Development and Pricing of a New Participating Contract

Abstract

This article designs and prices a new type of participating life insurance contract. Participating contracts are popular in the United States and European countries. They present many different covenants and depend on national regulations. In the present article we design a new type of participating contract very similar to the one considered in other studies, but with the guaranteed rate matching the return of a government bond. We prove that this new type of contract can be valued in closed form when interest rates are stochastic and when the company can default.     

Creating Customer Value in Participating Life Insurance

The value of a life insurance contract may differ depending on whether it is looked at from the customer's point of view or that of the insurance company. We assume that the insurer is able to replicate the life insurance contract's cash flows via assets traded on the capital market and can hence apply risk‐neutral valuation techniques. The policyholder, on the other hand, will take risk preferences and diversification opportunities into account when placing a value on that same contract. Customer value is represented by policyholder willingness to pay and depends on the contract parameters, that is, the guaranteed interest rate and the annual and terminal surplus participation rate. The aim of this article is to analyze and compare these two perspectives. In particular, we identify contract parameter combinations that—while keeping the contract value fixed for the insurer—maximize customer value. In addition, we derive explicit expressions for a selection of specific cases. Our results suggest that a customer segmentation in this sense, that is, based on the different ways customers evaluate life insurance contracts and embedded investment guarantees while ensuring fair values, is worthwhile for insurance companies as doing so can result in substantial increases in policyholder willingness to pay.     

Risk assessment of surplus appropriation schemes in participating life insurance

The aim of this paper is to analyze a life insurance company’s risk exposure with respect to different surplus appropriation schemes in participating life insurance. In this regard, three surplus appropriation schemes are considered, including the bonus system, the interest-bearing accumulation, and the system of shortening the contract term. We further examine an insurance company that offers all three schemes, i.e. each system is used for one third of the policyholders. Focus is laid on the effect of different asset portfolios and shocks to mortality on the insurer’s risk situation with respect to the policyholder’s age level at contract inception.     

Fair valuation of cliquet-style return guarantees in (homogeneous and) heterogeneous life insurance portfolios

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.     

Zur bedeutung einer Ausfallbedrohtheit von Versicherungskontrakten — ein Beitrag zur Behavioral Insurance

Kahneman / Tversky 1979 introduced the notion of so-called probabilistic insurance contracts. These are insurance policies involving a small probability that the consumer is not reimbursed because of a possible default of the insurance company. Extending the study ofWakker / Thaler / Tversky 1997, the present study contains an experimental analysis of the willingness of potential policyholders to pay for probabilistic insurance in dependency on the rating of the insurance company. It can be shown that people dislike probabilistic insurance and demand a substantial reduction in the premium to compensate for default risk. This reduction is rising with the default risk of the company. In addition, the results show a new phenomenon. The more an insurance company is threatened by default risk the less people are willing to accept contracts of this company at all. Finally the paper discusses implications for the control of insurance companies.     

Überlegungen zu einem fairen Risikomanagement-Mix in Versicherungsunternehmen

This article deals with the question of how a ?fair risk management mix“ that does not lead to a wealth transfer between shareholders and policyholders can be achieved in a joint-stock insurance company. In our financial model of an insurer, the ?fair“ situation, it is assumed that there is no wealth transfer between shareholders and policyholders when both parties receive a net present value of zero on their investments. Taking the default risk of the insurance company into account, we first model a ?fair“ situation for the insurer’s existing portfolio. Surprisingly, closing a new insurance contract that has been priced on a fair basis and then included in the insurer’s existing portfolio leads to a disequilibrium situation because the net present value for the shareholders is no longer zero. This new net present value can be viewed as the fair price of any risk management measure the insurer must take so as to reestablish an equilibrium for both parties, the shareholders and the policyholders.     

Guarantees in With-Profit and Unitized With-Profit Life Insurance Contracts: Fair Valuation Problem in Presence of the Default Option

The purpose of the article is to apply contingent claim theory to the valuation of the type of participating life insurance policies commonly sold in the UK. The article extends the techniques developed by Haberman, Ballotta, and Wang (2003) to allow for the default option. The default option is a feature of the design of these policies, which recognizes that the insurance company's liability is limited by the market value of the reference portfolio of assets underlying the policies that have been sold. The valuation approach is based on the classical contingent claim pricing “machinery,” underpinned by Monte Carlo techniques for the computation of fair values. The article addresses in particular the issue of a fair contract design for a complex type of participating policy and analyzes in detail the feasible set of policy design parameters that would lead to a fair contract and the trade‐offs between these parameters.     

