On Valuing Participating Life Insurance Contracts with Conditional Heteroscedasticity

In this paper, we consider a novel approach for the fair valuation of a participating life insurance policy when the dynamics of the reference portfolio underlying the policy are governed by an Asymmetric Power GARCH (APGARCH) model with innovations having a general parametric distribution. The APGARCH model provides a flexible way to incorporate the effect of conditional heteroscedasticity or time-varying conditional volatility and nests a number of important symmetric or asymmetric ARCH-type models in the literature. It also provides a flexible way to capture both the memory effect of the conditional volatility and the asymmetric effects of past positive and negative returns on the current conditional volatility, called the leverage effect. The key valuation tool here is the conditional Esscher transform of Bühlmann et al. (1996, 1998). The conditional Esscher transform provides a convenient and flexible way for the fair valuation under different specifications of the conditional heteroscedastic models. We illustrate the practical implementation of the model using the S&P 500 index as a proxy for the reference portfolio. We also conduct sensitivity analysis of the fair value of the policy with respect to the parameters in the APGARCH model to document the impacts of different conditional volatility models nested in the APGARCH model and the leverage effect on the fair value. The results of the analysis reveal that the memory effect of the conditional volatility has more significant impact on the fair value of the policy than the leverage effect.     

An Actuarial Analysis of Participating Life Insurance

An actuarial model is developed to reveal the intrinsic nature of participating life insurance. The basic safe-side criterion is examined. It is established how the first-order prospective net premium reserve includes safety margins or bonus loadings, and it is demonstrated how the bonus loadings are currently released. It is demonstrated how surplus may be distributed and accumulated as a terminal bonus in an equitable way. The level premium is divided into a variable recurrent single premium and a variable natural premium, and an alternative to the prospective net premium reserve is examined. A capitalization of future safety margins or bonus loadings, which are related to past premiums and the paid-up benefit, may allow the insurance company a considerable increase in investment freedom. The theory is illustrated by numerical results.     

Participating Insurance Contracts and the Rothschild-Stiglitz Equilibrium Puzzle

We extend the Rothschild-Stiglitz (RS) insurance market model with adverse selection by allowing insurers to offer either non-participating or participating policies, that is, insurance contracts with policy dividends or supplementary calls for premium. It is shown that an equilibrium always exists in such a setting. Participating policies act as an implicit threat that dissuades deviant insurers who aim to attract low-risk individuals only. The model predicts that the mutual corporate form should be prevalent in insurance markets where second-best Pareto efficiency requires cross-subsidisation between risk types.     

The Design of Optimal Insurance Contracts: A Topological Approach

This article deals with the optimal design of insurance contracts when the insurer faces administrative costs. If the literature provides many analyses of risk sharing with such costs, it is often assumed that these costs are linear. Furthermore, mathematical tools or initial conditions differ from one paper to another. We propose here a unified framework in which the problem is presented and solved as an infinite dimensional optimization program on a functional vector space equipped with an original norm. This general approach leads to the optimality of contracts lying on the frontier of the indemnity functions set. This frontier includes, in particular, contracts with a deductible, with total insurance and the null vector. Hence, we unify the existing results and point out some extensions.     

Overcoming Barriers to Life Insurance Coverage: A Behavioral Approach

While life insurance purchase decisions have long been studied, we still do not know how people decide if they need insurance or how much they need. Using in‐depth interviews, we peer into the black box of employee decision making to learn what people know about this employee benefit, and how they decide if it is of value for them. We find that individuals understand the need for life insurance, but find many behavioral economic barriers to getting adequate coverage, including mental accounting, money illusion, and a strong role of defaults. We then conduct an online experiment of the hypothetical employee‐benefit purchase scenario, and find a few, simple interventions could help individuals better decide their life insurance needs.     

Non-Linearity Between Life Insurance and Economic Development: A Revisited Approach

This paper investigates the non-linear link between economic development and activities of the life insurance market. We ask whether the relevance of institutional environments on the development of the life insurance market is different across countries. Applying a novel threshold model with the instrumental variable approach, we find overwhelming evidence in support of an income threshold. Moreover, legal and political circumstances have an overwhelming positive effect on life insurance in low-income countries, but the effect is marginal in high-income countries. Our findings clearly demonstrate that the role of institutions on activities in the life insurance market diminishes with the evolvement of economic development.     

