CAT Bonds and Other Risk-Linked Securities: State of the Market and Recent Developments

This article reviews the current status of the market for catastrophic risk (CAT) bonds and other risk-linked securities. CAT bonds and other risk-linked securities are innovative financial vehicles that have an important role to play in financing mega-catastrophes and other types of losses. The vehicles are especially important because they access capital markets directly, exponentially expanding risk-bearing capacity beyond the limited capital held by insurers and reinsurers. The CAT bond market has been growing steadily, with record amounts of risk capital raised in 2005, 2006, and 2007. CAT bond premia relative to expected losses covered by the bonds have declined by more than one-third since 2001. CAT bonds now appear to be priced competitively with conventional catastrophe reinsurance and comparably rated corporate bonds. CAT bonds have grown to the extent that they now play a major role in completing the market for catastrophic-risk finance and are spreading to other lines such as automobile insurance, life insurance, and annuities. CAT bonds are not expected to replace reinsurance but to complement the reinsurance market by providing additional risk-bearing capacity. Other innovative financing mechanisms such as risk swaps, industry loss warranties, and sidecars also are expected to continue to play an important role in financing catastrophic risk.     

The Optimal Write-Down Coefficients in a Percentage for a Catastrophe Bond

Catastrophe bonds, also known as CAT bonds, are insurance-linked securities that help to transfer catastrophe risks from insurance industry to bond holders. When the aggregate catastrophe loss exceeds a specified amount by the maturity, the CAT bond is triggered and the future bond payments are reduced. This article first presents a general pricing formula for a CAT bond with coupon payments, which can be adapted to various assumptions for a catastrophe loss process. Next, it gives formulas for the optimal write-down coefficients in a percentage, implemented by Monte Carlo simulations, which maximize two measurements of risk reduction, hedge effectiveness rate (HER) and hedge effectiveness (HE), respectively, and examines how the optimal write-down coefficients in a percentage help reinsurance or insurance companies to mitigate extreme catastrophe losses. Last, it demonstrates how the number of coupon payments, loss share, retention level, strike price, maturity, frequency, and severity parameters of the catastrophe loss process and different interest rate models affect the optimal write-down coefficients in a percentage with numerical examples for illustrations.     

Traditional versus non-traditional reinsurance in a dynamic setting

We consider a stochastic risk reserve process whose risk exposure can be controlled dynamically by applying proportional reinsurance and by issuing CAT Bonds. The CAT Bond payments are only partly correlated with the insurers losses. The aim is to minimize the probability of ruin. Using a two-dimensional diffusion approximation we obtain a controlled diffusion problem which can be solved explicitly with the help of the HJB equation. We present some numerical results and discuss to which extend the proportional reinsurance can be replaced by issuing CAT Bonds.     

Catastrophe Bonds and Reinsurance: The Competitive Effect of Information-Insensitive Triggers

We identify a new benefit of index or parametric triggers. Asymmetric information between reinsurers on an insurer's risk affects competition in the reinsurance market: reinsurers are subject to adverse selection, since only high-risk insurers may find it optimal to change reinsurers. The result is high reinsurance premiums and cross-subsidization of high-risk insurers by low-risk insurers. A contract with a parametric or index trigger (such as a catastrophe bond) is insensitive to information asymmetry and therefore alters the equilibrium in the reinsurance market. Provided that basis risk is not too high, the introduction of contracts with parametric or index triggers provides low-risk insurers with an alternative to reinsurance contracts, and therefore leads to less cross-subsidization in the reinsurance market.     

Pricing catastrophe options with stochastic claim arrival intensity in claim time

We model claim arrival and loss uncertainties jointly in a doubly-binomial framework to price an Asian-style catastrophe (CAT) option with a non-traded underlying loss index using the no-arbitrage martingale pricing methodology. We span these uncertainties by benchmarking to the shadow price of a one-claim bond and the premium of a reinsurance contract. We implement a stochastic time change from calendar time to claim time to more efficiently price the CAT option as a random sum – a binomial sum of claim time binomial Asian option prices. This choice of the operational time dimension allows us to incorporate different patterns of catastrophe arrivals by adjusting the claim arrival probability. We demonstrate this versatility by incorporating a mean-reverting Ornstein-Uhlenbeck intensity arrival process. Simulation results verify our model predictions and demonstrate how the claim arrival probability varies with the expected claim arrival intensity.     

