Some analytical results on bivariate stable distributions with an application in operational risk. Issue 7 (3rd July 2022) - Tafakori, L.; Bee, M.; Soltani, A.R.
Abstract : The multivariate stable distributions are widely applicable as they can accommodate both skewness and heavy tails. Although one-dimensional stable distributions are well known, there are many open questions in the multivariate regime, since the tractability of the multivariate Gaussian universe, does not extend to non-Gaussian multivariate stable distributions. In this work, we provide the Laplace transform of bivariate stable distributions and its certain cut in the first quadrant. Given the lack of a closed-form likelihood function, we propose to estimate the parameters by means of Approximate Maximum Likelihood, a simulation-based method with desirable asymptotic properties. Simulation experiments and an application to truncated operational losses illustrate the applicability of the model.