On multilevel and control variate Monte Carlo methods for option pricing under the rough Heston model
The rough Heston model is a form of a stochastic Volterra equation, which was proposed to model stock price volatility. It captures some important qualities that can be observed in the financial market—highly endogenous, statistical arbitrages prevention, liquidity asymmetry, and metaorders. Unlike...
| Main Authors: | , |
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| Format: | Article |
| Published: |
MDPI
2021
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| Online Access: | http://psasir.upm.edu.my/id/eprint/94432/ |
| _version_ | 1848861995420352512 |
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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 is a form of a stochastic Volterra equation, which was proposed to model stock price volatility. It captures some important qualities that can be observed in the financial market—highly endogenous, statistical arbitrages prevention, liquidity asymmetry, and metaorders. Unlike stochastic differential equation, the stochastic Volterra equation is extremely computationally expensive to simulate. In other words, it is difficult to compute option prices under the rough Heston model by conventional Monte Carlo simulation. In this paper, we prove that Euler’s discretization method for the stochastic Volterra equation with non-Lipschitz diffusion coefficient E[|Vt−Vnt|p]
is finitely bounded by an exponential function of t. Furthermore, the weak error |E[Vt−Vnt]|
and convergence for the stochastic Volterra equation are proven at the rate of O(n−H). In addition, we propose a mixed Monte Carlo method, using the control variate and multilevel methods. The numerical experiments indicate that the proposed method is capable of achieving a substantial cost-adjusted variance reduction up to 17 times, and it is better than its predecessor individual methods in terms of cost-adjusted performance. Due to the cost-adjusted basis for our numerical experiment, the result also indicates a high possibility of potential use in practice. |
| first_indexed | 2025-11-15T13:09:59Z |
| format | Article |
| id | upm-94432 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:09:59Z |
| publishDate | 2021 |
| publisher | MDPI |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-944322023-03-29T08:23:47Z http://psasir.upm.edu.my/id/eprint/94432/ On multilevel and control variate Monte Carlo methods for option pricing under the rough Heston model Siow, Woon Jeng Kilicman, Adem The rough Heston model is a form of a stochastic Volterra equation, which was proposed to model stock price volatility. It captures some important qualities that can be observed in the financial market—highly endogenous, statistical arbitrages prevention, liquidity asymmetry, and metaorders. Unlike stochastic differential equation, the stochastic Volterra equation is extremely computationally expensive to simulate. In other words, it is difficult to compute option prices under the rough Heston model by conventional Monte Carlo simulation. In this paper, we prove that Euler’s discretization method for the stochastic Volterra equation with non-Lipschitz diffusion coefficient E[|Vt−Vnt|p] is finitely bounded by an exponential function of t. Furthermore, the weak error |E[Vt−Vnt]| and convergence for the stochastic Volterra equation are proven at the rate of O(n−H). In addition, we propose a mixed Monte Carlo method, using the control variate and multilevel methods. The numerical experiments indicate that the proposed method is capable of achieving a substantial cost-adjusted variance reduction up to 17 times, and it is better than its predecessor individual methods in terms of cost-adjusted performance. Due to the cost-adjusted basis for our numerical experiment, the result also indicates a high possibility of potential use in practice. MDPI 2021-11-17 Article PeerReviewed Siow, Woon Jeng and Kilicman, Adem (2021) On multilevel and control variate Monte Carlo methods for option pricing under the rough Heston model. Mathematics, 9 (22). art. no. 2930. pp. 1-32. ISSN 2227-7390 https://www.mdpi.com/2227-7390/9/22/2930/html 10.3390/math9222930 |
| spellingShingle | Siow, Woon Jeng Kilicman, Adem On multilevel and control variate Monte Carlo methods for option pricing under the rough Heston model |
| title | On multilevel and control variate Monte Carlo methods for option pricing under the rough Heston model |
| title_full | On multilevel and control variate Monte Carlo methods for option pricing under the rough Heston model |
| title_fullStr | On multilevel and control variate Monte Carlo methods for option pricing under the rough Heston model |
| title_full_unstemmed | On multilevel and control variate Monte Carlo methods for option pricing under the rough Heston model |
| title_short | On multilevel and control variate Monte Carlo methods for option pricing under the rough Heston model |
| title_sort | on multilevel and control variate monte carlo methods for option pricing under the rough heston model |
| url | http://psasir.upm.edu.my/id/eprint/94432/ http://psasir.upm.edu.my/id/eprint/94432/ http://psasir.upm.edu.my/id/eprint/94432/ |