Some empirical studies for the applications of fractional $ G $-Brownian motion in finance
Since the fractional $ G $-Brownian motion (fGBm) generalizes the concepts of the standard Brownian motion, fractional Brownian motion, and $ G $-Brownian motion, while it can exhibit long-range dependence or antipersistence and feature the volatility uncertainty simultaneously, it can be a better a...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2025-01-01
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| Series: | Quantitative Finance and Economics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/QFE.2025001 |
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| Summary: | Since the fractional $ G $-Brownian motion (fGBm) generalizes the concepts of the standard Brownian motion, fractional Brownian motion, and $ G $-Brownian motion, while it can exhibit long-range dependence or antipersistence and feature the volatility uncertainty simultaneously, it can be a better alternative stochastic process in the financial applications. Thus, in this paper, some empirical studies for the financial applications of the fGBm were carried out, where the recent high-frequency data for some selected assets in the financial market are from the Oxford-Man Institute of Quantitative Finance Realized Library. There are two main empirical findings. One was that the H-$ G $-normal distributions associated with the fGBm are more suitable in describing the dynamics of daily returns and increments of log-volatility for these assets than the usual distributions, since they not only characterize the properties of skewness, excess kurtosis, and long-range dependence $ \left(\frac{1}{2} < H < 1\right) $ or antipersistence $ \left(0 < H < \frac{1}{2}\right) $, but also feature the volatility uncertainty. The other one was that the daily return and log-volatility both behave essentially as fGBm with different $ \underline{\sigma}^2 $ and $ \overline{\sigma}^2 $, but Hurst parameters $ H < \frac{1}{2} $, at any reasonable time scale. Then a generalized stochastic model for the dynamics of the assets called rough fractional stochastic volatility model driven by fGBm (RFSV-fGBm) was developed. Finally, some parameter estimates and numerical experiments for the RFSV-fGBm model were investigated and carried out. |
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| ISSN: | 2573-0134 |