Optimal Reinsurance Design: A Mean-Variance Approach

In this article, we study an optimal reinsurance model from the perspective of an insurer who has a general mean-variance preference. In order to reduce ex post moral hazard, we assume that both parties in a reinsurance contract are obligated to pay more for a larger realization of loss. We further assume that the reinsurance premium is calculated only based on the mean and variance of the indemnity. This class of premium principles is quite general in the sense that it includes many widely used premium principles such as expected value, mean value, variance, and standard deviation principles. Moreover, to protect the insurer's profit, a lower bound is imposed on its expected return. We show that any admissible reinsurance policy is dominated by a change-loss reinsurance or a dual change-loss reinsurance, depending upon the coefficient of variation of the ceded loss. Further, the change-loss reinsurance is shown to be optimal if the premium loading increases in the actuarial value of the coverage; while it becomes decreasing, the optimal reinsurance policy is in the form of dual change loss. As a result, the quota-share reinsurance is always optimal for any variance-related reinsurance premium principle. Finally, some numerical examples are applied to illustrate the applicability of the theoretical results.     

Catastrophe Bonds,Reinsurance, and the Optimal Collateralization of Risk Transfer

Catastrophe bonds feature full collateralization of the underlying risk transfer and thus abandon the reinsurance principle of economizing on collateral through diversification of risk transfer. Our analysis demonstrates that this feature places limits on catastrophe bond penetration, even if the structure possesses frictional cost advantages over reinsurance. However, we also show that catastrophe bonds have important uses when buyers and reinsurers cannot contract over the division of assets in the event of insolvency and, more generally, cannot write contracts with a full menu of state‐contingent payments. In this environment, segregation of collateral—in the form of multiple reinsurance companies, as well as catastrophe bond vehicles—can ameliorate inefficiencies due to reinsurance contracting constraints by improving welfare for those exposed to default risk. Numerical simulation illustrates how catastrophe bonds improve efficiency in market niches with correlated risks, or with uneven exposure of buyers to reinsurer default.     

The market for catastrophe risk: a clinical examination

This paper examines the market for catastrophe event risk – i.e., financial claims that are linked to losses associated with natural hazards, such as hurricanes and earthquakes. Risk management theory suggests protection by insurers and other corporations against the largest cat events is most valuable. However, most insurers purchase relatively little cat reinsurance against large events, and premiums are high relative to expected losses. To understand why the theory fails, we examine transactions that look to capital markets, rather than traditional reinsurance markets, for risk-bearing capacity. We develop eight theoretical explanations and find the most compelling to be supply restrictions associated with capital market imperfections and market power exerted by traditional reinsurers.     

Valuing catastrophe derivatives under limited diversification: A stochastic dominance approach

We present a new approach to the pricing of catastrophe event (CAT) derivatives that does not assume a fully diversifiable event risk. Instead, we assume that the event occurrence and intensity affect the return of the market portfolio of an agent that trades in the event derivatives. Based on this approach, we derive values for a CAT option and a reinsurance contract on an insurer’s assets using recent results from the option pricing literature. We show that the assumption of unsystematic event risk seriously underprices the CAT option. Last, we present numerical results for our derivatives using real data from hurricane landings in Florida.     

Hard markets,hard times: On the inefficiency of the CAT bond market

This study explores the existence of inefficiencies in catastrophe (CAT) bond secondary markets by investigating the impact of sponsor characteristics on the CAT bond premium. We show that the CAT bond market does not satisfy the demand for catastrophe risk transfer efficiently by revealing a significant effect of sponsor-related factors on the CAT bond premium. This inefficiency is particularly surprising given that a CAT bond isolates the insured risk from other sponsor-related risks through a special purpose vehicle. Remarkably, this inefficiency is even present among non-indemnity CAT bonds, which determine the payout through a mechanism that is exogenous to the sponsor. Our findings also reveal that sponsor-related pricing inefficiencies vary over time and are more relevant during hard and neutral phases compared to soft market phases. Among the sponsor-related determinants of the CAT bond premium are the sponsor's tenure, market coverage, rating, credit default swap spread, and his ability to issue innovative “on the run” CAT bonds.     

