Option pricing in Sandwiched Volterra Volatility model
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866917721154781184 |
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| author | Di Nunno, Giulia Mishura, Yuliya Yurchenko-Tytarenko, Anton |
| author_facet | Di Nunno, Giulia Mishura, Yuliya Yurchenko-Tytarenko, Anton |
| contents | We introduce a new model of financial market with stochastic volatility driven by an arbitrary Hölder continuous Gaussian Volterra process. The distinguishing feature of the model is the form of the volatility equation which ensures the solution to be ``sandwiched'' between two arbitrary Hölder continuous functions chosen in advance. We discuss the structure of local martingale measures on this market, investigate integrability and Malliavin differentiability of prices and volatilities as well as study absolute continuity of the corresponding probability laws. Additionally, we utilize Malliavin calculus to develop an algorithm of pricing options with discontinuous payoffs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_10688 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Option pricing in Sandwiched Volterra Volatility model Di Nunno, Giulia Mishura, Yuliya Yurchenko-Tytarenko, Anton Mathematical Finance Probability We introduce a new model of financial market with stochastic volatility driven by an arbitrary Hölder continuous Gaussian Volterra process. The distinguishing feature of the model is the form of the volatility equation which ensures the solution to be ``sandwiched'' between two arbitrary Hölder continuous functions chosen in advance. We discuss the structure of local martingale measures on this market, investigate integrability and Malliavin differentiability of prices and volatilities as well as study absolute continuity of the corresponding probability laws. Additionally, we utilize Malliavin calculus to develop an algorithm of pricing options with discontinuous payoffs. |
| title | Option pricing in Sandwiched Volterra Volatility model |
| topic | Mathematical Finance Probability |
| url | https://arxiv.org/abs/2209.10688 |