Inducing a desired value of correlation between two point-scale variables

Focusing on point-scale random variables, i.e., variables whose support space is given by the first m integers, we discuss how a desired value of Pearson’s correlation can be induced between two assigned probability distributions, which are linked to a joint distribution via a copula function. After recalling how the value of the desired is not free to vary within [1; +1], but is bounded to a narrower interval depending on the two marginal distributions, we devise a procedure to recover the same feasible value for different dependence structures, focusing on one-parameter copulas encompassing the entire dependence spectrum.