markets, in particular when priced in a market-consistent valuation framework. In addition, such guarantees lead to rather high capital requirements under risk-based solvency frameworks such as Solvency II or the Swiss Solvency Test (SST). Therefore, insurers in several countries have developed new forms of participating products with alternative (typically weaker and/or lower) guarantees that are less risky for the insurer. In a previous paper, it has been shown that such alternative product designs can lead to higher capital efficiency, i.e., higher and more stable profits and reduced capital requirements. As a result, the financial risk for the insurer is significantly reduced while the main guarantee features perceived and requested by the policyholder are preserved. Based on these findings, this paper now combines the insurer's and the policyholder's perspective by analyzing product versions that compensate policyholders for the less valuable guarantees. We particularly identify combinations of asset allocation and profit participation rate for the different product designs that lead to an identical expected profit for the insurer (and identical risk-neutral value for the policyholder), but differ with respect to the insurer's risk and solvency capital requirements as well as with respect to the real-world return distribution for the policyholder. We show that alternative products can be designed in a way that the insurer's expected profitability remains unchanged, the insurer's risk and hence capital requirement is substantially reduced and the policyholder's expected return is increased. This illustrates that such products might be able to reconcile insurers' and policyholders' interests and serve as an alternative to the rather risky cliquet-style products.

Section: The Financial Market Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Participating Life Insurance Products with Alternative Guarantees: Reconciling Policyholders’ and Insurers’ Interests

Reuß¹,

Ruß²,

Wieland³

2016

Self Cite

“…We stress the similarity with participating life insurance, although, there, the guarantee injection is settled at each update and not only at retirement. Compare for example Equation (13) to Equation (6). Again, we assume that the stochastic return on the assets, R X , does not jump at time points with an account update.…”

Section: Product Specification and Two-account Modelmentioning

confidence: 99%

“…The papers [8][9][10][11] are examples of recent literature that considers valuation in participating life insurance without (or with very limited) event risk. The papers [12][13][14] are other examples within the same area, but their focus is more risk-related. On the other hand, [15] models participating life insurance, taking into account the Markov model for the state of the policyholder, but the model is only tractable for a very simple financial environment, and it does not apply to unit-linked insurance.…”

Section: Introductionmentioning

confidence: 99%

A Two-Account Life Insurance Model for Scenario-Based Valuation Including Event Risk

Jensen

Schomacker²

2015

Using a two-account model with event risk, we model life insurance contracts taking into account both guaranteed and non-guaranteed payments in participating life insurance as well as in unit-linked insurance. Here, event risk is used as a generic term for life insurance events, such as death, disability, etc. In our treatment of participating life insurance, we have special focus on the bonus schemes "consolidation" and "additional benefits", and one goal is to formalize how these work and interact. Another goal is to describe similarities and differences between participating life insurance and unit-linked insurance. By use of a two-account model, we are able to illustrate general concepts without making the model too abstract. To allow for complicated financial markets without dramatically increasing the mathematical complexity, we focus on economic scenarios. We illustrate the use of our model by conducting scenario analysis based on Monte Carlo simulation, but the model applies to scenarios in general and to worst-case and best-estimate scenarios in particular. In addition to easy computations, our model offers a common framework for the valuation of life insurance payments across product types. This enables comparison of participating life insurance products and unit-linked insurance products, thus building a bridge between the two different ways of formalizing life insurance products. Finally, our model distinguishes itself from the existing literature by taking into account the Markov model for the state of the policyholder and, hereby, facilitating event risk.

“…Briys and De Varenne [10] study a model participating policy, focusing on the maturity value of the policy. Other studies including the minimum guarantee are Barbarin and Devolder [11], Graf et al [12], Grosen and Jørgensen [13], Hieber et al [14]. Guillén et al [15] analyze a policy that was launched by a Danish insurance company.…”

Section: Introductionmentioning

confidence: 99%

A Discussion of a Risk-Sharing Pension Plan

Donnelly

2017

I show that risk-sharing pension plans can reduce some of the shortcomings of defined benefit and defined contributions plans. The risk-sharing pension plan presented aims to improve the stability of benefits paid to generations of members, while allowing them to enjoy the expected advantages of a risky investment strategy. The plan does this by adjusting the investment strategy and benefits in response to a changing funding level, motivated by the with-profits contract proposed by Goecke (2013). He suggests a mean-reverting log reserve (or funding) ratio, where mean reversion occurs through adjustments to the investment strategy and declared bonuses. To measure the robustness of the plan to human factors, I introduce a measurement of disappointment, where disappointment is high when there are many consecutive years over which benefit payments are declining. Another measure introduced is devastation, where devastation occurs when benefit payments are zero. The motivation is that members of a pension plan who are easily disappointed or likely to get no benefit, are more likely to exit the plan. I find that the risk-sharing plan offers more disappointment than a defined contribution plan, but it eliminates the devastation possible in a plan that tries to accumulate contributions at a steadily increasing rate. The proposed risk-sharing plan can give a narrower range of benefits than in a defined contribution plan. Thus it can offer a stable benefit to members without the risk of running out of money.