Choosing Return Measures for Negative Electricity Prices
Summary
The discussion asks how to estimate historical volatility when electricity prices can be negative, making log returns undefined for some observations. It explains that the return measure should follow the assumed model: absolute price changes suit a model with normally distributed changes, while log returns are associated with a lognormal price model. The example of a move from a positive price to a negative one illustrates why the usual log-return calculation fails.
One response cautions that lognormal geometric Brownian motion may be a poor fit for power spot prices because it cannot represent negative prices and may not capture spikes, mean reversion, strong periodic patterns, or limits on hedging small products. Another response proposes a simple ratio-based return, but that expression also breaks when the previous price is zero and can be hard to interpret around negative values. The thread offers modeling considerations rather than a tested volatility estimator or a consensus method; the appropriate choice depends on the product and the pricing model.
Key ideas
- The return definition should match the assumed process for the underlying price.
- Log returns are unsuitable when prices are zero or negative.
- Normally distributed absolute changes imply modeling price changes directly rather than assuming lognormal prices.
- Power spot prices may exhibit spikes, mean reversion, periodicity, and hedging limits that a basic lognormal model misses.
- A simple ratio return does not resolve cases where the prior price is zero or negative.
Tags
Full text
# How to calculate return rates with negative prices?
# How to calculate return rates with negative prices?
I'm dealing with electricity options and I'm considering the possibilty of negative prices. I want two estimate the historic volatility. However, an arithmetic mean doesn't feel appropriate and $\log(\frac{P_i}{P_{i-1}})$ doesn't work if $P_{i-1}$ is less or equal than 0.
For example:
20th July: $P_1$= 24 euros/MWh 21st July: $P_2$= -70 euros/MWh
what do you suggest to properly calculate the return rate? what is the correct interpretation?
## Answer by Christian Fries (score 3)
https://quant.stackexchange.com/a/8546
The answer depends on what model you assume for the underlying. The situation, that the underlying can become negative also occures for interest rate spreads and even for interest rates. Here some people use absolute changes, that is $X_{i} - X_{i-1}$ instead of relative changes $\frac{X_{i} - X_{i-1}}{X_{i-1}}$ or (which is almost the same as relative returns) log-returns $\log(\frac{X_{i}}{X_{i-1}})$
If you model the return as normal distributed, you are assuming that your underlying is log-normal. Hence you estimate vol from log-returns.
If you model the absolute changes as normal distributed, you would estimate the historic vol from absolute changes.
Since you are speaking of options and vol, you should know what your model assumption is.
PS: More details on this can also be found in http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2194917
## Answer by airguru (score 1)
https://quant.stackexchange.com/a/8554
Abandon the idea to use lognormal (GBM) model for power spot market. Just don't do it. Spot power prices have totally different properties and Black-Scholes option prices will not make any sense. They won't be even remotely close to the correct option value!
Just a list of things that lognormal model does not capture and that are important for option pricing:
- Negative prices
- Price spikes (stochastic volatility)
- Mean reversion
- Strong periodicity (daily, weekly, yearly)
- Impossibility to hedge small products for sufficiently long time
## Answer by Hebe (score -1)
https://quant.stackexchange.com/a/8544
In this case,you shouldn't use log return.You should calculate return as (P(i)/P(i-1))-1.Shown 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.