Andreas Richter

Moral Hazard, Basis Risk, and Gap Insurance

This article addresses the trade-off between moral hazard and basis risk. A decision maker, e.g., a primary insurer, is considered who can purchase an index hedge and a (re)insurance contract that covers the gap between actual losses and the index-linked payout, or part of this gap. The results suggest that combining insurance with an index hedge may extend the possibility set and by that means lead to efficiency gains. Naturally, the results depend heavily on the transaction costs associated with both instruments. In particular, the authors show that if the index product is without transaction costs, at least some index-linked coverage is always purchased, so long as there is positive correlation between the index and the actual losses. So under these circumstances, there is in any case a benefit from the availability of index products. Furthermore, it is shown that the index hedge would always be supplemented by a positive amount of gap insurance.

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

This paper 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% 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. Our study demonstrates that regulators should be very careful in deciding which design of a distribution mechanism is to be enforced. Within our model framework, 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. Requiring “strong” guarantees puts companies at a significant competitive disad¬vantage relative to insurers which are subject to regulation that only requires the third type of surplus distribution mechanism. This is particularly true, if annual minimum participation in the insurer’s investment returns is mandatory for long term contracts.

The Design of Liability Rules for Highly Risky Activities - Is Strict Liability Superior When Risk Allocation Matters?

Strict liability is widely seen as the most suitable way to govern highly risky activities, such as environmentally dangerous production or genetic engineering. The reason which is usually given for applying strict liability to these areas, is that not only efficient care is supposed to be induced but also an efficient level of the risky activity itself. It is argued that, in case of no market relationship between injurers and victims, this could only be achieved through strict liability but not via the negligence rule. In this paper, we show that the superiority of strict liability does no longer persist in a world of risk averse parties. Our results suggest that in terms of risk allocation the negligence rule should be preferred for abnormally risky activities, if insurance markets are imperfect. The reason is that highly risky activities typically affect a large number of individuals, such that strict liability implies a quite unfavorable allocation of risk. Therefore, the negligence rule turns out to be superior, if a market relationship between the parties exists, since it incurs less cost of risk. If there is no market relationship between injurer and victims, no clear result can be derived. The paper concludes with some remarks on the usefulness of upper bounds to an injurer’s liability as well as regulations that exclude liability for “unforeseeable” losses. We argue that this kind of supplement to a strict liability rule can improve efficiency.

Mortality-Indexed Annuities - Managing Longevity Risk Via Product Design

Abstract Longevity risk has become a major challenge for governments, individuals, and annuity providers in most countries. In its aggregate form, the systematic risk of changes to general mortality patterns, it has the potential for causing large cumulative losses for insurers. Since obvious risk management tools, such as (re)insurance or hedging, are less suited for managing an annuity provider’s exposure to this risk, we propose a type of life annuity with benefits contingent on actual mortality experience. Similar adaptations to conventional product design exist with investment-linked annuities, and a role model for long-term contracts contingent on actual cost experience can be found in German private health insurance. By effectively sharing systematic longevity risk with policyholders, insurers may avoid cumulative losses. Policyholders also gain in comparison with a comparable conventional annuity product: Using a Monte Carlo simulation, we identify a significant upside potential for policyholders while downside risk is limited.

Optimales Vertragsdesign bei moralischem Risiko in der Rückversicherung

ZusammenfassungDieser Beitrag befasst sich mit der geeigneten Ausgestaltung von Risikoteilungsregeln in der Rückversicherung bei asymmetrischer Information hinsichtlich des Verhaltens des Erstversicherers. Letzterer hat üblicherweise massive unbeobachtbare Spielräume z. B. bei der Auswahl der von ihm versicherten Risiken, so dass ein typisches Problem moralischen Risikos entsteht. Es wird hier gezeigt, dass die Existenz von moralischem Risiko entscheidende Auswirkungen auf die Eigenschaften des im Rückversicherungsvertrag zu spezifizierenden Zusammenhangs zwischen Schaden und Entschädigung, der so genannten Rückversicherungsform, besitzt. Insbesondere stellt sich heraus, dass bei unbeobachtbarem Einfluss des Erstversicherers auf die Wahrscheinlichkeitsverteilung des Umfangs möglicher Ansprüche eine Pareto-optimale Entschädigungsfunktion an jeder Stelle flacher verläuft als bei vollständiger Information. Der Erstversicherer wird also an jeder marginalen Erhöhung des Schadens stärker beteiligt. Eine betragsmäßig fixierte Selbstbeteiligung in der Form einer so genannten Abzugsfranchise, die in der Literatur häufig als Lösungsansatz vorgeschlagen wird, erweist sich hingegen in diesem Zusammenhang nicht als geeignetes Instrument.AbstractThis paper addresses the optimal design of risk sharing arrangements in reinsurance contracts with asymmetric information concerning the primary insurer’s behavior. The latter usually has significant unobservable discretions, for instance with respect to risk selection, implying a moral hazard problem. We show that the existence of moral hazard strongly affects the characteristics of the reinsurance indemnification rule, i. e. the connection between the level of losses and the indemnity, which is specified in the contract. For this analysis, a standard model framework from the theory of optimal reinsurance with perfect information is modified by the assumption that the primary insurer has unobservable control of the probability distribution of the extent of losses. In particular, the solution indicates that for this situation, a Pareto-optimal indemnity rule is less steep, and therefore the primary insurer’s share in a marginal increase of the loss is greater, compared to the case of complete information. A deductible, however, turns out not to be a suitable approach in this context.

