Hedging Strategy and Electricity Contract Engineering - IFOR

R
P
3.6 Multi period risk management 65
max
n g z†m‡
J g j †ˆ‡
x†ˆ‡
s.t.
1
J
J
1
J
1 x G y jV
j… lS d L J j… 1 z j
H 1I
z j G x y RŒG jV lS z j 1G j 0G
C
G J.
(3.5)
P?P@P
If X is a polyhedral set, i. e. if the constraints are built up from a set of linear
inequalities, then the general constraint x X can be added to the above problems
without losing the linear feature. The two problems (3.4) and (3.5) deliver
the same solution if C is chosen to correspond to R and they will both be used
in this work. The former for determining hedging strategies and the latter for
portfolio optimization.
3.6. Multi period risk management
The risk management models used in the industry basically all measure the
risk today over a specified horizon. This horizon is, as mentioned, typically
determined by the time it takes to liquidate the positions. In some industries,
such as the electricity and the freight industry, this liquidation time can be
substantial. Especially for long time horizons the question arises if one, by
measuring the potential losses only at the end of the horizon, may underestimate
the risk prior to the time horizon.
Let current time be t, the time horizon be T and the risk over the whole period
be denoted by r S tG T V . More formally the question can be restated if the intermediate
risks r S t GuuV for any tG T may exceed the end horizon risk r S t G T V .
One approach to cope with the non-static nature of risk and avoid to miss any
information about the riskiness of a portfolio by only measuring the risk over
the whole period tG T would be to define the overall risk as
RS tG T V
Ž max r t T
GukV S tg †>
It should be noted that for portfolios with normally distributed returns, (i. e.
where the underlying price process follows a geometric Brownian motion)