The Dynamics of Insurance Prices

We develop a continuous-time general-equilibrium model to rationalise the dynamics of insurance prices in a competitive insurance market with financial frictions. Insurance companies choose underwriting and financing policies to maximise shareholder value. The equilibrium price dynamics are explicit, which allows simple numerical simulations and generates testable implications. In particular, we find that the equilibrium price of insurance is (weakly) predictable and the insurance sector always realises positive expected profits. Moreover, rather than true cycles, insurance prices exhibit asymmetric reversals caused by the reflection of the aggregate capacity process at the dividend and recapitalisation boundaries.     

Nonlinear Cointegration Relationships Between Non-Life Insurance Premiums and Financial Markets

The aim of this article is to study the adjustment dynamics of the non-life insurance premium (NLIP) and test its dependence to the financial markets in five countries (Canada, France, Japan, the United Kingdom, and the United States). First, we justify the linkage between the insurance and the financial markets by the underwriting cycle theory and financial models of insurance pricing. Second, we examine the relationship between the NLIP, the interest rate, and the stock price using the recent developments of nonlinear econometrics. We use threshold cointegration models: the switching transition error correction models (STECM). We show that STECM perform better than a linear error correction model (LECM) to reproduce the NLIP dynamics. Our empirical results show that the adjustment of the NLIP in France, Japan, and the United States is rather discontinuous, asymmetrical, and nonlinear. Moreover, we suggest a strong evidence of significant linkages between insurance and financial markets, show two regimes for the NLIP, and find that the NLIP adjustment toward equilibrium is time varying with a convergence speed that varies according to the insurance disequilibrium size.     

Portfolio Insurance Strategies when Hedging Affects Share Prices

Option-based portfolio insurance can result in coordinated buying and selling, which destabilizes markets such that hedgers fail to achieve their objective. Gennotte and Leland (1990) show portfolio insurance strategies can have an impact on price movements. Ramanlal and Mann (1996) show how price movements, in turn, can alter hedging strategies. In this paper, we combine these separate effects and develop an equilibrium, executable hedging strategy. This hedging strategy requires less rebalancing than traditional portfolio insurance; more important, it achieves downside protection with a less destabilizing impact on security prices.     

Background Risk and the Performance of Insurance Markets under Adverse Selection

Background risk can influence the performance of insurance markets that must deal with adverse selection when applicants are risk vulnerable, since they are more averse to bearing the insurable risk as a result of their exposures to background risk. We show that background risk always results in a lower deductible for the incentive constrained contract, and that a broader range of markets attains the stable sequential equilibrium cross-subsidized pair of separating contracts. We conclude that background risk always improves the performance of markets for coverage against (insurable) foreground risks that must deal with adverse selection. We also find, however, that these improvements are never sufficient to offset the cost to insureds of bearing the background risk.     

Home Equity Insurance

Home equity insurance policies—policies insuring homeowners against declines in the prices of their homes—would bear some resemblance both to ordinary insurance and to financial hedging vehicles. A menu of choices for the design of such policies is presented here, and conceptual issues are discussed. Choices include pass-through futures and options, in which the insurance company in effect serves as a retailer to homeowners of short positions in real estate futures markets or of put options on real estate indices. Another choice is a life-event-triggered insurance policy, in which the homeowner pays regular fixed insurance premia and is entitled to a claim if both a sufficient decline in the real estate price index and a specified life event (such as a move beyond a certain geographical distance) occur. Pricing of the premia to cover loss experience is derived, and tables of break-even policy premia are shown, based on estimated models of Los Angeles housing prices from 1971 to 1994.     

Insurance Derivatives: A New Asset Class for the Capital Markets and a New Hedging Tool for the Insurance Industry

The number and severity of natural catastrophes has increased dramatically over the last decade. As a result, there is now a shortage of capacity in the property catastrophe insurance industry in the U.S. This article discusses how insurance derivatives, particularly the Chicago Board of Trade's catastrophe options contracts, represent a possible solution to this problem. These new financial instruments enable the capital markets to provide the insurance industry with the reinsurance capacity it needs. The capital markets are willing to perform this role because of the new asset class characteristics of securitized insurance risk: positive excess returns and diversification benefits.
The article also demonstrates how insurance companies can use insurance derivatives such as catastrophe options and catastrophe-linked bonds as effective, low-cost risk management tools. In reviewing the performance of the catastrophe contracts to date, the authors report promising signs of growth and liquidity in these markets.     

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.     

