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| Format: | Recurso digital |
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| Veröffentlicht: |
Zenodo
2025
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| Online-Zugang: | https://doi.org/10.5281/zenodo.17834813 |
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Inhaltsangabe:
- This paper introduces Neural Jump-Diffusion (NJD), a novel data-driven framework for calibrating and extending stochastic volatility models, with a particular focus on the Heston model. Traditional calibration of the Heston model and its jump-diffusion extensions presents significant computational challenges, often leading to suboptimal fits to market option prices and struggles with capturing complex market phenomena like extreme skewness and kurtosis. NJD leverages the power of deep neural networks to learn the intricate dynamics of underlying asset prices and their volatility, including abrupt jumps, directly from observed market data. By representing the drift, diffusion, and jump components of a jump-diffusion process as neural networks, the framework enables a highly flexible and efficient calibration process that minimizes the discrepancy between model-implied and market option prices. This approach not only provides a more accurate and robust calibration for the Heston model but also offers a powerful pathway to generalize stochastic volatility models by learning non-parametric forms of their dynamics, effectively going "beyond" the rigid parametric assumptions of existing models. We demonstrate the theoretical underpinnings of NJD, its architectural design, training methodology, and highlight its potential to enhance option pricing accuracy, risk management, and the development of more adaptive financial models capable of capturing a wider range of empirical stylized facts.