Hedging Strategy and Electricity Contract Engineering - IFOR

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146 Power portfolio optimization
spot price in x spot
j kã
and scenario j
as in (6.33) we get the following loss function in period k
lÛ x Ü y j Ý k cë xëkã j
cì x ìkã j
m
c i x i 1 xi Ù X k
n
c i x i D kã jã i
S kã j x spot
j
Ü kã
iâ 2K ë
1
iâ m ë
1
where x denotes the decision variables, which in the static case is given by
Û x p Ü x c Ý , and in the dynamic case by Û õ Ü x c Ý . If we discount these periodic
losses and sum them up over the whole horizon, we get the overall loss function
in scenario j
lÛ x Ü y j Ý
K
kr
eì
cë xëkã j
cì x ìkã j
m
c i x i 1 xi Ù X k
n
c i x i D kã jã i
S kã j x spot
kã j
kâ 1
iâ 2K ë
1
iâ m ë
1
where r is a one-periodic continuously compounded discount rate. The
importance of the spot position x spot should not be underestimated. The profit
from the production is created here and also much of the risk arises from this
synthetic position. Actually all volume risk is modeled here.
Note that the positions are not closed at the end of the horizon. We assume
that the maturity of the futures and swing options do not exceed the horizon.
This assumption can easily be relaxed but, would introduce yet more notations,
since the contracts would need to be priced at the end of the horizon. Observe
further the great flexibility that our approach offers by working with scenarios,
and that essentially any contract can be modeled.
6.6.3. Static portfolio optimization
In this static optimization problem the goal is to find, except for the optimal
contract portfolio x c , the optimal production portfolio x p , given by