Modeling Electricity Returns When Prices Can Be Negative
Summary
The document raises a return-definition problem for electricity prices, which may fall below zero. Log returns based on the ratio of consecutive prices are then undefined in some observations. The questioner has used price differences as a substitute and asks whether a better approach is available for modeling GARCH volatility.
One answer proposes adding posted exchange collateral to the price before taking a logarithm, with the previous day’s collateral used in both terms. It notes that collateral requirements would need to be large enough to keep the adjusted value positive and suggests calibrating those requirements. Another answer mentions a hyperbolic-sine transformation as an alternative, without elaborating on its properties. These are suggestions rather than a comparison or validated recommendation: the post gives no empirical results, calibration procedure, or discussion of how transformations affect interpretation and volatility estimates. The choice depends on the market’s settlement and collateral mechanics as well as the modeling objective.
Key ideas
- Log price-ratio returns are undefined when either electricity price is nonpositive.
- Price differences avoid that domain problem but change the scale and interpretation of the modeled series.
- An answer proposes adding posted collateral to prices before calculating log returns.
- A hyperbolic-sine transformation is also suggested, but neither approach is evaluated with data or a calibration method.
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Full text
# How do you define returns when price may be negative (electricity price)?
# How do you define returns when price may be negative (electricity price)?
I'm trying to model GARCH volatility on electricity prices. Typically the first step is to use prices to obtain log returns to make them stationary. I have encountered a small problem however: electricity prices can go negative. So returns defined as
\begin{array}{cc} r_t:=\log(P_t / P_{t-1}) \end{array}
will produce some undefined values. I have gotten around it by using differences
\begin{array}{cc} r_t:=P_t - P_{t-1}, \end{array}
but I'm wondering if there is a better method out there.
## Answer by Mats Lind (score 1)
https://quant.stackexchange.com/a/85549
Trying to post my suggestion as an Answer: To make your asset have positive value, include the collateral you have to post on the exchange where you trade it. As long as daily collateral requirements on the exchange turn out to be large enough, you will have a defined value of returns and the exchange does not have to face losses on your behalf. \begin{array}{cc} r_t:=\log((P_t+Col_{t-1} )/ (P_{t-1}+Col_{t-1})) \end{array} edit: Google's AI bot includes this in its suggestions, however without reference to collateral requirements. Since the question concerns a modelling problem starting from a time-series of prices, may I also suggest that a working method for calibrating daily collateral requirements could be part of that excercise?
## Answer by Qbik (score 0)
https://quant.stackexchange.com/a/32092
are hyperbolic sine transformation, could also not to take log of p(t)/p(t-1),
https://mpra.ub.uni-muenchen.de/29958/1/MPRA_paper_29958.pdfShown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.