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

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

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.

Suggested Citation

  • L. C. G. Rogers & S. E. Satchell, 2000. "Does the behaviour of the asset tell us anything about the option price formula? A cautionary tale," Applied Financial Economics, Taylor & Francis Journals, vol. 10(1), pages 37-39.
    • Handle: RePEc:taf:apfiec:v:10:y:2000:i:1:p:37-39
    DOI: 10.1080/096031000331905
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    Cited by:

    1. Max Stevenson, 2001. "Filtering and Forecasting Spot Electricity Prices in the Increasingly Deregulated Australian Electricity Market," Research Paper Series 63, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Winsen, Joseph K., 2010. "An overview of project finance binomial loan valuation," Review of Financial Economics, Elsevier, vol. 19(2), pages 84-89, April.
    3. Damiano Brigo & Fabio Mercurio, 2008. "Discrete Time vs Continuous Time Stock-price Dynamics and implications for Option Pricing," Papers 0812.4010, arXiv.org.
    4. Joseph K. Winsen, 2010. "An overview of project finance binomial loan valuation," Review of Financial Economics, John Wiley & Sons, vol. 19(2), pages 84-89, April.

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