Modeling and Fitting Price Distributions

  • Nigel Da Costa Lewis
Part of the Finance and Capital Markets Series book series (FCMS)


Throughout the energy sector, risk managers, and analysts face the challenge of uncovering the price and return distributions of various products. Knowledge about the underlying probability distributions generating returns is used both in pricing models and risk management. The selected probability distribution(s) can have a significant impact on the calculated Value at Risk measure of a company’s exposure from trading floor transactions and in the use of derivative pricing tools. It is imperative that risk management metrics such as Value at Risk are calculated using a statistical distribution tailored to the specific characteristics of the energy product of interest. Fitting probability distributions by carefully analyzing energy price returns is an important, although often neglected, activity. This may be partly because the number and variety of distributions to choose from is very large. For a specific product such as the forward price of Brent Crude, or price return of an Electricity index, which of the dozens of distributions should we use? This chapter outlines the process by which the practicing risk manager can begin to answer this question. It starts by assessing the validity of a simple model based on the normal distribution. When normality fails we can adjust the percentiles of the normal probability distribution. If this does not appear to help we might select an alternative probability distribution or else consider a mixture of normal distributions.


Ordinary Little Square Maximum Likelihood Estimator Logistic Distribution Sample Standard Deviation Price Return 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Further Reading

  1. Aitchison, J. and Brown, J. A. C. (1957) The Log-normal distribution, Cambridge University Press, New York and London.Google Scholar
  2. Ascher, H. (1981) “Weibull Distribution vs Weibull Process,” Proceedings, Annual Reliability and Maintainability Symposium, pp. 426–31.Google Scholar
  3. Deb, P. and Sefton, M. (1996) The distribution of a Lagrange multiplier test of normality, Economics Letters, 51, 123–30.CrossRefGoogle Scholar
  4. Gumbel, E. J. (1954) Statistical Theory of Extreme Values and Some Practical Applications, National Bureau of Standards Applied Mathematics Series 33, US Government Printing Office, Washington, DC.Google Scholar
  5. Hahn, G. J. and Shapiro, S. S. (1967) Statistical Models in Engineering, John Wiley & Sons, Inc., New York.Google Scholar
  6. Johnson, N. L., Kotz, S., and Balakrishnan, N. (1994) Continuous Univariate Distributions Volume 1, 2nd edn, John Wiley & Sons, Inc., New York.Google Scholar
  7. Johnson, N. L., Kotz, S., and Balakrishnan, N. (1995), Continuous Univariate Distributions Volume 2, 2nd edn, John Wiley & Sons, Inc., New York.Google Scholar
  8. Lewis, Nigel Da Costa (2003) Market Risk Modeling: Applied Statistical Methods for Practitioners. Risk Books, London.Google Scholar
  9. Lewis, Nigel Da Costa (2004) Operational Risk with Excel and VBA: Applied Statistical Methods for Risk Management. John Wiley & Sons, Inc., New York.Google Scholar
  10. Urzúa, C. M. (1996) “On the correct use of omnibus tests for normality,” Economics Letters, 53, 247–51 (corrigendum, 1997, 54: 301).CrossRefGoogle Scholar

Copyright information

© Nigel Da Costa Lewis 2005

Authors and Affiliations

  • Nigel Da Costa Lewis

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