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Defining copulas

Copulas - a function for creating a joint probability distribution for two or more marginal distributions - have become part of the derivatives pricing mainstream. In this article, the first in a series explaining recent developments in risk management and derivatives pricing, John Hull gives a brief explanation of Gaussian, Student-t and multivariate copulas

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Copulas have become increasingly significant in risk management and derivatives valuation in recent years. They are an important way of quickly defining a correlation structure between two or more variables. Recently, they have been used extensively in the valuation of collateralised debt obligations and other credit derivatives.

But how do copulas work? Consider two correlated variables V1 and V2

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