Cutting edge: Kriging smooth energy futures curves

Applying kriging to extract smooth curves from energy futures prices

The Nelson-Siegel curve and how to calibrate its parameters to a set of futures prices is recalled

A range of different approaches exists to extract a continuous curve of futures prices from market-observed prices. At Nymex, accessible futures prices for delivery of WTI crude oil are available every month over a time horizon up to several years. The Nelson-Siegel curve (see Nelson & Siegel (1987)) adopted from fixed-income markets is a way to derive a continuous curve of oil futures prices from such market data. It is a four-parameter family of curves, allowing for a long-term constant level, flexibility of backwardation and contango, as well as incoporating the possibility of humps along the futures curve. A drawback with the Nelson-Siegel curve is that it will not in general match the observed futures prices, but provide a best fit to data in a least-squares sense.

An alternative to Nelson-Siegel smoothing is to apply the technique of splines. Polynomial splines with seasonality was proposed in Benth et al (2007) to smooth power futures prices observed in the Nord Pool market. There, the futures contracts deliver power (financially) over a period of time rather than at a fixed settlement date. Other examples of energy markets where futures contracts settle over delivery periods are gas and temperature.

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• Topics
• Commodity derivatives
• Commodity futures
• Futures
• Natural gas
• Oil
• Quantitative analysis
• Term structure
• Energy
• Energy