Empirical Risk Analysis of Pension Insurance: The Case of Germany

The book reserve system is the most widespread method of financing occupational pension plans in Germany. The pension liabilities are mutually insured by the Pensions-Sicherungs-Verein VVaG (PSVaG) against bankruptcy. The PSVaG recently stated that the insurance system needed to be reformed. In the future, risk-adjusted premiums as foreseen for the newly established Pension Protection Fund in the United Kingdom could become feasible. We perform a credit portfolio analysis to determine the risk profile of the PSVaG. The magnitude of a tail risk event suggests that under the current financing system it can only be smoothed out over decades. Under an expected loss pricing plan insurance premiums would vary greatly. In a marginal risk contribution approach the variation of the premiums would be less pronounced.     

The Allocation of Governmental Regulatory Authority: Federalism and the Case of Insurance Regulation

We investigate the incentives states have to provide insurance regulatory services in an efficient manner. Regulation of the insurance industry in the United States is unique, as it is conducted primarily at the state level whereas the majority of insurance sales are interstate. Consistent with predictions from the federalism literature, we find evidence of trans‐state externalities, as states with small domestic insurance markets are less efficient producers of insurance regulation and appear to allow states that choose to expend the greatest resources to regulate for them. In addition, states with more profitable domestic insurers are shown to export greater levels of regulation, suggesting extraterritorial regulation may erect modest barriers to entry. We find evidence of increasing economies of scale in the production of insurance regulation after controlling for these regulatory externalities.     

存款保险定价研究:期权定价法和预期损失定价法的进展

合理的存款保险定价可有效减少道德风险和逆向选择问题。本文梳理了国内外关于存款保险定价的两种主要方法——期权定价法和预期损失定价法及其最新发展情况。期权定价法的核心是将存款保险看作存款保险机构以银行资产为标的发行的一份看跌期权,之后学者从股利发放、监管宽容、系统性风险等多个角度进行拓展。预期损失定价法主要根据边际损失与边际保费收入相等来进行保费厘定,以探寻如何通过更科学的方法更精确地测量银行的预期损失。此外,本文讨论了存款保险定价方法对我国的启示。     

Cybersecurity Insurance: Modeling and Pricing

Cybersecurity risk has attracted considerable attention in recent decades. However, the modeling of cybersecurity risk is still in its infancy, mainly because of its unique characteristics. In this study, we develop a framework for modeling and pricing cybersecurity risk. The proposed model consists of three components: the epidemic model, loss function, and premium strategy. We study the dynamic upper bounds for the infection probabilities based on both Markov and non-Markov models. A simulation approach is proposed to compute the premium for cybersecurity risk for practical use. The effects of different infection distributions and dependence among infection processes on the losses are also studied.     

The Effects of Macroeconomic Factors on Pricing Mortgage Insurance Contracts

Numerous empirical studies, including Abraham and Hendershott (1996) , Muellbauer and Murphy (1997) , Leung (2004) , and Oikarinen (2009) , have identified a significant relationship between housing prices and macroeconomic factors. Using a linear regression on the comovement of macroeconomic factors and housing prices, this article employs an option‐pricing framework to price and hedge the fair premia of mortgage insurance (MI). Our model provides improved performance in terms of MI premium pricing, especially during periods that are characterized by high housing prices. Ignoring the impacts of macroeconomic factors on housing prices will lead to an underestimation of MI premia.     

Market Pricing of Deposit Insurance

We provide an approach to the market valuation of deposit insurance that is based on reduced-form methods for the pricing of fixed-income securities under default risk. By reference to bank debt prices as well as qualitative-response models of the probability of bank failure, we suggest how a risk-neutral valuation model for deposit insurance can be applied both to the calculation of fair-market deposit insurance premia and to the valuation of long-term claims against the insurer.     

