Some analytical results on bivariate stable distributions with an application in operational risk. Issue 7 (3rd July 2022)

• Record Type: Journal Article
• Authors: Tafakori, L.; Bee, M.; Soltani, A.R.
• Is Part Of: Quantitative finance. Volume 22:Issue 7(2022)
• Page Start: 1355
• Page End: 1369
• Publication Date: 2022-07-03
• Subjects: Characteristic function -- One-sided Bivariate Laplace transform -- Bivariate stable distributions -- Approximate Maximum Likelihood; Finance -- Periodicals; Business mathematics -- Periodicals; Finance -- Mathematical models -- Periodicals; Investments -- Mathematics -- Periodicals; Economics -- Periodicals; Finances -- Modèles mathématiques -- Périodiques; 332.015118
• DOI: 10.1080/14697688.2022.2046285
• Languages: English
• ISSNs: 1469-7688

Abstract

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.