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Correlated Default Risks and Bank Regulations

Bank regulatory design relies critically on bank risk modeling. Traditionally, the bank's aggregate value is assumed to obey an exogenously specified process (e.g., a lognormal diffusion). We demonstrate that this assumption is generally invalid given the truncated and correlated payoff structure of individual bank loans. Instead, the bank's aggregate terminal payoff is significantly (left) fat tailed. This skewness remains even when the bank holds an infinitely large number of loans in its portfolio unless they are uncorrelated. By ignoring skewness in bank payoffs, deposit insurance premia and capital requirements have traditionally been significantly mis-calculated.