On nonexistence of non-constant volatility in the Black-Scholes formula
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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- Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
- Schönbucher, Philpp J., "undated". "A Market Model for Stochastic Implied Volatility," Discussion Paper Serie B 453, University of Bonn, Germany, revised May 1999.
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