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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

Kais Hamza 1, and  Fima C. Klebaner 1,

1. 

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

Received  February 2005 Revised  November 2005 Published  April 2006

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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