Defining copulas



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. The marginal distribution of V1 (sometimes also referred to as the unconditional distribution) is its distribution assuming we know nothing about V2; similarly, the marginal distribution of V2 is its distribution assuming we know nothing about V1. Suppose we have estimated the marginal distributions of V1 and V2. How can we make an assumption about the correlation structure between the two variables to define their joint distribution?

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