[We develop a model for markets for catastrophic risk. The model explains why insurance providers may choose not to offer insurance for catastrophic risks and not to participate in reinsurance markets, even though there is a large enough market capacity to reach full risk sharing through diversification in a reinsurance market. This is a "nondiversification trap." We show that nondiversification traps may arise when risk distributions have heavy left tails and insurance providers have limited liability. When they are present, there may be a coordination role for a centralized agency to ensure that risk sharing takes place.]

Abstract We study a competitive market for risk-sharing, in which risk-tolerant providers of risk protection, who face frictional costs in holding capital, offer coverage over a range of risk classes to risk-averse agents. We distinguish monoline and multiline industry structures and characterize when each structure is optimal. Markets for which the risks are limited in number, asymmetric or correlated will be served by monoline structures, whereas markets characterized by a large number of essentially independent risks will be served by many multiline firms. Our results are consistent with observed structures within insurance, and also have general implications for the financial services industry.

Recent results in value at risk analysis show that, for extremely heavy-tailed risks with unbounded distribution support, diversification may increase value at risk, and that generally it is difficult to construct an appropriate risk measure for such distributions. We further analyze the limitations of diversification for heavy-tailed risks. We provide additional insight in two ways. First, we show that similar non-diversification results are valid for a large class of risks with bounded support, as long as the risks are concentrated on a sufficiently large interval. The required length of the support depends on the number of risks available and on the degree of heavy-tailedness. Second, we relate the value at risk approach to more general risk frameworks. We argue that in markets for risky assets where the number of assets is limited compared with the (bounded) distribution support of the risks, unbounded heavy-tailed risks may provide a reasonable approximation. We suggest that this type of analysis may have a role in explaining various types of market failures in markets for assets with possibly large negative outcomes.

Suppose estimating a model on each of a small number of potentially heterogeneous clusters yields approximately independent, unbiased, and Gaussian parameter estimators. We make two contributions in this setup. First, we show how to compare a scalar parameter of interest between treatment and control units using a two-sample t-statistic, extending previous results for the one-sample t-statistic. Second, we develop a test for the appropriate level of clustering; it tests the null hypothesis that clustered standard errors from a much finer partition are correct. We illustrate the approach by revisiting empirical studies involving clustered, time series, and spatially correlated data.

The recent financial crisis has revealed significant externalities and systemic risks that arise from the interconnectedness of financial intermediaries’ risk portfolios. We develop a model in which the negative externality arises because intermediaries’ actions to diversify that are optimal for individual intermediaries may prove to be suboptimal for society. We show that the externality depends critically on the distributional properties of the risks. The optimal social outcome involves less risk-sharing, but also a lower probability for massive collapses of intermediaries. We derive the exact conditions under which risk-sharing restrictions create a socially preferable outcome. Our analysis has implications for regulation of financial institutions and risk management.

We develop a model for markets for catastrophic risk. The model explains why insurance providers may choose not to offer insurance for catastrophic risks and not to participate in reinsurance markets, even though there is a large enough market capacity to reach full risk sharing through diversification in a reinsurance market. This is a “nondiversification trap.” We show that nondiversification traps may arise when risk distributions have heavy left tails and insurance providers have limited liability. When they are present, there may be a coordination role for a centralized agency to ensure that risk sharing takes place.

Emerging countries are held to be subject to more frequent and more pronounced external and internal shocks than their developed counter-parts. This suggests that key variables pertaining to their markets, including their exchange rates, will be marked by greater likelihood of extreme observations and large fluctuations. We focus on the hypothesis that compared to developed country exchange rates, emerging country exchange rates will be more pronouncedly heavy-tailed. We find support for the hypothesis using recently proposed robust tail index estimation methods which, in particular, perform well under heavy-tailed dependent GARCH processes that are often used for modeling exchange rates. According to the estimation results reported in the paper, variances may be infinite for several emerging country exchange rates. Tail index values ζ=p∈(2.6,2.8) appear to be at the dividing boundary between the two sets of countries: while the moments of order p∈(2.6,2.8) are finite for most of the developed country exchange rates, they may be (or are) infinite for most of the emerging country exchange rates. We also study the impact of the on-going financial and economic crisis, and find that heavy-tailedness properties of most exchange rates did not change significantly with the onset of the crisis. At the same time, some foreign exchange markets have experienced structural changes in their heavy-tailedness properties during the crisis.