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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2017
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1701.06001 |
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| _version_ | 1866914162091753472 |
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| author | Cozma, Andrei Mariapragassam, Matthieu Reisinger, Christoph |
| author_facet | Cozma, Andrei Mariapragassam, Matthieu Reisinger, Christoph |
| contents | We propose a novel and generic calibration technique for four-factor foreign-exchange hybrid local-stochastic volatility models with stochastic short rates. We build upon the particle method introduced by Guyon and Labordère [Nonlinear Option Pricing, Chapter 11, Chapman and Hall, 2013] and combine it with new variance reduction techniques in order to accelerate convergence. We use control variates derived from a calibrated pure local volatility model, a two-factor Heston-type LSV model (both with deterministic rates), and the stochastic (CIR) short rates. The method can be applied to a large class of hybrid LSV models and is not restricted to our particular choice of the diffusion. The calibration procedure is performed on real-world market data for the EUR-USD currency pair and has a comparable run-time to the PDE calibration of a two-factor LSV model alone. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1701_06001 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Calibration of a Hybrid Local-Stochastic Volatility Stochastic Rates Model with a Control Variate Particle Method Cozma, Andrei Mariapragassam, Matthieu Reisinger, Christoph Mathematical Finance We propose a novel and generic calibration technique for four-factor foreign-exchange hybrid local-stochastic volatility models with stochastic short rates. We build upon the particle method introduced by Guyon and Labordère [Nonlinear Option Pricing, Chapter 11, Chapman and Hall, 2013] and combine it with new variance reduction techniques in order to accelerate convergence. We use control variates derived from a calibrated pure local volatility model, a two-factor Heston-type LSV model (both with deterministic rates), and the stochastic (CIR) short rates. The method can be applied to a large class of hybrid LSV models and is not restricted to our particular choice of the diffusion. The calibration procedure is performed on real-world market data for the EUR-USD currency pair and has a comparable run-time to the PDE calibration of a two-factor LSV model alone. |
| title | Calibration of a Hybrid Local-Stochastic Volatility Stochastic Rates Model with a Control Variate Particle Method |
| topic | Mathematical Finance |
| url | https://arxiv.org/abs/1701.06001 |