A copula is a cumulative probability distribution for multiple interdependent variables. Values are input for each variable, and the copula produces a single probability: the probability of each variable having a smaller value than its input value – for example, the probability that a portfolio loses less than $50.
For example, to determine the probability that portfolio A loses less than $50 will require specifying whether portfolio B simultaneously loses less than $100 or perhaps $1000. If, instead, portfolio B is specified to allow any size of loss, the distribution of losses of A will be uniform.
Gaussian copulas, which are built on a multivariate normal distribution, gained notoriety during the 2008 financial crisis as, when used for the pricing of derivatives such as collateralised debt obligations, they produced an unrealistically low probability of extreme events occurring for two variables simultaneously.
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