About the exact simulation of bivariate (reciprocal) Archimax copulas

Abstract We provide an exact simulation algorithm for bivariate Archimax copulas, including instances with negative association. In contrast to existing simulation approaches, the feasibility of our algorithm is directly linked to the availability of an exact simulation algorithm for the probability measure described by the derivative of the parameterizing Pickands dependence function. We demonstrate that this hypothesis is satisfied in many cases of interest and, in particular, it is satisfied for piece-wise constant Pickands dependence functions, which can approximate the general case to a given level of desired accuracy. Finally, the algorithm can be leveraged to an exact simulation algorithm for bivariate copulas associated with max-infinitely divisible random vectors whose exponent measure has norm-symmetric survival function, so-called reciprocal Archimax copulas.