Generalized measure Black-Scholes equation: Towards option self-similar pricing
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910402389999616 |
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| author | Riane, Nizar David, Claire |
| author_facet | Riane, Nizar David, Claire |
| contents | In this work, we give a generalized formulation of the Black-Scholes model. The novelty resides in considering the Black-Scholes model to be valid on 'average', but such that the pointwise option price dynamics depends on a measure representing the investors' 'uncertainty'. We make use of the theory of non-symmetric Dirichlet forms and the abstract theory of partial differential equations to establish well posedness of the problem. A detailed numerical analysis is given in the case of self-similar measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05214 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized measure Black-Scholes equation: Towards option self-similar pricing Riane, Nizar David, Claire Mathematical Finance 28A80 - 91G20 - 65L12 - 65L20 In this work, we give a generalized formulation of the Black-Scholes model. The novelty resides in considering the Black-Scholes model to be valid on 'average', but such that the pointwise option price dynamics depends on a measure representing the investors' 'uncertainty'. We make use of the theory of non-symmetric Dirichlet forms and the abstract theory of partial differential equations to establish well posedness of the problem. A detailed numerical analysis is given in the case of self-similar measures. |
| title | Generalized measure Black-Scholes equation: Towards option self-similar pricing |
| topic | Mathematical Finance 28A80 - 91G20 - 65L12 - 65L20 |
| url | https://arxiv.org/abs/2404.05214 |