# Modeling electricity prices ($/kWh) for Simulation I want to run a Simulation in Matlab that involves the running costs of an electronic device which consists of the power consumption of this said device. The simulation should run for the next 1-5 years. Since the (daily/monthly/yearly) \$/kWh electricity prices are not constant over time, my thought was to model them using a stochastic process which captures the changes over time. I want to calibrate the parameters of said stochastic process using historical data of $/kWh electricity prices. Upon my research I found a lot about the modeling of electricity spot prices (e.g. Comparison of Electricity Spot Price Modelling and Risk Management Applications), but from my understanding (and please correct me if I am wrong) electricity spot prices do not reflect/represent \$/kWh electricity prices that I need for the running costs calculations. The explanations about mean-reverting models in different paper of spot price modeling are sound, however I am yet to find something that models \$/kWh electricity prices. I even thought about using Geometric Brownian Motion to simulate it, but in my opinion this would not fit. Can someone point me in the right direction to a stochastic process that is frequently used to model$/kWh electricity prices and that can be used in my simulation?

• Hi. One way of conveying a solution to your problem, is to figure out the stylized facts of $/kWh electricity prices. Then you can find a model that accomodates for some of these stylized returns (eg. seasonality, stationarity and mean-reversion). – Pleb Dec 28 '20 at 10:21 • Am not sure if you're the same person as the previous asker of a question like this (it now says 404 not found). But i asked there - what exactly do you care about - given it's running costs, i'm guesing base/peak load averages. Will you be consuming power 24/7? or do you have some flexibility to consume it during cheaper (i.e. baseload) hours? – will Dec 28 '20 at 11:57 • And another question actually, which may significantly simplify things - why do you want to model it stochastically? Do you have some level at which it stops being profitable to run your device such that you'll turn it off? As if your payout is linear as a function of electricity cost, then you can just use the expected future cost. – will Dec 28 '20 at 12:00 • @will Yes, for simplicity reasons I will be consuming power 24/7. To give you a better idea about this: this is about running a bot on a computer. The bot will make revenues but yields to power consumption costs. I was thinking about running the simulation e.g. 100000 times, the final result (i.e. the average of all simulation runs) should then tell me if it was profitable or not. This simulation should then help make a decision whether running the bot would be profitable or not. – Arely Dec 29 '20 at 8:14 • @will The reasoning to model it stochastically was that the$/kWh electricity price varies over time and is not constant. To reflect those changes I thought about using a stochastic process. Similar as to stock prices which are not constant over time and therefore are modelled e.g. to follow a GBM. – Arely Dec 29 '20 at 8:16