Simulation of square-root processes made simple: applications to the Heston model
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908409924681728 |
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| author | Jaber, Eduardo Abi |
| author_facet | Jaber, Eduardo Abi |
| contents | We introduce a simple, efficient and accurate nonnegative preserving numerical scheme for simulating the square-root process. The novel idea is to simulate the integrated square-root process first instead of the square-root process itself. Numerical experiments on realistic parameter sets, applied for the integrated process and the Heston model, display high precision with a very low number of time steps. As a bonus, our scheme yields the exact limiting Inverse Gaussian distributions of the integrated square-root process with only one single time-step in two scenarios: (i) for high mean-reversion and volatility-of-volatility regimes, regardless of maturity; and (ii) for long maturities, independent of the other parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11264 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simulation of square-root processes made simple: applications to the Heston model Jaber, Eduardo Abi Mathematical Finance Computational Finance We introduce a simple, efficient and accurate nonnegative preserving numerical scheme for simulating the square-root process. The novel idea is to simulate the integrated square-root process first instead of the square-root process itself. Numerical experiments on realistic parameter sets, applied for the integrated process and the Heston model, display high precision with a very low number of time steps. As a bonus, our scheme yields the exact limiting Inverse Gaussian distributions of the integrated square-root process with only one single time-step in two scenarios: (i) for high mean-reversion and volatility-of-volatility regimes, regardless of maturity; and (ii) for long maturities, independent of the other parameters. |
| title | Simulation of square-root processes made simple: applications to the Heston model |
| topic | Mathematical Finance Computational Finance |
| url | https://arxiv.org/abs/2412.11264 |