On non-uniqueness in the option valuation problem
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913671756644352 |
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| author | Ladykova, Ekaterina A. Rozanova, Olga S. |
| author_facet | Ladykova, Ekaterina A. Rozanova, Olga S. |
| contents | It is known that the value of a call option in the case of constant elasticity processes (CEV) with the indicator $α$ exceeding the critical $α=1$ is determined in a non-unique way.
We show how, based on an already existing mathematical theory concerning the correctness of boundary conditions for degenerate parabolic equations on the semi-axis $[0,\infty)$, this phenomenon can be explained. Namely, for $1<α\le \frac32$ the non-uniqueness is due to the fact that the initial data of the call option are outside the Täcklind class, and for $α> \frac32$ it is due to the absence boundary condition for $x=\infty$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_18721 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On non-uniqueness in the option valuation problem Ladykova, Ekaterina A. Rozanova, Olga S. Analysis of PDEs Mathematical Finance 35K65 35G16 35A02 It is known that the value of a call option in the case of constant elasticity processes (CEV) with the indicator $α$ exceeding the critical $α=1$ is determined in a non-unique way. We show how, based on an already existing mathematical theory concerning the correctness of boundary conditions for degenerate parabolic equations on the semi-axis $[0,\infty)$, this phenomenon can be explained. Namely, for $1<α\le \frac32$ the non-uniqueness is due to the fact that the initial data of the call option are outside the Täcklind class, and for $α> \frac32$ it is due to the absence boundary condition for $x=\infty$. |
| title | On non-uniqueness in the option valuation problem |
| topic | Analysis of PDEs Mathematical Finance 35K65 35G16 35A02 |
| url | https://arxiv.org/abs/2501.18721 |