Perspectives of Risk Sharing

In this paper we present an overview of the standard risk sharing model of insurance. We discuss and characterize a competitive equilibrium, Pareto optimality, and representative agent pricing, including its implications for insurance premiums. We only touch upon the existence problem of a competitive equilibrium, primarily by presenting several examples. Risk tolerance and aggregation is the subject of one section. Risk adjustment of the probability measure is one topic, as well as the insurance version of the capital asset pricing model. The competitive paradigm may be a little demanding in practice, so we alternatively present a game theoretic view of risk sharing, where solutions end up in the core. Properly interpreted, this may give rise to a range of prices of each risk, often visualized in practice by an ask price and a bid price. The nice aspect of this is that these price ranges can be explained by "first principles", not relying on transaction costs or other frictions. We also include a short discussion of moral hazard in risk sharing between an insurer and a prospective insurance buyer. We end the paper by indicating the implications of our results for a pure stock market. In particular we find it advantageous to discuss the concepts of incomplete markets in this general setting, where it is possible to use results for closed, convex subspaces of an L 2 -space to discuss optimal risk allocation problems in incomplete financial markets.     

Convergence of Insurance and Financial Markets: Hybrid and Securitized Risk-Transfer Solutions

One of the most significant economic developments of the past decade has been the convergence of the financial services industry, particularly the capital markets and (re)insurance sectors. Convergence has been driven by the increase in the frequency and severity of catastrophic risk, market inefficiencies created by (re)insurance underwriting cycles, advances in computing and communications technologies, the emergence of enterprise risk management, and other factors. These developments have led to the development of hybrid insurance/financial instruments that blend elements of financial contracts with traditional reinsurance as well as new financial instruments patterned on asset-backed securities, futures, and options that provide direct access to capital markets. This article provides a survey and overview of the hybrid and pure financial markets instruments and provides new information on the pricing and returns on contracts such as industry loss warranties and Cat bonds.     

Arbitrage and Viability in Insurance Markets

Insurance markets are subject to transaction costs and constraints on portfolio holdings. Therefore, unlike the frictionless asset markets case, viability is not equivalent to absence of arbitrage possibilities. We use the concept of unbounded arbitrage to characterize viable prices on a complete and an incomplete insurance market. In the complete market, there is an insurance contract for every possible event. In the incomplete market, risk can be insured through proportional and excess of loss like insurance contracts. We show how the the structure of viable prices is affected by the portfolio constraints, the transaction costs, and the structure of marketed contracts.     

Effects of Competition on Insurance Contract Formation

For an insurance transaction between a single risk-averse buyer and single risk-neutral seller with positive transaction costs, it is well known that the buyer will prefer a policy contract with an ordinary deductible. More detailed results demonstrate the Pareto optimality of an insurance contract characterized by a deductible (followed by coinsurance) for a single risk-averse buyer and single risk-averse seller. In the present work, we employ a market-game model to solve for the equilibrium insurance contract. This formulation, which approximates the behavior of excess property insurance and property catastrophe reinsurance markets, reveals that the equilibrium policy is described by full insurance up to a given policy limit, with no deductible or coinsurance. Our analysis shows further that this solution persists regardless of the numbers of buyers and sellers in the market, and in particular that the market-game equilibrium does not converge to a Pareto-optimal result because of boundary constraints on the number of sellers. Finally, we test our price-formation mechanism against an important generalization, and find that the policy-limit contract persists.     

逆向选择、系统性风险与政策性农业保险可持续发展

本文介绍了政策性农业保险在发达国家的成功经验和我国的发展状况,对政府补贴情境下的农业保险市场均衡模型进行了研究,并得到了市场均衡条件下的免赔率方程。利用上述市场均衡模型,针对农业保险市场普遍存在的系统性风险、逆向选择和道德风险问题,从统一的政策性农业保险公司、多层次再保险体系建设等方面阐述了政策性农业保险体系的可持续发展策略。     

The Shareholder Wealth Effects of Insurance Securitization: Preliminary Evidence from the Catastrophe Bond Market

Insurance securitization has long been hailed as an important tool to increase the underwriting capacity for companies exposed to catastrophe-related risks. However, global volumes of insurance securitization have remained surprisingly low to date which raises questions over its benefits. In this paper, we examine changes in the market value of insurance and reinsurance firms which announce their engagement in insurance securitization by issuing catastrophe (Cat) bonds. Consistent with the hitherto underwhelming contribution of Cat bonds to global catastrophe coverage, we do not find evidence that Cat bonds lead to strong wealth gains for shareholders in the issuing firm. More importantly, we report large variations in the distribution of wealth effects in response to the issue announcement. We show that the wealth effects for shareholders in firms which issue Cat bonds appear to be driven by explanations according to which Cat bonds offer cost savings relative to other forms of catastrophe risk management (and less by the potential of Cat bonds to hedge catastrophe risk). Thus, abnormal returns are particularly large for issues by firms which face low levels of loss uncertainty (which reduces the information acquisition costs in financial markets) as well as for issues during periods when prices for catastrophe coverage (including Cat bonds) are low.     

