Hedging Strategy and Electricity Contract Engineering - IFOR

F Û 0Ü 3Ý
í
è
F Û 0Ü 1Ý?Ü í xë3
í x ì1 á
6.6 Power portfolio optimization with CVaR 153
Future price
+
F(0,3)
*
F(0,7)
*
F(0,5)
*
F(0,1)
*
2 3 4 5 6 7
' ( ) & % $ 1#
Period
"
Fig. 6.5: Illustration of ’arbitrage’ between futures with pumping capacity.
The relative difference between the future price in the first off-peak period
Û 0Ü 1Ý F and in the first peak period Û F 0 3Ý is according to (6.46) big enough to
offset the non-perfect efficiency of the pump è á . If the optimal dispatch in period
3, where no pumping is xú é allowed p max , and if there is enough capacity
in the dam to swallow the pumped up water, then pumping will be conducted
in period 1. This water will then be stored and used for production in period 3,
adding the following deterministic profit
í xë3
x ì1
(6.47)
Since the transaction does not involve any risk and according to the assumption
(6.46), the value in (6.47) will be strictly positive, this does fulfill the
definitions of arbitrage (see Definition 3.6). The optimal choice í of xë3
and
í hence x ì1 will be given by max p max xú?Ü p min Ý , since one naturally wants
to maximize this risk free profit. From (6.46) we note that between the second
off-peak and second peak period, no such ’arbitrage’ strategy exists, since
Û
the relative price difference between Û 0Ü 5Ý F and Û 0Ü 7Ý F simply is too low
compared to the efficiency of the pump.
We can now draw two conclusions. Firstly, if hourly futures do exist, the value
of pumping ! ! will be given by the optimal combination of such arbi-