Modeling and Fitting Price Distributions
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.
KeywordsOrdinary Little Square Maximum Likelihood Estimator Logistic Distribution Sample Standard Deviation Price Return
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