Credit Derivatives and the Default Risk of Large Complex Financial Institutions

This paper proposes and implements a multivariate model of the coevolution of the first and second moments of two broad credit default swap indices and the equity prices of sixteen large complex financial institutions. We use this empirical model to build a bank default risk model, in the vein of the classic Merton-type, which utilises a multi-equation framework to model forward-looking measures of market and credit risk using the credit default swap (CDS) index market as a measure of the conditions of the global credit environment. In the first step, we estimate the dynamic correlations and volatilities describing the evolution of the CDS indices and the banks’ equity prices and then impute the implied assets and their volatilities conditional on the evolution and volatility of equity. In the second step, we show that there is a substantial ‘asset shortfall’ and that substantial capital injections and/or asset insurance are required to restore the stability of our sample institutions to an acceptable level following large shocks to the aggregate level of credit risk in financial markets.     

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.     

Mandatory Pensions and the Intensity of Adverse Selection in Life Insurance Markets

This article examines the impact of varying mandatory pensions on saving, life insurance, and annuity markets in an adverse selection economy. Under reasonable restrictions, we find unambiguous effects on market size, participation rates, and equilibrium prices. The degree of adverse selection, whether a market is active or inactive, and social welfare are analyzed.     

Market Price of Insurance Risk Implied by Catastrophe Derivatives

Abstract

Insurance derivatives facilitate the trading of insurance risks on capital markets, such as catastrophe derivatives that were traded on the Chicago Board of Trade. Simultaneously, insurance risks are traded through reinsurance portfolios. In this paper we make inferences about the market price of risk implied by the information embedded in the prices of these two assets.     

Limits to arbitrage and hedging: Evidence from commodity markets

We build an equilibrium model of commodity markets in which speculators are capital constrained, and commodity producers have hedging demands for commodity futures. Increases in producers' hedging demand or speculators' capital constraints increase hedging costs via price-pressure on futures. These in turn affect producers' equilibrium hedging and supply decision inducing a link between a financial friction in the futures market and the commodity spot prices. Consistent with the model, measures of producers' propensity to hedge forecasts futures returns and spot prices in oil and gas market data from 1979 to 2010. The component of the commodity futures risk premium associated with producer hedging demand rises when speculative activity reduces. We conclude that limits to financial arbitrage generate limits to hedging by producers, and affect equilibrium commodity supply and prices.     

Competition and Insurance Twenty Years Later

We are honored to address the European Group of Risk and Insurance Economists and will take the opportunity to make some reflections on the rather uneasy relationship between insurance and competition. Economists generally prescribe competition as a solution for markets that do not work well. Competition allocates resources efficiently and encourages innovation and attention to what customers want. Insurance markets differ from most other markets because in insurance markets competition can destroy the market rather than make it work better. One of the dimensions along which insurance companies compete is underwriting—trying to ensure that the risks covered are “good” risks or that if a high risk is insured, the premium charged is at least commensurate with the potential cost. The resulting partitioning of risk limits the amount of insurance that potential insurance customers can buy. In the extreme case, such competitive behavior will destroy the insurance market altogether. A simple model illustrates.     

The no-arbitrage condition and financial markets with transaction costs and heterogeneous information: The bid-ask spread

This paper investigates the implications of the no-arbitrage (NA) condition in markets with transaction costs and heterogeneous information. Dermody and Prisman (1993) showed that, in financial markets with increasing marginal transaction costs, the NA condition is equivalent to the existence of a valuation operator. They explore the exact dependence of this operator on the structure of transaction costs. They show that equilibrium prices in the “corresponding” perfect markets plus a certain factor determine the valuation operator in markets with increasing marginal transaction costs. This paper emphasizes that their result is applicable to financial markets with decreasing marginal transaction costs. Furthermore, this paper shows that, in financial markets with transaction costs and heterogeneous information, the NA condition imposes a constraint on the bid-ask spread.