Modeling Electricity Futures Risk Premiums Before Their Peak
Summary
The document describes a forecasting problem for electricity futures, where delivery spans a period rather than occurring on a single date. It explains that the usual spot-and-carry pricing relationship does not capture the observed risk premium, which is described as changing nonlinearly with contract maturity: it rises, reaches a peak, then falls toward delivery. The author asks how to forecast contracts whose premiums have not yet peaked.
The author reports that ARIMA models with no differencing or first differencing did not represent this turning point, and wonders whether fitting only the rising segment and reflecting it could help. They also explain that the input series consists of daily geometric returns, whose cumulative products are applied to the latest price. Illustrations are mentioned but no data or quantitative evaluation is supplied. The document is an open modeling question rather than a tested forecasting method; its proposed half-curve construction is speculative, and the premium’s shape may require a model that explicitly represents maturity and turning points.
Key ideas
- Electricity futures deliver power over a period, so standard point-delivery futures pricing may not describe their risk premium.
- The described premium rises with maturity, reaches a peak, and declines toward zero at contract maturity.
- The author reports that ARIMA specifications with zero or one order of differencing did not capture the observed inflection.
- The proposed approach of fitting the rising portion and mirroring it is a hypothesis, not a demonstrated solution.
- The model input is daily geometric returns, compounded to project from the latest observed price.
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Full text
# Electricity Futures Risk Premiums With ARIMA # Electricity Futures Risk Premiums With ARIMA I am attempting to model long-term electricity prices using today's futures prices. Unlike most futures, electricity is delivered over a period of time (usually a month), rather than at a point in time (a date). The traditional futures equation of F = S * exp(t*(r + u - y)) breaks down here. Rather, the industry refers to the disparity between the theoretical price of electricity using our traditional equation and the actual futures price of electricity as the risk premium, which is concave with respect to time: the premium increases for long-dated contracts, peaks, and finally declines until it reaches zero at contract maturity. Consequently, my attempts to model this situation using ARIMA with d=0 or d=1 has failed, as neither picks up that inflection. But I suspect that would be the case with d=2 as well, unless that inflection has already occurred during the training sample. My question is the following: how can I model the evolution of that risk premium for contracts whose risk premia have not yet peaked? Thank you for your assistance. Monotonic increase of December 2026 Futures as of late January 2021 (legend shows values at various confidence levels): Monotonic decrease in February 2021 contract settlements as of late January (legend showing similar confidence levels) Edit 1: I cannot attach sample data, but the included images illustrate the issue I'm facing: at some point the increasing function should inflect; I assume the way to do that is to somehow "tell" the program that the data I'm fitting to the model are only in the increasing portion -- i.e., fit half a parabola to the data and then mirror that increase to the downside. Edit 2: I should add that I have passed daily geometric returns, i.e., y(t) / y(t-1) into the ARIMA model, and than applied their cumulative products to the last observed prices. This gives the model a first-order (not arithmetic) integration by default.
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