# Off-Peak Delta on Baseload Power Deals

#### by Richard Knight

This article provides an explanation for unexpected price exposure arising from a one-day power deal pricing from the monthly part of the forward curve.

Scenario

Deal : A one-day fixed px Baseload Pwr-Swap with settlement period 1d where the price is being stripped from the monthly part of the forward curve. The DeltaByLeg simulation result shows both Peak and Baseload exposure because for this part of the forward curve, the off-peak curve formula is based on monthly gridpoint tenor whereas my deal (although stripping a monthly price) is just for a single day. This means that when the delta exposure is calculated using the off-peak formula, both peak and base delta are calculated.

Explanation

Since there are 12 peak hours per day, Monday thru Friday, on average about 35% of the hours in a month will be peak and 65% offpeak.
The offpeak price price on the curve is then being calculated from the formula:
baseload_price = 0.35*peak_price + 0.65*offpeak_price
offpeak_price = (baseload_price – 0.35*peak_price) / 0.65
= (approx) 1.5*baseload_price – 0.5*peak_price

For a weekday (12 hours peak and 12 hours offpeak), the average price for the day will be:

avg_price = (12*peak_price + 12*offpeak_price) / 24
= 0.5*peak_price + 0.5*offpeak_price
= 0.5*peak_price + 0.5*(1.5*baseload_price – 0.5*peak_price)
= 0.25*peak_price + 0.75*baseload_price
which results in the delta values seen.

For a weekend or holiday (24 offpeak hours) the price for the day would be:
avg_price = off_peak_price
=1.5*baseload_price – 0.5*peak_price

so you will see deltas corresponding to the 1.5 and -0.5 factors.

In summary, you can expect to see odd delta values for a forward month whenever you have this combination of a formula-derived offpeak price and a non-full month schedule on the deal. This is because you never have a single day in which the distribution of hours in the day by priceband matches the distribution of hours in the month by priceband. While not intuitive, these values are mathematically consistent given the scenario.