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

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July 2006, 6(4): 829-834. doi: 10.3934/dcdsb.2006.6.829

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

1.	School of Mathematical Sciences, Monash University, VIC 3800, Australia, Australia

Received February 2005 Revised November 2005 Published April 2006

Abstract
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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.

Keywords: stochastic implied volatility, local volatility models., stochastic volatility, Black-Scholes formula.

Mathematics Subject Classification: Primary: 60G44, 60H30; Secondary: 91B28, 91B7.

Citation: Kais Hamza, Fima C. Klebaner. On nonexistence of non-constant volatility in the Black-Scholes formula. Discrete & Continuous Dynamical Systems - B, 2006, 6 (4) : 829-834. doi: 10.3934/dcdsb.2006.6.829

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