One identity turns two quoted forwards into the third price, and the hour count decides whether it is right.
The off-peak price is whatever is left of the baseload value once the peak hours are paid for: baseload times all hours, less peak times peak hours, divided by the off-peak hours. With an illustrative calendar 2027 baseload at 85.00 and peak at 98.00, and 3,132 peak hours out of 8,760, the implied off-peak price is 77.77 per MWh, not the 72.00 a simple average gives.
Worked in full in Energy Trading by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Peak here is the block from 08:00 to 20:00, Monday to Friday, public holidays included, which is the convention of the main German exchange product. Other markets cut the day differently, and the hour count is the first thing to check. Prices are illustrative, in euros per MWh; they are not market quotes.
| Input | Value |
|---|---|
| Baseload forward, per MWh | 85.00 |
| Peak forward, per MWh | 98.00 |
| Days in the year | 365 |
| Weekdays | 261 |
| Hours in the year | 8,760 |
| Peak hours (261 × 12) | 3,132 |
| Off-peak hours | 5,628 |
A baseload contract delivers 1 MW in every hour of the year, so it is a peak contract plus an off-peak contract. Its value must equal the sum of the two, hour-weighted. That single identity gives the off-peak price.
Baseload value of 1 MW = 85.00 × 8,760 = 744,600
Peak part = 98.00 × 3,132 = 306,936
Off-peak part = 744,600 − 306,936 = 437,664
Off-peak price = 437,664 / 5,628 = 77.77
Excel: =(Base*Hours-Peak*PeakHours)/(Hours-PeakHours)
Check it back: 98.00 on 35.75 per cent of the hours and 77.77 on the rest average to 85.00. The peak sits 20.23 above off-peak; as ratios, peak is 1.153 times base and off-peak 0.915 times.
The identity works for any delivery period, not only the calendar year: a quarter, a month or a week, each with its own hour count. Do it period by period rather than deriving a monthly off-peak from annual ratios, because the peak premium is seasonal and the share of peak hours moves with the number of weekdays in the month. And because off-peak is a residual, it carries the errors of both quoted prices: a bid-offer spread of a few tenths on peak shows up, scaled by the hour ratio, in the implied off-peak price.
A supplier's customer draws 60 MW in peak hours and 35 MW off-peak. The standard hedge is 35 MW of baseload, which covers every hour at the lower level, plus 25 MW of peak on top.
| Product | MW | Hours | Price | Cost |
|---|---|---|---|---|
| Baseload | 35 | 8,760 | 85.00 | 26,061,000 |
| Peak | 25 | 3,132 | 98.00 | 7,673,400 |
| Hedge | 87.64 | 33,734,400 |
The customer consumes 187,920 MWh in peak hours and 196,980 off-peak, 384,900 MWh in all, at an average hedge cost of 87.64. Priced the other way, peak MWh at 98.00 and off-peak MWh at 77.77, the total is the same 33,734,400: base and peak, and peak and off-peak, are two descriptions of one set of prices. The shaped load costs 2.64 per MWh more than baseload, a 3.1 per cent premium, because it takes more of its energy in the expensive hours. That is before the within-block shape, which is a separate cost.
The same decomposition reads a position report. A desk long 100 MW of calendar baseload and short 100 MW of calendar peak shows a net 562,800 MWh long. In hours it is flat in every peak hour and 100 MW long in every off-peak hour, so a 1.00 move in the off-peak price, not the baseload price, moves it by 562,800.
Hold baseload at 85.00 and move the peak forward. The off-peak price falls by 0.56 for every 1.00 on peak, the ratio of peak to off-peak hours.
| Peak | Peak / base | Off-peak | Simple average reading | Error | Hedge cost per MWh |
|---|---|---|---|---|---|
| 88.00 | 1.035 | 83.33 | 82.00 | 1.33 | 85.61 |
| 92.00 | 1.082 | 81.10 | 78.00 | 3.10 | 86.42 |
| 98.00 | 1.153 | 77.77 | 72.00 | 5.77 | 87.64 |
| 104.00 | 1.224 | 74.43 | 66.00 | 8.43 | 88.87 |
| 110.00 | 1.294 | 71.09 | 60.00 | 11.09 | 90.09 |
The error of the shortcut grows with the peak premium, so it is smallest when nobody would check and largest in the markets where solar and evening ramps have made the shape matter most.
Treating baseload as the simple average of peak and off-peak, which gives off-peak as twice base less peak: 72.00 here. That is only true if peak and off-peak have the same number of hours, and they do not: off-peak has 5,628 hours against 3,132. A second route to the same wrong answer is counting peak as twelve hours on every day of the year, 4,380 hours, which makes the two blocks equal and also gives 72.00. Either way the off-peak price is understated by 5.77, and on the customer's 196,980 off-peak MWh that is 1,135,680 of hedge cost that the pricing sheet does not show. The way the shape inside each block then eats a fixed-price margin is worked in how much of a fixed-price retail margin the load shape takes.
The price duration curve behind the averages, with the book's eight rows of hours, is in the free workbooks for this book.
On the 08:00 to 20:00 Monday to Friday block, twelve hours times the number of weekdays. Calendar 2027 has 261 weekdays, so 3,132 peak hours and 5,628 off-peak hours out of 8,760. Other markets define peak differently, and a leap year or a year starting on a weekend changes the count, so compute it from the calendar each time.
Only weighted by hours. Baseload of 85.00 with peak at 98.00 implies off-peak of 77.77, because off-peak covers 5,628 hours against 3,132 for peak. The unweighted average would put off-peak at 72.00, an error of 5.77 per MWh that grows as the peak premium widens: 11.09 when peak is 110.00.
Buy baseload for the off-peak level and peak for the difference. A customer drawing 60 MW in peak and 35 MW off-peak is hedged with 35 MW of base and 25 MW of peak, costing 33,734,400 for 384,900 MWh, or 87.64 per MWh at 85.00 base and 98.00 peak. The shape inside each block still has to be priced separately.
This article is one calculation from Energy Trading. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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