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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2021
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2112.02440 |
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| _version_ | 1866911910173081600 |
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| author | Fontana, Claudio Gnoatto, Alessandro Szulda, Guillaume |
| author_facet | Fontana, Claudio Gnoatto, Alessandro Szulda, Guillaume |
| contents | We develop a stochastic volatility framework for modeling multiple currencies based on CBI-time-changed Lévy processes. The proposed framework captures the typical risk characteristics of FX markets and is coherent with the symmetries of FX rates. Moreover, due to the self-exciting behavior of CBI processes, the volatilities of FX rates exhibit self-exciting dynamics. By relying on the theory of affine processes, we show that our approach is analytically tractable and that the model structure is invariant under a suitable class of risk-neutral measures. A semi-closed pricing formula for currency options is obtained by Fourier methods. We propose two calibration methods, also by relying on deep-learning techniques, and show that a simple specification of the model can achieve a good fit to market data on a currency triangle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_02440 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | CBI-time-changed Lévy processes for multi-currency modeling Fontana, Claudio Gnoatto, Alessandro Szulda, Guillaume Pricing of Securities We develop a stochastic volatility framework for modeling multiple currencies based on CBI-time-changed Lévy processes. The proposed framework captures the typical risk characteristics of FX markets and is coherent with the symmetries of FX rates. Moreover, due to the self-exciting behavior of CBI processes, the volatilities of FX rates exhibit self-exciting dynamics. By relying on the theory of affine processes, we show that our approach is analytically tractable and that the model structure is invariant under a suitable class of risk-neutral measures. A semi-closed pricing formula for currency options is obtained by Fourier methods. We propose two calibration methods, also by relying on deep-learning techniques, and show that a simple specification of the model can achieve a good fit to market data on a currency triangle. |
| title | CBI-time-changed Lévy processes for multi-currency modeling |
| topic | Pricing of Securities |
| url | https://arxiv.org/abs/2112.02440 |