Signature volatility models: pricing and hedging with Fourier
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915316195393536 |
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| author | Jaber, Eduardo Abi Gérard, Louis-Amand |
| author_facet | Jaber, Eduardo Abi Gérard, Louis-Amand |
| contents | We consider a stochastic volatility model where the dynamics of the volatility are given by a possibly infinite linear combination of the elements of the time extended signature of a Brownian motion. First, we show that the model is remarkably universal, as it includes, but is not limited to, the celebrated Stein-Stein, Bergomi, and Heston models, together with some path-dependent variants. Second, we derive the joint characteristic functional of the log-price and integrated variance provided that some infinite dimensional extended tensor algebra valued Riccati equation admits a solution. This allows us to price and (quadratically) hedge certain European and path-dependent options using Fourier inversion techniques. We highlight the efficiency and accuracy of these Fourier techniques in a comprehensive numerical study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01820 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Signature volatility models: pricing and hedging with Fourier Jaber, Eduardo Abi Gérard, Louis-Amand Pricing of Securities 60L10, 91G20, 91G60 We consider a stochastic volatility model where the dynamics of the volatility are given by a possibly infinite linear combination of the elements of the time extended signature of a Brownian motion. First, we show that the model is remarkably universal, as it includes, but is not limited to, the celebrated Stein-Stein, Bergomi, and Heston models, together with some path-dependent variants. Second, we derive the joint characteristic functional of the log-price and integrated variance provided that some infinite dimensional extended tensor algebra valued Riccati equation admits a solution. This allows us to price and (quadratically) hedge certain European and path-dependent options using Fourier inversion techniques. We highlight the efficiency and accuracy of these Fourier techniques in a comprehensive numerical study. |
| title | Signature volatility models: pricing and hedging with Fourier |
| topic | Pricing of Securities 60L10, 91G20, 91G60 |
| url | https://arxiv.org/abs/2402.01820 |