Series expansion and fourth-order global pade approximation for rough Heston solution
The rough Heston model has recently been shown to be extremely consistent with the observed empirical data in the financial market. However, the shortcoming of the model is that the conventional numerical method to compute option prices under it requires great computational effort due to the presenc...
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| Format: | Article |
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MDPI AG
2020
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| Online Access: | http://psasir.upm.edu.my/id/eprint/85799/ |
| _version_ | 1848860185299255296 |
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| author | Siow, Woon Jeng Kilicman, Adem |
| author_facet | Siow, Woon Jeng Kilicman, Adem |
| author_sort | Siow, Woon Jeng |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The rough Heston model has recently been shown to be extremely consistent with the observed empirical data in the financial market. However, the shortcoming of the model is that the conventional numerical method to compute option prices under it requires great computational effort due to the presence of the fractional Riccati equation in its characteristic function. In this study, we contribute by providing an efficient method while still retaining the quality of the solution under varying Hurst parameter for the fractional Riccati equations in two ways. First, we show that under the Laplace–Adomian-decomposition method, the infinite series expansion of the fractional Riccati equation’s solution corresponds to the existing expansion method from previous work for at least up to the fifth order. Then, we show that the fourth-order Padé approximants can be used to construct an extremely accurate global approximation to the fractional Riccati equation in an unexpected way. The pointwise approximation error of the global Padé approximation to the fractional Riccati equation is also provided. Unlike the existing work of third-order global Padé approximation to the fractional Riccati equation, our work extends the availability of Hurst parameter range without incurring huge errors. Finally, numerical comparisons were conducted to verify that our methods are indeed accurate and better than the existing method for computing both the fractional Riccati equation’s solution and option prices under the rough Heston model. |
| first_indexed | 2025-11-15T12:41:13Z |
| format | Article |
| id | upm-85799 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T12:41:13Z |
| publishDate | 2020 |
| publisher | MDPI AG |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-857992023-09-07T00:57:37Z http://psasir.upm.edu.my/id/eprint/85799/ Series expansion and fourth-order global pade approximation for rough Heston solution Siow, Woon Jeng Kilicman, Adem The rough Heston model has recently been shown to be extremely consistent with the observed empirical data in the financial market. However, the shortcoming of the model is that the conventional numerical method to compute option prices under it requires great computational effort due to the presence of the fractional Riccati equation in its characteristic function. In this study, we contribute by providing an efficient method while still retaining the quality of the solution under varying Hurst parameter for the fractional Riccati equations in two ways. First, we show that under the Laplace–Adomian-decomposition method, the infinite series expansion of the fractional Riccati equation’s solution corresponds to the existing expansion method from previous work for at least up to the fifth order. Then, we show that the fourth-order Padé approximants can be used to construct an extremely accurate global approximation to the fractional Riccati equation in an unexpected way. The pointwise approximation error of the global Padé approximation to the fractional Riccati equation is also provided. Unlike the existing work of third-order global Padé approximation to the fractional Riccati equation, our work extends the availability of Hurst parameter range without incurring huge errors. Finally, numerical comparisons were conducted to verify that our methods are indeed accurate and better than the existing method for computing both the fractional Riccati equation’s solution and option prices under the rough Heston model. MDPI AG 2020 Article PeerReviewed Siow, Woon Jeng and Kilicman, Adem (2020) Series expansion and fourth-order global pade approximation for rough Heston solution. Mathematics, 18 (11). pp. 1-26. ISSN 2227-7390 https://www.mdpi.com/2227-7390/8/11/1968 10.3390/math8111968 |
| spellingShingle | Siow, Woon Jeng Kilicman, Adem Series expansion and fourth-order global pade approximation for rough Heston solution |
| title | Series expansion and fourth-order global pade approximation for rough Heston solution |
| title_full | Series expansion and fourth-order global pade approximation for rough Heston solution |
| title_fullStr | Series expansion and fourth-order global pade approximation for rough Heston solution |
| title_full_unstemmed | Series expansion and fourth-order global pade approximation for rough Heston solution |
| title_short | Series expansion and fourth-order global pade approximation for rough Heston solution |
| title_sort | series expansion and fourth-order global pade approximation for rough heston solution |
| url | http://psasir.upm.edu.my/id/eprint/85799/ http://psasir.upm.edu.my/id/eprint/85799/ http://psasir.upm.edu.my/id/eprint/85799/ |