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On nonexistence of non-constant volatility in the Black-Scholes formula

K. Hamza·F. C. Klebaner
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Abstract

We prove that if the Black-Scholes formula holds with the spot volatility for call options with all strikes, then the volatility parameter is constant. The proof relies some result on semimartingales (Theorem 2) of independent interest.

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K. Hamza, F. C. Klebaner. 2005-02-10. On nonexistence of non-constant volatility in the Black-Scholes formula. https://arxiv.org/abs/math/0502201

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