Copulas are used to model joint distribution of multiple underlyings. They permit a rich "correlation" structure between underlyings.They are used for pricing,for risk management,for pairs trading,etc.,and are especially popular in credit derivatives.

For example,you have a basket of stocks which during normal days exhibit little relationship with each other.We might say that they are uncorrelated.But on days when the market moves dramatically they all move together. Such behaviour can be modelled by copulas.

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