Hedging Strategy and Electricity Contract Engineering - IFOR

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3.7 Valuation models 73
formula can be derived. Instead the price can be calculated by numerical methods
and often Monte Carlo simulation is needed. The spot price is then sampled
under the probability measure Q, the derivative payoff in each scenario j X Tg j
calculated and discounted, whereby the derivative’s price “ t is given by the
expectation [CS00]
t
e I r H
T I tL
1
J
J
j… 1
X Tg j G (3.10)
assuming that J scenarios where sampled. The drawback of Monte Carlo
simulation is the computational time and a trader typically needs immediate
price information.
However the arbitrage free price in (3.6) and consequently (3.10) is because of
the incompleteness of the electricity market not unique. The only constraint
that can be put on the probability measure Q is that the arbitrage pricing
formula should resemble the current market prices. This however leaves a
large set of possible measures Q, why a wide range of derivatives prices can
be obtained. By definition, in an incomplete market replication of certain
contracts cannot be done, yet one could ask how can one replicate a payoff that
is equal to or greater than a given contract’s payoff in the cheapest possible
way. Such a trading strategy is called a minimum cost strategy for a given
payoff. The cost of such a strategy does according to [Nai95] give an upper
bound on the price of the contingent claim. A lower bound can be derived
similarly by taking the position of the buyer. For more information on pricing
in incomplete markets, see for example [KQ95] or [DS94].
A weakness of using a pricing model based on absence of arbitrage in the electricity
market is that it is based on the idea of building a replicating portfolio.
This is however, because of the non-storability, not possible if spot contracts
are considered as underlying. And we would like to stress that (3.6) and hence
(3.10) only make sense if replication is possible.