Modeling Stock Returns and Volatility Using Bivariate Gamma Generalized Laplace Law
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913079693934592 |
|---|---|
| author | Kozubowski, Tomasz J. Sarantsev, Andrey Spiker, James A. |
| author_facet | Kozubowski, Tomasz J. Sarantsev, Andrey Spiker, James A. |
| contents | We consider a generalization of the variance-gamma (generalized asymmetric Laplace) distribution, defined as a normal mean - variance mixture with a gamma mixing distribution. While this model is typically studied in the univariate setting, we assume that the gamma mixing variable is observed alongside the primary variable, resulting in a bivariate framework. In this setting, maximum likelihood estimation becomes significantly simpler than in the standard univariate case, reducing to a form of classical linear regression. We derive explicit expressions for the resulting estimators. For certain parameter configurations, the estimators exhibit nonstandard convergence rates, exceeding the usual square-root rate. Finally, we illustrate the applicability of this model in financial contexts by analyzing stock index returns and associated volatility for several major indices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00196 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Modeling Stock Returns and Volatility Using Bivariate Gamma Generalized Laplace Law Kozubowski, Tomasz J. Sarantsev, Andrey Spiker, James A. Methodology Probability Statistics Theory Statistical Finance 62H05, 60E05, 60E07, 62F10, 62F12, 62J05, 62P05 We consider a generalization of the variance-gamma (generalized asymmetric Laplace) distribution, defined as a normal mean - variance mixture with a gamma mixing distribution. While this model is typically studied in the univariate setting, we assume that the gamma mixing variable is observed alongside the primary variable, resulting in a bivariate framework. In this setting, maximum likelihood estimation becomes significantly simpler than in the standard univariate case, reducing to a form of classical linear regression. We derive explicit expressions for the resulting estimators. For certain parameter configurations, the estimators exhibit nonstandard convergence rates, exceeding the usual square-root rate. Finally, we illustrate the applicability of this model in financial contexts by analyzing stock index returns and associated volatility for several major indices. |
| title | Modeling Stock Returns and Volatility Using Bivariate Gamma Generalized Laplace Law |
| topic | Methodology Probability Statistics Theory Statistical Finance 62H05, 60E05, 60E07, 62F10, 62F12, 62J05, 62P05 |
| url | https://arxiv.org/abs/2605.00196 |