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

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, doe...

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Bibliographic Details
Published in:Quantitative finance 2022-07, Vol.22 (7), p.1355-1369
Main Authors: Tafakori, L., Bee, M., Soltani, A.R.
Format: Article
Language:English
Subjects:
Approximate Maximum Likelihood
Bivariate stable distributions
Characteristic function
One-sided Bivariate Laplace transform
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Summary: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.
ISSN:1469-7688
1469-7696
DOI:10.1080/14697688.2022.2046285