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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1911.00877 |
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| _version_ | 1866912715572772864 |
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| author | Bain, Alan Mariapragassam, Matthieu Reisinger, Christoph |
| author_facet | Bain, Alan Mariapragassam, Matthieu Reisinger, Christoph |
| contents | We propose a generic calibration framework to both vanilla and no-touch options for a large class of continuous semi-martingale models. The method builds upon the forward partial integro-differential equation (PIDE) derived in Hambly et al. (2016), which allows fast computation of up-and-out call prices for the complete set of strikes, barriers and maturities. It also utilises a novel two-states particle method to estimate the Markovian projection of the variance onto the spot and running maximum. We detail a step-by-step procedure for a Heston-type local-stochastic volatility model with local vol-of-vol, as well as two path-dependent volatility models where the local volatility component depends on the running maximum. In numerical tests, we benchmark these new models against standard models for a set of EURUSD market data, all three models are seen to calibrate well within the market no-touch bid--ask. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_00877 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Calibration of Local-Stochastic and Path-Dependent Volatility Models to Vanilla and No-Touch Options Bain, Alan Mariapragassam, Matthieu Reisinger, Christoph Mathematical Finance We propose a generic calibration framework to both vanilla and no-touch options for a large class of continuous semi-martingale models. The method builds upon the forward partial integro-differential equation (PIDE) derived in Hambly et al. (2016), which allows fast computation of up-and-out call prices for the complete set of strikes, barriers and maturities. It also utilises a novel two-states particle method to estimate the Markovian projection of the variance onto the spot and running maximum. We detail a step-by-step procedure for a Heston-type local-stochastic volatility model with local vol-of-vol, as well as two path-dependent volatility models where the local volatility component depends on the running maximum. In numerical tests, we benchmark these new models against standard models for a set of EURUSD market data, all three models are seen to calibrate well within the market no-touch bid--ask. |
| title | Calibration of Local-Stochastic and Path-Dependent Volatility Models to Vanilla and No-Touch Options |
| topic | Mathematical Finance |
| url | https://arxiv.org/abs/1911.00877 |