Tax arbitrage in the German insurance market

SummaryIn this paper we analyze the attractiveness of a so called “mortality swap”, which combines an immediate annuity and a whole life insurance contract, in the German insurance market. The analysis follows a methodology introduced by Charupat and Milevsky (2001). Using theoretical products based on actuarially fair calculation, we find that depending on the level of interest rates there exist significant arbitrage opportunities in particular for elderly and high income people which can mainly be explained by an inadequate and unsatisfactory tax legislation. Empirical results based on products offered in the market confirm these findings.ZusammenfassungIn der vorliegenden Arbeit analysieren wir die Attraktivität eines so genannten “mortality-swap”, d. h. einer Kombination einer Todesfallversicherung mit einer sofort beginnenden Leibrente. Die Analyse folgt einer Methodik, die von Charupat und Milevsky (2001) eingeführt wurde. Mittels theoretischer Produkte, die auf aktuariellen Kalkulationsgrundlagen basieren, finden wir -abhängig vom aktuellen Zinsniveau - signifikante Arbitragemöglichkeiten, vor allem für ältere und besser verdienende Versicherungsnehmer. Die Arbitragemöglichkeiten resultieren in erster Linie aus unzulänglichen Steuergesetzen. Empirische Analysen auf Basis von Produktangeboten am deutschen Markt bekräftigen diese Ergebnisse.

Intermediation and (Mis‐)Matching in Insurance Markets - Who Should Pay the Insurance Broker?

This article addresses the role of independent insurance intermediaries in markets where matching is important. We compare fee-based and commission-based compensation systems and show that they are payoff equivalent if the intermediary is completely honest. Allowing for strategic behavior, we discuss the impact of remuneration on the quality of advice. The possibility of mismatching gives the intermediary substantial market power, which will not translate into mismatching if consumers are rational. Furthermore, we offer a rationale for the use of contingent commissions and address whether or not the ban of any commission payments is an appropriate market intervention.

Sovereign Cat Bonds and Infrastructure Project Financing

We examine the opportunities for using catastrophe-linked securities (or equivalent forms of nondebt contingent capital) to reduce the total costs of funding infrastructure projects in emerging economies. Our objective is to elaborate on methods to reduce the necessity for unanticipated (emergency) project funding immediately after a natural disaster. We also place the existing explanations of sovereign-level contingent capital into a catastrophic risk management framework. In doing so, we address the following questions. (1) Why might catastrophe-linked securities be useful to a sovereign nation, over and above their usefulness for insurers and reinsurers? (2) Why are such financial instruments ideally suited for protecting infrastructure projects in emerging economies, under third-party sponsorship, from low-probability, high-consequence events that occur as a result of natural disasters? (3) How can the willingness to pay of a sovereign government in an emerging economy (or its external project sponsor), who values timely completion of infrastructure projects, for such instruments be calculated? To supplement our treatment of these questions, we use a multilayer spreadsheet-based model (in Microsoft Excel format) to calculate the overall cost reductions possible through the judicious use of catastrophe-based financial tools. We also report on numerical comparative statics on the value of contingent-capital financing to avoid project disruption based on varying costs of capital, probability and consequences of disasters, the feasibility of strategies for mid-stage project abandonment, and the timing of capital commitments to the infrastructure investment. We use these results to identify high-priority applications of catastrophe-linked securities so that maximal protection can be realized if the total number of catastrophe instruments is initially limited. The article concludes with potential extensions to our model and opportunities for future research.

Endogenous information, adverse selection, and prevention: Implications for genetic testing policy

We examine public policy toward the use of genetic information by insurers. Individuals engage in unobservable primary prevention and have access to different prevention technologies. Thus, insurance markets are affected by moral hazard and adverse selection. Individuals can choose to take a genetic test to acquire information about their prevention technology. Information has positive decision-making value, that is, individuals may adjust their behavior based on the result of the test. However, testing also exposes individuals to uncertainty over the available insurance contract, so-called classification risk, which lowers the value of information. In our analysis we distinguish between four different policy regimes, determine the value of information under each regime and associated equilibrium outcomes on the insurance market. We show that the policy regimes can be Pareto ranked, with a duty to disclose being the preferred regime and an information ban the least preferred one.

Moderne Finanzinstrumente im Rahmen des Katastrophen-Risk-Managements — Basisrisiko versus Ausfallrisiko

SummaryA major problem for insuring catastrophic risk is that, as a disaster causes damages to many insureds at the same time, such insurance and in particular reinsurance contracts are often subject to considerable default risk. On the other hand, the securitization of insurance risk, for example via a catastrophe bond, can be designed to completely avoid default risk. Typically, however, the payout from an insurance-linked security is tied to some stochastic variable, an index, which is correlated, but not identical, with the insured’s actual losses. Therefore, such an instrument will usually not provide a perfect hedge. There will be some mismatch, the so-called basis risk. This paper investigates how the trade off between default respectively credit risk and basis risk affects optimal risk management solutions, when (re)insurance and index-linked risk securitization are used simultaneously. In particular, the impact of credit risk and risk securitization on the optimal reinsurance contract is analyzed.