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

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  • Nizar Riane
  • Claire David

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. "Generalized measure Black-Scholes equation: Towards option self-similar pricing," Papers 2404.05214, arXiv.org.
    • Handle: RePEc:arx:papers:2404.05214
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    References listed on IDEAS

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    1. V. L. Martin & G. M. Martin & G. C. Lim, 2005. "Parametric pricing of higher order moments in S&P500 options," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(3), pages 377-404.
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