Computation of Greeks under rough Volterra stochastic volatility models using the Malliavin calculus approach
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912463261270016 |
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| author | Al-Foraih, Mishari Burés, Òscar Pospíšil, Jan Vives, Josep |
| author_facet | Al-Foraih, Mishari Burés, Òscar Pospíšil, Jan Vives, Josep |
| contents | Using Malliavin calculus techniques, we obtain formulas for computing Greeks under different rough Volterra stochastic volatility models. Due to the fact that underlying prices are not always square integrable, we extend the classical integration by parts formula to integrable but not necessarily square integrable functionals. First of all, we obtain formulas for general stochastic volatility (SV) models, concretely the Greeks Delta, Gamma, Rho, Vega and we introduce the Greek with respect to the roughness parameter. Then, the particular case of rough Volterra SV models is analyzed. Finally, three examples are treated in detail: the family of alpha-RFSV models, that includes rough versions of SABR and Bergomi models, a mixed alpha-RFSV model with two different Hurst parameters representing short (roughness) and long memory, and the rough Stein-Stein model. For different models and Greeks we show a numerical convergence of our formulas in Monte Carlo simulations and depict for example a dependence of the Greeks on the roughness parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_00405 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Computation of Greeks under rough Volterra stochastic volatility models using the Malliavin calculus approach Al-Foraih, Mishari Burés, Òscar Pospíšil, Jan Vives, Josep Mathematical Finance 60G22, 91G20, 91G60 G.3 Using Malliavin calculus techniques, we obtain formulas for computing Greeks under different rough Volterra stochastic volatility models. Due to the fact that underlying prices are not always square integrable, we extend the classical integration by parts formula to integrable but not necessarily square integrable functionals. First of all, we obtain formulas for general stochastic volatility (SV) models, concretely the Greeks Delta, Gamma, Rho, Vega and we introduce the Greek with respect to the roughness parameter. Then, the particular case of rough Volterra SV models is analyzed. Finally, three examples are treated in detail: the family of alpha-RFSV models, that includes rough versions of SABR and Bergomi models, a mixed alpha-RFSV model with two different Hurst parameters representing short (roughness) and long memory, and the rough Stein-Stein model. For different models and Greeks we show a numerical convergence of our formulas in Monte Carlo simulations and depict for example a dependence of the Greeks on the roughness parameter. |
| title | Computation of Greeks under rough Volterra stochastic volatility models using the Malliavin calculus approach |
| topic | Mathematical Finance 60G22, 91G20, 91G60 G.3 |
| url | https://arxiv.org/abs/2312.00405 |