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. © 2022 Informa UK Limited, trading as Taylor & Francis Group.

Some analytical results on bivariate stable distributions with an application in operational risk / Bee, Marco; Tafakori, Laleh; Soltani, Ahmad Reza. - In: QUANTITATIVE FINANCE. - ISSN 1469-7688. - STAMPA. - 22:7(2022), pp. 1355-1369. [10.1080/14697688.2022.2046285]

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

Bee, Marco;
2022-01-01

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. © 2022 Informa UK Limited, trading as Taylor & Francis Group.
2022
7
Bee, Marco; Tafakori, Laleh; Soltani, Ahmad Reza
Some analytical results on bivariate stable distributions with an application in operational risk / Bee, Marco; Tafakori, Laleh; Soltani, Ahmad Reza. - In: QUANTITATIVE FINANCE. - ISSN 1469-7688. - STAMPA. - 22:7(2022), pp. 1355-1369. [10.1080/14697688.2022.2046285]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/332468
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