  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.
