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

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  • L. Tafakori
  • M. Bee
  • A.R. Soltani

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.

Suggested Citation

  • L. Tafakori & M. Bee & A.R. Soltani, 2022. "Some analytical results on bivariate stable distributions with an application in operational risk," Quantitative Finance, Taylor & Francis Journals, vol. 22(7), pages 1355-1369, July.
    • Handle: RePEc:taf:quantf:v:22:y:2022:i:7:p:1355-1369
    DOI: 10.1080/14697688.2022.2046285
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