G32 Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure
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This paper analyzes the scope of the private market for pandemic insurance. We develop a framework that explains theoretically how the equilibrium price of pandemic insurance depends on accumulation risk, covariance between pandemic claims and other claims, and covariance between pandemic claims and the stock market performance. Using the natural catastrophe (NatCat) insurance market as a laboratory, we estimate the relationship between the insurance price markup and the tail characteristics of the loss distribution. Then, by using the high-frequency data tracking the economic impact of the COVID-19 pandemic in the United States, we calibrate the loss distribution of a hypothetical insurance contract designed to alleviate the impact of the pandemic on small businesses. The pandemic insurance contract price markup corresponds to the top 20% markup observed in the NatCat insurance market. Then we analyze an intertemporal risk-sharing scheme that can reduce the expected shortfall of the loss distribution by 50%.
Tail-correlation matrices are an important tool for aggregating risk measurements across risk categories, asset classes and/or business segments. This paper demonstrates that traditional tail-correlation matrices—which are conventionally assumed to have ones on the diagonal—can lead to substantial biases of the aggregate risk measurement’s sensitivities with respect to risk exposures. Due to these biases, decision-makers receive an odd view of the effects of portfolio changes and may be unable to identify the optimal portfolio from a risk-return perspective. To overcome these issues, we introduce the “sensitivity-implied tail-correlation matrix”. The proposed tail-correlation matrix allows for a simple deterministic risk aggregation approach which reasonably approximates the true aggregate risk measurement according to the complete multivariate risk distribution. Numerical examples demonstrate that our approach is a better basis for portfolio optimization than the Value-at-Risk implied tail-correlation matrix, especially if the calibration portfolio (or current portfolio) deviates from the optimal portfolio.