国际财务报告准则第4号:保险合同

目标 1.本国际财务报告准则的目标是在理事会完成保险合同项目第二阶段之前,规范所有签发保险合同的实体(本国际财务报告准则称之为承保人)对保险合同的财务报告.特别是,本国际财务报告准则要求:(1)承保人对保险合同的会计处理作有限的改进.(2)披露相关信息,明确和解释承保人财务报表中因保险合同而产生的金额,以帮助这些财务报表的使用者理解保险合同未来现金流量的金额、时间及其不确定性.     

One Approach to Dual Randomness in Life Insurance

Abstract

1. The Unnatural Hypothesis of a Constant Rate of Interest

There are loan contracts which assume a constant interest during several years and thereafter payment of the amount borrowed, but nowadays clauses are as a rule admitted giving the debtor right of conversion or repayment after a certain period, generally ten years. Low interest loans can be considered as perpetuities from a practical point of view, as long as no possibility is meant to exist that the market rate will fall under their nominal rate. Such a loan—as e.g. Consols—with the nominal rate i ₀ ought to be valued at a discount if the market rate is higher, say i > i ₀, the value being equal to the fraction i ₀ : i. But constant rates are no rule in practice.     

Fair Valuation of a Guaranteed Life Insurance Participating Contract Embedding a Surrender Option

In this article we deal with the problem of pricing a guaranteed life insurance participating policy, sold in the Italian market, which embeds a surrender option. This feature is an American‐style put option that enables the policyholder to sell back the contract to the insurer at the cash surrender value. Employing a recursive binomial formula patterned after the Cox, Ross, and Rubinstein (1979) discrete option pricing model we compute, first of all, the total price of the contract, which also includes a compensation for the participation feature (“participation option,” henceforth). Then this price is split into the value of three components: the basic contract, the participation option, and the surrender option. The numerical implementation of the model allows us to catch some comparative statics properties and to tackle the problem of suitably fixing the contractual parameters in order to obtain the premium computed by insurance companies according to standard actuarial practice.     

IASB和我国保险会计准则的比较分析:基于保险合同计量部分

随着国际保险会计的迅速发展,我国保险行业的会计也深受国际潮流的影响。2010年8月,国际会计准则委员会(IASB)发布了《征求意见稿——保险合同》,进一步完善了保险会计的规定。我国财政部于2009年12月正式发布了《保险合同相关会计处理规定》。本文主要对IASB最新发布的IFRS 4征求意见稿——保险合同与我国保险会计准则中的保险合同计量部分进行了较为详细的比较分析,并讨论了新准则对我国保险实务的影响,望能为我国保险会计的发展提供一定的参考。     

A Finite Difference Approach to the Valuation of Path Dependent Life Insurance Liabilities

This paper sets up a model for the valuation of traditional participating life insurance policies. These claims are characterized by their explicit interest rate guarantees and by various embedded option elements, such as bonus and surrender options. Owing to the structure of these contracts, the theory of contingent claims pricing is a particularly well-suited framework for the analysis of their valuation.The eventual benefits (or pay-offs) from the contracts considered crucially depend on the history of returns on the insurance company's assets during the contract period. This path-dependence prohibits the derivation of closed-form valuation formulas but we demonstrate that the dimensionality of the problem can be reduced to allow for the development and implementation of a finite difference algorithm for fast and accurate numerical evaluation of the contracts. We also demonstrate how the fundamental financial model can be extended to allow for mortality risk and we provide a wide range of numerical pricing results.     

保险合同会计--进展、反思与启示

国际会计准则委员会近期发布的“国际财务报告准则第4号”(IFRS4)是保险合同会计第一阶段的成果。为了理解国际上保险合同会计的这一进展,本文首先从设问的角度界定了一个保险会计的框架;在此基础上,归纳和分析了IFRS4中的主要议题,并从概念与现实的权衡及会计错配两方面对其过渡特征进行了剖析;在界定的框架范围内,依据对IFRS4的分析评价,提出了我国保险会计规范中值得注意的几个问题。     

人寿保险需求探析

与其他形式的保险相比,人寿保险更具有储蓄的功能,因而对寿险需求动机的分析可以在储蓄动机的分析框架内进行。对保险需求的研究,大部分文献是从投保人最大化其自身期望效用出发,里维斯（Lewis,1989）拓宽了这一研究视角,从被赡养人期望效用的角度研究人寿保险需求。寿险需求的影响因素：期望寿命、保险价格、赡养率、收入与财富、社会保障、预期通货膨胀率、教育水平。     