Die Arglistanfechtung des Versicherungsvertrags bei fehlender textförmiger Nachfrage nach Gefahrumständen

The article treats the issue of disputing an insurance contract for reasons of malice in the event of an insurance company failing to comply with the requirements pertaining to the risk-issue-conversation provided by the VVG. According to §19 Abs. 1 VVG, the policy holder is merely required to answer questions about risk issues that are presented to him in writing and timewise before the policy holder has submitted his offer respectively in the time frame between submission of the offer by the policy holder and the acceptance by the insurance company. It is contentious whether an insurance company that has violated §19 Abs. 1 VVG may nevertheless dispute the insurance contract for reasons of malice in case of misrepresentation or omission of information on part of the policy holder. The article argues for an application of §241 Abs. 2 BGB in conjunction with §123 Abs. 1 BGB in addition to §19 Abs. 1 VVG—and thus in favor of an insurance company’s possibility to dispute the insurance contract. The protection of the policy holder’s rights is not an issue in the problem of applying the correct provision. They must rather be considered when determining the requirements of the contract dispute.     

比较法视域下公司董事赔偿责任保险立法问题研究——基于日本第二次《公司法》修改的比较考察

D&O保险的立法问题是我国司法实践中一个亟需澄清的问题,同时亦是保险法学界关注较多的基础理论问题。本文通过考察D&O保险合同在公司治理中的价值,细致分析在2019年日本第二次《公司法》修改之际学界对D&O保险规则立法与否的争论及立法演进历程,并对增设D&O保险合同规定的初衷以及在决定该保险合同内容时的决策程序进行系统阐释。研究发现,增设D&O保险合同规定、明确公司有权全额负担保险费用,有助于提高管理层的风险承担水平和管理效率,进而促进企业创新。在探讨我国《公司法》是否应当构建D&O保险规则这一问题时,应注意到公司法上的补偿制度是D&O保险存在的前提。就D&O保险合同内容的信息披露问题,一方面,为防止公司费用无限地用于提升填补限额,可采披露D&O合同信息的手段;另一方面,就具体的信息披露事项,不可盲目“照搬”美国做法。     

The 1999 Small Employer Retirement Survey

Abstract

In this article we examine to what extent policyholders buying a certain class of participating contracts (in which they are entitled to receive dividends from the insurer) can be described as standard bondholders. Our analysis extends the ideas of Biihlmann and sequences the fundamental advances of Merton, Longstaff and Schwartz, and Briys and de Varenne. In particular, we develop a setup where these participating policies are comparable to hybrid bonds but not to standard risky bonds (as done in most papers dealing with the pricing of participating contracts). In this mixed framework, policyholders are only partly protected against default consequences. Continuous and discrete protections are also studied in an early default Black and Cox-type setting. A comparative analysis of the impact of various protection schemes on ruin probabilities and severities of a life insurance company that sells only this class of contracts concludes this work.     

Risk Mutualization and Competition in Insurance Markets

The aim of this paper is to analyze the impact of mutual firms on competition in the insurance market. We distinguish two actors in this market: mutual firms, which belong to their pooled members, and traditional companies, which belong to their shareholders. Our approach differs from the literature by one crucial assumption: the expected utility of the consumers depends on the size of their insurance firm, which generates network externalities in this market. Thus, the choice of a contract results in a trade-off between the premium level and the probability of that premium being ex-post adjusted. The optimal contract offered by a mutual firm involves a systematic ex-post adjustment (negative or positive), while the contracts a company offers imply a fixed premium that is possibly negatively adjusted at the end of the contractual period. In an oligopoly game, we show that three types of configurations are possible at equilibrium: either one mutual firm or insurance company is active, or a mixed structure emerges in which two or more companies share the market with or without a mutual firm.     

The Impact of Surplus Distribution on the Risk Exposure of With Profit Life Insurance Policies Including Interest Rate Guarantees

This article analyzes the numerical impact of different surplus distribution mechanisms on the risk exposure of a life insurance company selling with profit life insurance policies with a cliquet‐style interest rate guarantee. Three representative companies are considered, each using a different type of surplus distribution: a mechanism, where the guaranteed interest rate also applies to surplus that has been credited in the past, a slightly less restrictive type in which a guaranteed rate of interest of 0 percent applies to past surplus, and a third mechanism that allows for the company to use former surplus in order to compensate for underperformance in “bad” years. Although at the outset all contracts offer the same guaranteed benefit at maturity, a distribution mechanism of the third type yields preferable results with respect to the considered risk measure. In particular, throughout the analysis, our representative company 3 faces ceteris paribus a significantly lower shortfall risk than the other two companies. Offering “strong” guarantees puts companies at a significant competitive disadvantage relative to insurers providing only the third type of surplus distribution mechanism.     

