The bilateral generalized inverse Gaussian process with applications to financial modeling
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909255215349760 |
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| author | Agazzotti, Gaetano Aguilar, Jean-Philippe |
| author_facet | Agazzotti, Gaetano Aguilar, Jean-Philippe |
| contents | We introduce and document a class of probability distributions, called bilateral generalized inverse Gaussian (BGIG) distributions, that are obtained by convolution of two generalized inverse Gaussian distributions supported by the positive and negative semi-axis. We prove several results regarding their analyticity, shapes and asymptotics, and we introduce the associated Lévy processes as well as their main properties. We study the behaviour of these processes under change of measure, their simulations and the structure of their sample paths, and we introduce a stock market model constructed by means of exponential BGIG processes. Based on real market data, we show that this model is easy to calibrate thanks notably to idiosyncratic properties of BGIG distributions, and that it is well suited to Monte Carlo and Fourier option pricing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10557 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The bilateral generalized inverse Gaussian process with applications to financial modeling Agazzotti, Gaetano Aguilar, Jean-Philippe Probability 60G51, 60G46, 60E07, 60E10, 91B28 We introduce and document a class of probability distributions, called bilateral generalized inverse Gaussian (BGIG) distributions, that are obtained by convolution of two generalized inverse Gaussian distributions supported by the positive and negative semi-axis. We prove several results regarding their analyticity, shapes and asymptotics, and we introduce the associated Lévy processes as well as their main properties. We study the behaviour of these processes under change of measure, their simulations and the structure of their sample paths, and we introduce a stock market model constructed by means of exponential BGIG processes. Based on real market data, we show that this model is easy to calibrate thanks notably to idiosyncratic properties of BGIG distributions, and that it is well suited to Monte Carlo and Fourier option pricing. |
| title | The bilateral generalized inverse Gaussian process with applications to financial modeling |
| topic | Probability 60G51, 60G46, 60E07, 60E10, 91B28 |
| url | https://arxiv.org/abs/2407.10557 |