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arXiv · 2404.05214

Generalized measure Black-Scholes equation: Towards option self-similar pricing

Nizar Riane·Claire David
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Abstract

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.

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Nizar Riane, Claire David. 2024-04-08. Generalized measure Black-Scholes equation: Towards option self-similar pricing. https://arxiv.org/abs/2404.05214

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