Enhancing Insurer Value Using Reinsurance and Value-at-Risk Criterion

The quest for optimal reinsurance design has remained an interesting problem among insurers, reinsurers, and academicians. An appropriate use of reinsurance could reduce the underwriting risk of an insurer and thereby enhance its value. This paper complements the existing research on optimal reinsurance by proposing another model for the determination of the optimal reinsurance design. The problem is formulated as a constrained optimization problem with the objective of minimizing the value-at-risk of the net risk of the insurer while subjecting to a profitability constraint. The proposed optimal reinsurance model, therefore, has the advantage of exploiting the classical tradeoff between risk and reward. Under the additional assumptions that the reinsurance premium is determined by the expectation premium principle and the ceded loss function is confined to a class of increasing and convex functions, explicit solutions are derived. Depending on the risk measure's level of confidence, the safety loading for the reinsurance premium, and the expected profit guaranteed for the insurer, we establish conditions for the existence of reinsurance. When it is optimal to cede the insurer's risk, the optimal reinsurance design could be in the form of pure stop-loss reinsurance, quota-share reinsurance, or a combination of stop-loss and quota-share reinsurance.     

Reinsurance for Natural and Man-Made Catastrophes in the United States: Current State of the Market and Regulatory Reforms

U.S. insurers are heavily dependent on global reinsurance markets to enable them to provide adequate primary market insurance coverage. This article reviews the response of the world's reinsurance industry to recent mega-catastrophes and provides recommendations for regulatory reforms that would improve the efficiency of reinsurance markets. The article also considers the supply of insurance and reinsurance for terrorism and makes recommendations for joint public–private responses to insuring terrorism losses. The analysis shows that reinsurance markets responded efficiently to recent catastrophe losses and that substantial amounts of new capital enter the reinsurance industry very quickly following major catastrophic events. Considerable progress has been made in improving risk and exposure management, capital allocation, and rate of return targeting. Insurance price regulation for catastrophe-prone lines of business is a major source of inefficiency in insurance and reinsurance markets. Deregulation of insurance prices would improve the efficiency of insurance markets, enabling markets to deal more effectively with mega-catastrophes. The current inadequacy of the private terrorism reinsurance market suggests that the federal government may need to remain involved in this market, at least for the next several years.     

巨灾风险债券溢价之谜的行为金融学解释

作为一种新型金融工具,巨灾风险债券自发行以来所附带的风险收益就远高于同等级传统债券的收益.尽管均值方差分析方法已证明"溢价之谜"确实存在,但从传统理论角度出发的研究并不能充分解释巨灾风险债券高溢价的成因.本文尝试用行为金融理论分析以获得较合理的解释补充.通过探讨投资者的心理、行为因素在巨灾风险债券溢价之谜中所起的重要作用,得出结论:风险厌恶、固定教育成本、模糊厌恶和羊群效应等行为导致了溢价之谜的出现.这些影响因素的发现不仅是对国际巨灾风险债券市场中的高溢价现象进行解释的重要依据,同时也为我国科学发行巨灾风险债券提供了思路.     

A constraint-free approach to optimal reinsurance

Reinsurance is available for a reinsurance premium that is determined according to a convex premium principle H. The first insurer selects the reinsurance coverage that maximizes its expected utility. No conditions are imposed on the reinsurer's payment. The optimality condition involves the gradient of H. For several combinations of H and the first insurer's utility function, closed-form formulas for the optimal reinsurance are given. If H is a zero utility principle (for example, an exponential principle or an expectile principle), it is shown, by means of Borch's Theorem, that the optimal reinsurer's payment is a function of the total claim amount and that this function satisfies the so-called 1-Lipschitz condition. Frequently, authors impose these two conclusions as hypotheses at the outset.     

The Design of Private Reinsurance Contracts

This article examines the effect of asymmetric information on the trading of underwriting risk between insurers and reinsurers and how it is mitigated in a context of long-term relationships. It begins by explaining how information problems affect the efficiency of the allocation of risk between insurers and reinsurers and how long-term implicit contracts allow the inclusion of new information in the pricing of reinsurance coverage. A key feature of these relationships is the reliance on loss-contingent rebates and commissions in the pricing of reinsurance coverage. We argue that when information is revealed only over time, long-term implicit contracts between insurers and reinsurers allow the inclusion of new information into reinsurance pricing. Because of this feature, the allocation of risk between insurers and reinsurers is more efficient. Specifically, such arrangements lead to more reinsurance coverage, higher insurer profits, and lower expected distress in the industry. Journal of Economic Literature Classification Numbers: G22, G13, L15, D81.     

