Hedging Strategy and Electricity Contract Engineering - IFOR

Let lS x G y 1V?G
P
62 Risk management
available, especially not in the immature electricity market with its OTC
contracts. One is thus left with no choices, but to work with a non-analytical
estimation of CVaR. One can either work with historical simulation or Monte
Carlo simulation to estimate CVaR. In the former case one, once again,
faces the problem of lacking historical data and the only feasible approach is
probably to simulate the value of the often very complex portfolio with Monte
Carlo simulation, based on the chosen process for the underlying driver, e. g. a
mixed diffusion and jump process.
with increasing severity lS x G y 1V
intuitive estimator of CVaR with a confidence level c of
is then given by
proposed by [BLS00]
P@P?P
lS x G y JV be a sample of J losses of the portfolio x, ordered
G
lS x G y JV and let K S 1 c V J . An
P@PaP
1
K
K
lS x G y jV
1 j…
U d S xV
3.5.3. Optimizing with CVaR
Measuring risk is a passive activity. Simply knowing the amount of risk does
not provide much guidance on how to manage risk. Rather risk management
is a dynamic process and it requires tools to optimize the utilization of
risk. In this chapter we will describe such a tool, namely how a portfolio
can be optimized using the risk measure CVaR. The approach was developed
independently by Rockafellar & Uryasev [RU00] and Bertsimas et al. [BLS00].
With the motivation of CVaR as an appropriate risk measure in the electricity
market it is natural to introduce the notion of an optimal portfolio x solving
min
n
U d S xV
x†ˆ‡
s.t. lS E G YV x R,
(3.2)
where the risk, measured as CVaR with a confidence level c of is minimized,
subject to constraint, R on the expected profit. Or differently formulated