Hedging Strategy and Electricity Contract Engineering - IFOR

3.4 Traditional risk management models 51
management models can however give some insight into the challenges that the
electricity market is facing.
3.4.1. Risk measures
Whereas deterministic problems are characterized by ’real’ numbers, such as
costs or returns, stochastic problems are characterized by random variables.
Naturally it is this stochastic variability that adds the risk component to the
problem. We know that risk should be managed, but a natural question is
how this risk should be measured. The simile taken from Gumerlock & Litterman
[GL98] exemplifies the problem of how to measure risk:
Leaving aside risk for a moment, consider the measurement of human
size. Everyone knows qualitatively what large and small mean,
but life gets more difficult when we want to express size in a single
number. Either height or weight can be useful, depending on
the problem being addressed. Each metric is appropriate for a given
problem, and neither serves all purposes. Indeed, if one asks for a
definite answer to the question of which metric is the best measure
of size, the answer is that neither height, nor weight, nor a linear
combination of them is the best measure of size. The best measure
of size is the one most appropriate to the purpose for which it is
intended.
As with human size, the same problem arises when measuring risk. Actually
risk is too complex to characterize with one number. On the other hand,
management calls for a simple measure of risk, which should be easy to
interpret. One single number has therefore traditionally characterized risk.
A typical risk measure developed for this purpose is Value at Risk. Another
type of risk measure is variance, which however does not possess a natural
interpretation from a management point of view. On the other hand, it has
been derived from the utility maximizing agent theory as the risk measure that
would concern such an agent, of course under certain assumptions.
We will here present the traditional risk measure, variance, the quantile based
Value at Risk and the blunt stress test to give an idea of the variety of risk