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Dummy Power Forward Curve

©N.Rouveyrollis 2009

Forward curve models for electricity market may be managed using sophisticated approaches involving a multitude of parameters. As a simple first insight, here we will present a simple rule of thumb for building in a straightforward way a seasonal Power Forward Curve involving only the choice a shape factor given by the market and preserving the non arbitrage splitting condition. Basically, this procedure can be easily implemented for the initial guess rule when considering more sophisticated model prior calibration.

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Electric Models

There are some recurrent key words in academic littérature surrounding electricity markets & prices, and top ranking is

Non storability Spikes and Variability Clustering Seasonnal Patterns every where Possible zero or negative price level (but very rare)

As a direct consequence : a very quantitative and attractive challenge and a large variety of models with nice sophisticated mathematics.

Most of them : focus on spot price (i.e. short dated Day-Ahead future price) and many times hourly granularity is not considered (just focus on the average daily price … cheers !)

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The Day-Ahead Present

And now comes the stupid question : is a sophisticated spot price model really usefull ?

Surely if you are able to hedge and manage the spikes Surely on a short time horizon (namely the BoM) for the physical

scheduling and management Surely if your trader’s will buy several Power Plants on the spot

market

Not sure if your core business is not the physical management Not sure if you have no skills in hedging the spikes and your risk

manager have restricted the spot business on a couple of MWh Not sure if you will be globally short on spot markets

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The Future

Forward market used to be great places for traders since the stone age of finance

Modelling forwards is indeed fundamental since it represents the biggest volumes on electricity markets.

In particular a very popular product is the physical power swap allowing you to buy some electricity over a given period at a fixed price

There are many monthly maturities availables on OTC and OTC clearing can be available for you convenience.

Given the incredible spot price dynamic, maybe you will decide bringing brightness to forward markets with sophisticated models and nice numerical methods for modelling the forward curve ?

……..

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Modelling the Future

For the purpose of pricing the most liquid instruments (swaps), do you think a model like the one below

will be easily calibrated on this yearly available curve ?

Sure a model should be an approximation of the real world, but it does not suppose bringing to much sophistication of it at the trading floor ………….

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The Dummy Challenge

…. in particular if the trading desk is a vanilla one.

Focus on the core power business, since there is no deep liquidity for non linear payoff, and good one for linear ones (swap in particular), the quantitative challenge becomes reduced :

From now, let assume Trading Desk wants to deal with monthly swaps

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The Imcomplete Market for data

Let’s have a look at available market datas, typically only a couple of maturities available : a couple of months, some quarters and a limited number of calendar prices

Typically you need to build a monthly forward curve, and if you can do it, you will generalize the procedure for the granularity of your dreams (the half hourly one ?)

You simply need to transform calendar into quarter and quarter into month

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The non arbitrage condition

Before stepping into the splitter, must be recalled the non arbitrage condition : you cannot split a period into sub period and generate arbitrage ….

Eg : considering a quarter Q and its 3 months (M1, M2 & M3), let assume n1, n2 and n3 the number of hours for each months, in this case, denoting by P(.) the price function, we have the simple relation :

Price for P(Q) =(n1.P(M1) + n2.P(M2) + n3.P(M3) ) / (n1+n2+n3)

The non arbitrage condition is simply an aritmethic average rule

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The Splitter

Finally a simple splitting procedure for a given observed average price P (quarterly or yearly) will consist in :

Choosing a shape factor for the granularity

eg : a monthly shape factor for an observed quarter, year ….

Compute the average level from this shape factor L

Compute the ratio convertion R = P/L

Apply this ratio to the shape factor for getting your granular pattern

Now the question is choosing the best shape factor … the answer : OTC

markets or cointegrated market with much more availables maturities (eg EEX vs Powernext )

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Simple Example

Initial French Power Forward Curve

+ German EEX Power Curve Monthly Factor