新型保险合同会计——问题、进展及启示

新型保险业务占比大幅增加、国际国内证券市场大幅下跌和保单持有人抱怨新型保险会计信息不透明,使得充分披露其存在的风险变得更为紧迫。本文首先回顾保险合同会计的发展历程,然后提出了新型保险会计存在的问题,接着跟踪IASB新型保险会计的最新进展,并对其作出评价,最后是我国新型保险会计发展的启示。     

寿险资金运用中的投资理念分析

投资理念是主导金融机构投资行为的关键,有什么样的投资理念就会有相应的投资策略和投资组合。简单地说,投资理念就是投资的指导思想,是投资者理论与实践的总结。     

The Insurance Is the Lemon: Failing to Index Contracts

We model the widespread failure of contracts to share risk using available indices. A borrower and lender can share risk by conditioning repayments on an index. The lender has private information about the ability of this index to measure the true state that the borrower would like to hedge. The lender is risk-averse and thus requires a premium to insure the borrower. The borrower, however, might be paying something for nothing if the index is a poor measure of the true state. We provide sufficient conditions for this effect to cause the borrower to choose a nonindexed contract instead.     

Optimal Contracts Under Adverse Selection and Moral Hazard: A Continuous-Time Approach

This article presents a continuous-time agency model in thepresence of adverse selection and moral hazard with a risk-averseagent and a risk-neutral principal. Under the model setup, weshow that the optimal controls are constant over time, and thusthe optimal menu consists of contracts that are linear in thefinal outcome. We also show that when a moral hazard problemadds to an adverse selection problem, the monotonicity conditionwell known in the pure adverse selection literature needs tobe modified to ensure the incentive compatibility for informationrevelation. The model is applied to a few managerial compensationproblems involving managerial project selection and capitalbudgeting decisions. We argue that in the third-best world,the relationship between the volatility of the outcome and thesensitivity of the contract depends on interactions betweenthe managerial cost and the firm’s production functions.Contrary to conventional wisdom, sometimes the higher the volatility,the higher the sensitivity of the contract. The firm receivinggood news sometimes chooses safer projects or invests less thanit does with bad news. We also examine the effects of the observabilityof the volatility on corporate investment decisions.     

Pricing Double-Trigger Reinsurance Contracts: Financial Versus Actuarial Approach

This article discusses various approaches to pricing double‐trigger reinsurance contracts—a new type of contract that has emerged in the area of ‘‘alternative risk transfer.’’ The potential coverage from this type of contract depends on both underwriting and financial risk. We determine the reinsurer's reservation price if it wants to retain the firm's same safety level after signing the contract, in which case the contract typically must be backed by large amounts of equity capital (if equity capital is the risk management measure to be taken). We contrast the financial insurance pricing models with an actuarial pricing model that has as its objective no lessening of the reinsurance company's expected profits and no worsening of its safety level. We show that actuarial pricing can lead the reinsurer into a trap that results in the failure to close reinsurance contracts that would have a positive net present value because typical actuarial pricing dictates the type of risk management measure that must be taken, namely, the insertion of additional capital. Additionally, this type of pricing structure forces the reinsurance buyer to provide this safety capital as a debtholder. Finally, we discuss conditions leading to a market for double‐trigger reinsurance contracts.     

国内居民个人寿险产品购买行为的规范分析

今天,个人寿险产品的购买成为越来越普及的一种消费活动,按着消费者购买行为规范分析的框架,分析发现:个人寿险产品兼有选购品和非渴求商品的特征;其消费者的购买决策行为属于一种“高介入度-理性”的活动;收入、教育水平、年龄、家庭生命周期、职业、产品提供的利益、消费态度和顾客品牌忠诚度等成为影响消费者对其进行购买的主要因素。     

A Hidden Markov Approach to Disability Insurance

Point and interval estimation of future disability inception and recovery rates is predominantly carried out by combining generalized linear models with time series forecasting techniques into a two-step method involving parameter estimation from historical data and subsequent calibration of a time series model. This approach may lead to both conceptual and numerical problems since any time trend components of the model are incoherently treated as both model parameters and realizations of a stochastic process. We suggest that this general two-step approach can be improved in the following way: First, we assume a stochastic process form for the time trend component. The corresponding transition densities are then incorporated into the likelihood, and the model parameters are estimated using the Expectation-Maximization algorithm. We illustrate the modeling procedure by fitting the model to Swedish disability claims data.