The Liability Regime of Insurance Pools and Its Impact on Pricing

This work formally derives fairly priced premiums for the policyholder of an insurance pool and the risk-adequate equity contributions of the pool insurers’ equity holders in a contingent claims approach. The approach distinguishes between two liability regimes: joint liability and several liability. These regimes regulate the pool’s indemnification when one or more of the pool insurers cannot meet their full obligations because of insolvency. Joint liability is deduced to be the preferable regime for the policyholder in cost-savings terms if corporate income taxation is introduced as a market friction. This regime advantage vanishes if the pool insurers’ asset correlation is substantial or if their risk sharing becomes unbalanced. Additionally, we address risk-shifting problems and their regime-dependent effects on both stakeholder groups.     

基于DFA方法的中国洪水保险定价研究

对洪水保险进行精确有效的定价十分困难.动态财务分析模型(DFA)能够有效的将多种因素综合在一起进行分析,弥补了以往洪水保险定价方法以单一时点统计数据作为定价基础的缺陷;再保险安排是洪水保险计划中的一个重要组成部分,购买60%比例再保险是最适当的;购买再保险能够极大的降低洪水保险计划的破产概率.     

产险定价模型中的周期性比较

产险市场具有周期性,表现为"硬"市场与"软"市场的交替出现.这种周期性反映在保险价格、承保利润的变化上,保险价格变化与周期性之间存在内在联系.基于承保周期是保险定价行为所引发的假设出发,本文列举当前六个保险定价模型,对模型中所暗含的周期性因素进行比较,考察模型中所隐含的长期与短期因素影响作用的差别.     

Pricing Risk-Adjusted Deposit Insurance: An Option-Based Model

This paper presents a methodology for arriving at empirical estimates of deposit insurance premiums from market data by using isomorphic relationships between equity and a call option, and insurance and a put option. The data utilizes the market value of equity to solve for the asset value and its volatility. Market perceptions of FDIC bailout policies are explicitly modeled so as to eliminate the bias in inverted values of assets and their volatility. Sensitivity analyses are performed to show that rank orderings based on premiums are robust to changes in specification, thus facilitating allocation of aggregate premium across banks.     

Asset Pricing of Insurance Loss Liabilities: Some Examples

I construct examples of valuing insurance loss liabilities with asset pricing models, comparing the Rubinstein‐Leland model with the better‐known CAPM. The two models give different values only if the loss payment is asymmetric and correlated with the market portfolio, conditions which can result from the nature of the underlying loss or from the impact of insolvency on the insurer's payment.
In examples where insolvency is not possible and there is no liquidity cost of raising new equity on short notice, the value of a loss liability is equal to the value of the underlying loss, i.e., of the promised coverage, and depends neither on (1) the size of the loss pool; nor on (2) the unsystematic risk of the insurer's liabilities; nor on (3) the composition of an insurer's investment portfolio; nor on (4) the amount of insurer equity.
These factors do affect the value of a loss liability in examples where insolvency and liquidity costs are considered. Other things equal, if a factor increases the likelihood of insolvency, the fair value of a loss liability is lower because the insured is partially self‐insuring; but the liquidity cost of maintaining solvency by raising new equity on short notice is higher, implying a higher fair value of the loss liability.     

Fuzzy Financial Pricing of Property-Liability Insurance

Abstract

This paper uses fuzzy set theory (FST) to solve a problem in actuarial science, the financial pricing of property-liability insurance contracts. The fundamental concept of FST is the alternative formalization of membership in a set to include the degree or strength of membership. FST provides consistent mathematical rules for incorporating vague, subjective, or judgmental information into complex decision processes. It is potentially important in insurance pricing because much of the information about cash flows, future economic conditions, risk premiums, and other factors affecting the pricing decision is subjective and thus difficult to quantify by using conventional methods. To illustrate the use of FST, we “fuzzify” a well-known insurance financial pricing model, provide numerical examples of fuzzy pricing, and propose rules for project decision-making using FST. The results indicate that FST can lead to significantly different decisions than the conventional approach.     

