August 19, 2025MathematicsOpen Access

Revisiting Black–Scholes: A Smooth Wiener Approach to Derivation and a Self-Contained Solution

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Self-contained derivation of the Black and Scholes PDE using a smoothed Wiener process, indicating new insights for financial modeling.

The new smooth wiener approach reaffirms the robustness of the black and scholes framework in derivative pricing, highlighting its versatility.
Findings show how a smoothed wiener process can serve as a differentiable stochastic process, simplifying earlier complex methods.
This self-contained derivation provides a bridge between heuristic financial reasoning and rigorous mathematical principles in finance.
Ultimately, it suggests that fundamental properties like volatility and no arbitrage are preserved across different stochastic processes.

Saccal et al. (2025) studied this question.

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