Some analytical results on bivariate stable distributions with an application in operational risk

L. Tafakori, Marco Bee and A.R. Soltani

Quantitative Finance, 2022, vol. 22, issue 7, 1355-1369

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.

Date: 2022
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DOI: 10.1080/14697688.2022.2046285

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