VAR and CTE Criteria for Optimal Quota-Share and Stop-Loss Reinsurance

Abstract

It is well known that reinsurance can be an effective risk management tool for an insurer to minimize its exposure to risk. In this paper we provide further analysis on two optimal reinsurance models recently proposed by Cai and Tan. These models have several appealing features including (1) practicality in that the models could be of interest to insurers and reinsurers, (2) simplicity in that optimal solutions can be derived in many cases, and (3) integration between banks and insurance companies in that the models exploit explicitly some of the popular risk measures such as value-at-risk and conditional tail expectation. The objective of the paper is to study and analyze the optimal reinsurance designs associated with two of the most common reinsurance contracts: the quota share and the stop loss. Furthermore, as many as 17 reinsurance premium principles are investigated. This paper also highlights the critical role of the reinsurance premium principles in the sense that, depending on the chosen principles, optimal quota-share and stop-loss reinsurance may or may not exist. For some cases we formally establish the sufficient and necessary (or just sufficient) conditions for the existence of the nontrivial optimal reinsurance. Numerical examples are presented to illustrate our results.     

The Impact of Institutional Ownership on the Reinsurance Decision

Risk management has a central role in corporate America. Insurance companies frequently manage risk by purchasing reinsurance because it reduces the downside risk (i.e., bankruptcy risk) of an insurer. Because reinsurance is costly, Mayers and Smith (1990, Journal of Business , 63: 19-40) argue that reinsurance purchases should be negatively associated with the diversification of the owners' portfolios. Further, institutional owners play a significant role in equity markets yet we know little about their effect on firm behavior. The purpose of this study is to examine empirically the influence of institutional ownership on reinsurance for a sample of widely held property-liability insurers. We hypothesize that insurers with higher levels of institutional ownership purchase less reinsurance. Using a sample of 45 publicly traded property-liability insurers from 1995 to 1997, we demonstrate that the utilization of reinsurance decreases as the level of institutional ownership increases. This suggests that the diversification of the owners' portfolios is a determinant of the insurers' reinsurance decisions.     

Reinsurance Brokers and Advice Quality: Is There a Need for Regulation?

Brokers play an increasing role in the distribution of reinsurance. In order to analyse reinsurance brokers' advice quality, we employ a model in which a monopoly broker advises cedents to buy a particular one out of similar reinsurance policies that cost the same but differ in details. The broker decides on how much to invest in his advice quality and on the price to charge for his service. We find that the broker's advice quality is generally lower and the price for his service higher than in the social optimum, even in the presence of a potential new entrant.     

Risk-sharing function in internal capital markets: Evidence from intragroup reinsurance activities

This study explicitly investigates the risk-sharing function of internal capital markets by analyzing intragroup reinsurance (a substitute for capital) activities in the United States' non-life insurance sector. We find supporting evidence that intragroup reinsurance participants are generally associated with smoother income flows, and such an income smoothing effect exists for both ceding and assuming firms. Further to prior studies, we find that internal reinsurance ceded exerts both direct and indirect effects on premiums growth in the aftermath of the financial crisis in 2007 and 2008. In addition to direct capacity support, the reduction in income volatility is another channel through which intragroup reinsurance enhances ceding firms' premiums growth. In the presence of market turmoil, the risk-sharing function can lower member firms' insolvency risk and thus enable them to pursue business growth.     

A unifying approach to risk-measure-based optimal reinsurance problems with practical constraints

The design of optimal reinsurance treaties in the presence of multifarious practical constraints is a substantive but underdeveloped topic in modern risk management. To examine the influence of these constraints on the contract design systematically, this article formulates a generic constrained reinsurance problem where the objective and constraint functions take the form of Lebesgue integrals whose integrands involve the unit-valued derivative of the ceded loss function to be chosen. Such a formulation provides a unifying framework to tackle a wide body of existing and novel distortion-risk-measure-based optimal reinsurance problems with constraints that reflect diverse practical considerations. Prominent examples include insurers’ budgetary, regulatory and reinsurers’ participation constraints. An elementary and intuitive solution scheme based on an extension of the cost–benefit technique in Cheung and Lo [Cheung, K.C. & Lo, A. (2015, in press). Characterizations of optimal reinsurance treaties: a cost–benefit approach Scandinavian Actuarial Journal. doi:10.1080/03461238.2015.1054303.] is proposed and illuminated by analytically identifying the optimal risk-sharing schemes in several concrete optimal reinsurance models of practical interest. Particular emphasis is placed on the economic implications of the above constraints in terms of stimulating or curtailing the demand for reinsurance, and how these constraints serve to reconcile the possibly conflicting objectives of different parties.