注册会计师职业责任保险合约的差异化定价与审计质量效应

注册会计师职业责任保险作为会计师事务所的一项风险分散机制,近年来受到我国政府主管部门和公共会计行业组织的关注.一方面,事务所购买注责险可能使审计人员的尽责程度下降,不利于审计质量的维护;另一方面,保险公司作为风险被转移方,有动机对高风险事务所加以约束,以避免审计失败对自身利益造成损失.基于近年来我国证券业务会计师事务所的注责险合约数据,我们发现保险公司对中小型证券所购买注责险收取了显著更高的保费,且更不倾向于与其签订特殊赔偿条款.双重差分模型结果显示,中小型证券所购买注责险后,审计调整(尤其是调减利润的审计调整)幅度显著提高.这些证据支持保险合约对高风险审计中介的治理功能.     

The Impact of Introducing Insurance Guaranty Schemes on Pricing and Capital Structure

The introduction of an insurance guaranty scheme can have significant influence on the pricing and capital structures in a competitive market. The aim of this article is to study this effect on competitive equity–premium combinations while considering a framework with policyholders and equity holders where guaranty fund charges are volume‐based, as levied in existing schemes. Several settings with regard to the origin of the fund contributions are assessed and the immediate effects on the incentives of the policyholders and equity holders are analyzed through a one‐period contingent claim approach. One result is that introducing a guaranty scheme in a market with competitive conditions entails a shift of equity capital towards minimum solvency requirements. Hence, adverse incentives may arise with regard to the overall security level of the industry.     

Equilibrium Pricing of General Insurance Policies

Abstract

A model is developed for determining the price of general insurance policies in a competitive, noncooperative market. This model extends previous single-optimizer pricing models by supposing that each participant chooses an optimal pricing strategy. Specifically, prices are determined by finding a Nash equilibrium of an N-player differential game. In the game, a demand law describes the relationship between policy sales and premium, and each insurer aims to maximize its (expected) utility of wealth at the end of the planning horizon. Two features of the model are investigated in detail: the effect of limited total demand for policies, and the uncertainty in the calculation of the breakeven (or cost price) of an insurance policy.

It is found that if the demand for policies is unlimited, then the equilibrium pricing strategy is identical for all insurers, and it can be found analytically for particular model parameterizations. However, if the demand for policies is limited, then, for entrants to a new line of business, there are additional asymmetric Nash equilibria with insurers alternating between maximal and minimal selling. Consequently it is proposed that the actuarial cycle is a result of price competition, limited demand, and entry of new insurers into the market. If the breakeven premium is highly volatile, then the symmetric equilibrium premium loading tends to a constant, and it is suggested that this will dampen the oscillatory pricing of new entrants.     

Corporate Insurance Strategy: The Case of British Petroleum

The authors provide a fundamental rethinking of how corporations should evaluate various kinds of risks and risk management solutions—a rethinking that leads to a major shift in British Petroleum's approach to insuring property and casualty losses, product liability suits, and other insurable events. Conventional corporate practice—and until the early 1990s (when this article was written) the longstanding policy of BP and most large oil companies—was to insure against large losses while self‐insuring against smaller ones. In this article, the authors explain why BP has chosen to go against the conventional wisdom and instead buy insurance for mainly smaller losses while self‐insuring larger ones. The BP decision came down to factors affecting the market supply of insurance as well as the corporate demand for it. On the demand side, the authors demonstrate that the primary source of demand for insurance by large public companies is not, as standard insurance textbooks assume, to transfer risk away from the corporation's owners. Because corporate stockholders and bondholders effectively manage the effects of such risks by diversifying their own portfolios, the corporate demand for insurance in BP's case stems from the insurers' comparative advantage in evaluating and monitoring BP's smaller risks and in processing claims. On the supply side, the authors explain why the capacity of insurance companies and markets to underwrite very large or highly specialized exposures—when compared to the industry expertise and financial resources of companies like BP—is quite limited, and likely to remain so. Since premiums would be experience‐rated and prior years' losses simply rolled into the following years' premiums, there would be no effective transfer of risk, and so no gain to BP from buying insurance.