VaR for Stationary Electricity Prices and Mean-Reverting Paths

Summary

The document considers whether stationary electricity futures prices can be simulated directly from a fitted distribution to estimate value at risk, or whether a multi-step simulation is needed. It distinguishes a one-horizon risk estimate from a path-dependent, multi-period analysis: simulating a single future point may be sufficient when only that point matters, while multiple dates require modeling the dependence between observations.

The response cautions that stationarity established by an Augmented Dickey–Fuller test does not settle the modeling question. Power prices may have changing volatility, potentially increasing with price, so volatility dynamics should be modeled, for example with an exponential GARCH specification or a suitable power-price volatility model. Strong mean reversion can also make successive prices dependent and negatively serially correlated, meaning independent draws from one distribution would misrepresent a multi-step path. The advice is qualitative and offers no fitted model or empirical validation for the particular series.

Key ideas

• A stationarity test alone does not establish that a price distribution is adequate for risk modeling.
• A single simulated horizon can support VaR when only one future date is relevant.
• Multi-period risk requires modeling serial dependence rather than drawing every date independently.
• Electricity prices may require explicit treatment of changing volatility and mean reversion.

Tags

# Do stationary prices need to be differenced for VaR?


# Do stationary prices need to be differenced for VaR?












I have a time series of electricity futures prices that I have shown to be stationary via the Augmented Dickey Fuller test (alpha = 0.05). Does that mean that, in calculating their individual values-at-risk, I can just simulate a set of prices based on the distribution that best fits them -- and then report the nth percentile on those simulations? In other words: is essentially a one-step simulation the same thing as an n-step simulation when directly modeling a stationary underlying?

Thank you.

## Answer by kurtosis (score 2, accepted)

https://quant.stackexchange.com/a/57093

I worry that power prices are very unlikely to be stationary.

It is possible the mean does not vary wildly over time, and the price process may not be integrated, i.e. prices may not require differencing. However, prices (or returns) almost surely require correcting for heteroskedasticity.

If you have a powerstack function estimated, perhaps you could use that to predict volatility. Otherwise, you could use an exponential GARCH model (since commodity prices get more volatile as price rises).

Regarding your last question: if you only care about one point in time, then you can just simulate that one point in time. If you care about multiple points in time, however, you cannot pull all of them from the same distribution -- since prices tend to be strongly mean reverting. That would make your $n$ samples negatively serially correlated.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.