Optimal investment of an insurer with regime-switching and risk constraint

We investigate an optimal investment problem of an insurance company in the presence of risk constraint and regime-switching using a game theoretic approach. A dynamic risk constraint is considered where we constrain the uncertainty aversion to the ‘true’ model for financial risk at a given level. We describe the surplus of an insurance company using a general jump process, namely, a Markov-modulated random measure. The insurance company invests the surplus in a risky financial asset whose dynamics are modeled by a regime-switching geometric Brownian motion. To incorporate model uncertainty, we consider a robust approach, where a family of probability measures is cosidered and the insurance company maximizes the expected utility of terminal wealth in the ‘worst-case’ probability scenario. The optimal investment problem is then formulated as a constrained two-player, zero-sum, stochastic differential game between the insurance company and the market. Different from the other works in the literature, our technique is to transform the problem into a deterministic differential game first, in order to obtain the optimal strategy of the game problem explicitly.     

Sovereign debt renegotiation and credit default swaps

A credit default swap (CDS) contract provides insurance against default. This paper incorporates the contract into a sovereign default model and demonstrates that the existence of a CDS market results in lower default probability, higher debt levels, and lower financing costs for the country. Uncertainty over the insurance payout when the debt is renegotiated explains why in the data, as the output declines, the CDS spread becomes lower than the bond spread. Finally, my results show that the 2012 CDS naked ban, that decreased the levels of CDS for European countries, is a welfare reducing policy.     

Corporate Insurance as a Necessary Form of Consultant–Investigator Contract

Existing literature argues that corporate insurance is purchased because the insurance company produces risk management information for publicly held corporations. In this article, we address a fundamental question as to why other financial intermediaries cannot perform the same information production function as the insurance company. We argue that when the risk manager of the firm performs multiple tasks and needs consulting and investigation services from an outside agent for efficient risk management, the optimal contract with the agent has to be in the form of an insurance contract. Other types of contracts, such as flat-fee contracts, cannot be optimal. Therefore, the insurance company is ideally suited to provides these services.     

Betriebliche Altersversorgung durch Direktversicherungen: Eine finanzwirtschaftliche Analyse aus Arbeitnehmerund Eigentümersicht

Corporate pension schemes are part of the total remuneration of employees. In this paper we analyze the?Direktversicherung“ — a life insurance on behalf of the employee paid for by the employer — from the viewpoints of shareholders and employees alike. Firstly we examine, what implications this life insurance contract has on the cash flows to shareholders and employees. Social security payments and tax payments on individual and company level are accounted for. Secondly, we deduce possible substitution quotas q: We ask, what insurance premium the employer can afford to pay at most in place of a given amount of salary, without penalizing his shareholders. Next we deduce the minimum insurance premium an employee has to ask for to replace a given part of his salary in order not to worsen his financial position. From the findings, we conclude that a corporate pension scheme via the?Direktversicherung“ has the potential to lead to a win-win situation, with both parties better off than before. Our findings are also interesting for insurance companies offering those contracts to employers.     

Life insurance in a contingent claim framework: Pricing and regulatory implications

In this paper we develop a contingent claim model to evaluate the equity and liabilities of a life insurance company. The limited liability of shareholders is explicitly modelled. We focus on a specific type of life insurance policy—namely, the profit-sharing policy. In this policy, the policyholder is entitled to a guaranteed interest rate and a percentage of the company's yearly financial revenues. The implicit equilibrium interest rate and profit-sharing ratio are derived and analyzed. We finally discuss regulatory measures frequently encountered in the life insurance business such as rate ceilings, capital ratios, and asset restrictions.     

Lapse rate modeling: a rational expectation approach

The surrender option embedded in many life insurance products is a clause that allows policyholders to terminate the contract early. Pricing techniques based on the American Contingent Claim (ACC) theory are often used, though the actual policyholders' behavior is far from optimal. Inspired by many prepayment models for mortgage backed securities, this paper builds a Rational Expectation (RE) model describing the policyholders' behavior in lapsing the contract. A market model with stochastic interest rates is considered, and the pricing is carried out through numerical approximation of the corresponding two-space-dimensional parabolic partial differential equation. Extensive numerical experiments show the differences in terms of pricing and interest rate elasticity between the ACC and RE approaches as well as the sensitivity of the contract price with respect to changes in the policyholders' behavior.