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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.08805 |
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| _version_ | 1866917001349300224 |
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| author | Zaugg, Nicola F. Grzelak, Lech A. |
| author_facet | Zaugg, Nicola F. Grzelak, Lech A. |
| contents | The lifted Heston model is a stochastic volatility model emerging as a Markovian lift of the rough Heston model and the class of rough volatility processes. The model encodes the path dependency of volatility on a set of N square-root state processes driven by a common stochastic factor. While the system is Markovian, simulation schemes such as the Euler scheme exist, but require a small-step, multidimensional simulation of the state processes and are therefore numerically challenging. We propose a novel simulation scheme of the class of implicit integrated variance schemes. The method exploits the near-linear nature between the stochastic driver and the conditional integrated variance process, which allows for a consistent and efficient sampling of the integrated variance process using an inverse Gaussian distribution. Since we establish the linear relation using a linear projection in the L2 space, the method is optimal in an L2 sense and offers a significant efficiency gain over similar methods. We demonstrate that our scheme achieves near-exact accuracy even for coarse discretizations and allows for efficient pricing of volatility options with large time steps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08805 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lifted Heston Model: Efficient Monte Carlo Simulation with Large Time Steps Zaugg, Nicola F. Grzelak, Lech A. Mathematical Finance 60-04 The lifted Heston model is a stochastic volatility model emerging as a Markovian lift of the rough Heston model and the class of rough volatility processes. The model encodes the path dependency of volatility on a set of N square-root state processes driven by a common stochastic factor. While the system is Markovian, simulation schemes such as the Euler scheme exist, but require a small-step, multidimensional simulation of the state processes and are therefore numerically challenging. We propose a novel simulation scheme of the class of implicit integrated variance schemes. The method exploits the near-linear nature between the stochastic driver and the conditional integrated variance process, which allows for a consistent and efficient sampling of the integrated variance process using an inverse Gaussian distribution. Since we establish the linear relation using a linear projection in the L2 space, the method is optimal in an L2 sense and offers a significant efficiency gain over similar methods. We demonstrate that our scheme achieves near-exact accuracy even for coarse discretizations and allows for efficient pricing of volatility options with large time steps. |
| title | Lifted Heston Model: Efficient Monte Carlo Simulation with Large Time Steps |
| topic | Mathematical Finance 60-04 |
| url | https://arxiv.org/abs/2510.08805 |