Does the behaviour of the asset tell us anything about the option price formula? A cautionary tale

L. C. G. Rogers and S. E. Satchell

Applied Financial Economics, 2000, vol. 10, issue 1, 37-39

Abstract: If Y = (Y 1,…,Y N) are the log-returns of an asset on succeeding days, then under the assumptions of the Black-Scholes option pricing formula, these are independent normal random variables with common mean and variance in the risk-neutral measure. If we can show empirically that Y does not have these properties in the realworld measure, does this mean that the Black-Scholes option pricing formula fails? It does not; as we show in this note, so long as the joint distribution of Y in the realworld measure has a strictly positive density, then the Black-Scholes option price formula may still be correct. We conclude that attempts to argue that the Black-Scholes formula must fail because observed log returns appear to be fat-tailed, or appear to have nonconstant volatility, or appear to have serial correlation are fallacious.

Date: 2000
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DOI: 10.1080/096031000331905

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