We compute the improved bounds on the copula of a bivariate random vector  when partial information is available, such as the values of the copula on the subset of [0,1]^2, or the value of a functional of the copula, monotone with respect to the concordance order. These results are then used to compute model-free bounds on the prices of two-asset options which make use of extra information about the dependence structure, such as the price of another two-asset option.
Improved bounds on the copula of a bivariate random vector are computed when partial information is available, such as the values of the copula on a given subset of [0,1]^2, or the value of a functional of the copula, monotone with respect to the concordance order. These results are then used to compute model-free bounds on the prices of two-asset options which make use of extra information about the dependence structure, such as the price of another two-asset option.
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