## Energy Pricing and Risk

It is a necessary consequence of power that it will never be possible to predict real time energy prices exactly. Even if an exact model could be found, there is too much uncertainty to the inputs to ever be precise. If we define risk as statisticians, that is as the sum-total of the uncertainty, then a discussion of energy pricing can not be had without simultaneously discussing risk. As such, we believe very strongly that **every pricing model must include an adequate measure of the uncertainty involved. **Furthermore, the use of confidence intervals pre-supposes a Gaussian distribution to the noise, a mistake that few traders make twice. At the very least, confidence intervals must be asymmetric to reflect the fact that energy prices are typically much more volatile to the upside. Ad hoc methods are useful insofar as they provide an accurate understanding of the risk, but they frequently have difficulty coping with the myriad scenarios that each new day presents. On the right and below we outline the results of a principled approach.

Above we show the simulations of the day ahead price against the real time price. As expected, the two are strongly correlated, with the most simulations falling in the 20-40 range in the day ahead. If we were to sample a different day it may be the case that the slope between these two exceeds one, in which case it would be a signal to buy. This plot gives us a good idea of the density of the predicted real time, and the predicted day ahead; it allows us to see that while the model for the day ahead is nearly Gaussian with a slight positive skew, the skew in the real time is substantial. Once again this aligns with our intuition, and provide a good sanity check that the prices of our model are not wholly unrealistic. Further confirmation would, of course, be required, but a failure here would prompt us to reconsider a fundamental aspect of the model rather than subject it to a costly backtest.

Above we have energy price predictions, along with uncertainty estimates derived by warping our error space. We point out a few artefacts of the plot. The day ahead price typically falls on or near the most likely price (that is, the region where the grey curves are most dense). Our trade price in this instance is slightly above that curve, to reflect the upside uncertainty. If we were to create multiple tranches, we could use the grey curves to keep our total risk (as measured by the uncertainty multiplied by the size) constant across the tranches. We notice also that during the morning peak the downside risk evaporates, this has an intuitive fundamental appeal as we are unlikely to see prices below the price that it costs a coal plant to run during the peak hours. Finally, we notice that a price escaped our simulations. This is to be expected, as we ran fewer than 100 simulations in order to make the plot more easily legible. Had we run one thousand or more the probability of a point falls outside of the bounds of the simulation becomes exceedingly unlikely.