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arXiv · 2501.18721

On non-uniqueness in the option valuation problem

Ekaterina A. Ladykova·Olga S. Rozanova
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Abstract

It is known that the value of a call option in the case of constant elasticity processes (CEV) with the indicator $\alpha$ exceeding the critical $\alpha=1$ 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 $1<\alpha\le \frac32$ the non-uniqueness is due to the fact that the initial data of the call option are outside the T\"acklind class, and for $\alpha> \frac32$ it is due to the absence boundary condition for $x=\infty$.

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Ekaterina A. Ladykova, Olga S. Rozanova. 2025-01-30. On non-uniqueness in the option valuation problem. https://arxiv.org/abs/2501.18721

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