Exact simulation scheme for the Ornstein-Uhlenbeck driven stochastic volatility model with the Karhunen-Loève expansions
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913087590760448 |
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| author | Choi, Jaehyuk |
| author_facet | Choi, Jaehyuk |
| contents | This study proposes a fast exact simulation scheme for the Ornstein-Uhlenbeck driven stochastic volatility model. With the Karhunen-Loève expansions, the stochastic volatility path (Ornstein-Uhlenbeck process) is expressed as a sine series, and the time integrals of volatility and variance are analytically derived as infinite series of independent normal random variables. The new method is several hundred times faster than the existing method using numerical transform inversion. The simulation variance is further reduced with conditional simulation and the control variate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09243 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exact simulation scheme for the Ornstein-Uhlenbeck driven stochastic volatility model with the Karhunen-Loève expansions Choi, Jaehyuk Computational Finance Mathematical Finance Pricing of Securities This study proposes a fast exact simulation scheme for the Ornstein-Uhlenbeck driven stochastic volatility model. With the Karhunen-Loève expansions, the stochastic volatility path (Ornstein-Uhlenbeck process) is expressed as a sine series, and the time integrals of volatility and variance are analytically derived as infinite series of independent normal random variables. The new method is several hundred times faster than the existing method using numerical transform inversion. The simulation variance is further reduced with conditional simulation and the control variate. |
| title | Exact simulation scheme for the Ornstein-Uhlenbeck driven stochastic volatility model with the Karhunen-Loève expansions |
| topic | Computational Finance Mathematical Finance Pricing of Securities |
| url | https://arxiv.org/abs/2402.09243 |