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Dynamic Risk Management of Electricity Contracts with Contingent Portfolio Programming. Janne Kettunen, Ahti Salo, and Derek Bunn Systems Analysis Laboratory Helsinki University of Technology Management Science and Operations London Business School. Background and Motivation. - PowerPoint PPT Presentation
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1
Helsinki University of Technology Systems Analysis Laboratory
London Business SchoolManagement Science and Operations
Dynamic Risk Management of Electricity Contracts with
Contingent Portfolio Programming
Janne Kettunen, Ahti Salo, and Derek Bunn
Systems Analysis LaboratoryHelsinki University of Technology
Management Science and OperationsLondon Business School
Helsinki University of Technology Systems Analysis Laboratory
2
London Business SchoolManagement Science and Operations
Background and Motivation Background and Motivation Electricity market deregulation has increased competition and uncertainties Uniqueness of electricity market (Bunn, 2004)
– Non-storable, stakeholders bear price and load risk
– Correlation between price and load (exponentially increasing in load)
– Mean reversion
– Spikes and seasonal variations
– Volatility clustering
– High and volatile risk premiums in futures
How should an electricity generator or distributor hedge its risks using futures?
Requirements on model formulation– Correlation, arbitrage free, mean reversions, volatility clustering scenario tree (Ho, et. al., 1995)
– Risk management Conditional Cash Flow at Risk and risk constraint matrix (Kettunen and Salo, 2006)
– Path dependencies Contingent Portfolio Programming (Gustafsson and Salo, 2005
Helsinki University of Technology Systems Analysis Laboratory
3
London Business SchoolManagement Science and Operations
Scenario Tree with Two Example Paths HighlightedScenario Tree with Two Example Paths Highlighted
1
1
1 1
1 1
1 1 1 1
1 0 0 1
1
0
0
0
0
1
1 1
0 0
1 0 0 1
1 1 1 1
1 0 0 1
0 1
0 1
1 0 1 0
1 0
0 1
0 0
1 1
0 0 0 0
1 0 0 1
0 0
0 0
1 0 0 1
0 0 0 0
Time0 1 2
Ho, Stapleton, Subrahmanyam (1995), Peterson Stapleton (2002)
1,11
1,1
2 2,1 ,22
2 2,1 ,2
1 1 0 0, , ,
1 0 1 0
1 1 1 1 1 1 0 0, , ,...,
1 1 1 0 0 1 0 0
P
L
P P
L L
s
s
s s
s s
S
S
sp = spot pricesl = load
Helsinki University of Technology Systems Analysis Laboratory
4
London Business SchoolManagement Science and Operations
VAR Maximum LossCVARPortfolioloss
Probability
Probability 1-β
( , )
1( ) min ( , ) ( )
1 f
CVAR f p d
x y
x x y y y
f(x,y) = loss function y = uncertaintyp(y) = probability density function
β = confidence levelx = portfolio decision strategy = threshold value (=VAR)
(Rockafeller and Uryasev, 2000)
Conditional Value-At-RiskConditional Value-At-Risk
Helsinki University of Technology Systems Analysis Laboratory
5
London Business SchoolManagement Science and Operations
CCFAR can be derived from CVAR– A discrete CVAR – Portfolio loss framed using cash position beyond the threshold level ( )tRT CP s
( ) ( ) ( ( ) )t t ts p s RT CP s
( ) 0ts
, ( )
1( ) min ( )
1tt t
t
ss S
CCFAR X s
s.t.
Definitions
= threshold value (=CFAR at optimum)
= confidence level
X = portfolio decision strategy
p( ) = probability of scenario
RT = reference target amount
CP( ) =
t t
t
s s
s cash position in scenario ts
Conditional-Cash-Flow-At-Risk (CCFAR)Conditional-Cash-Flow-At-Risk (CCFAR)
Computation
(Kettunen and Salo, 2006)
Helsinki University of Technology Systems Analysis Laboratory
6
London Business SchoolManagement Science and Operations
Electricity Contract Portfolio OptimizationElectricity Contract Portfolio Optimization
Risk management constraints for conditionalcash flow at risk (CCFAR)
… cash position and trading constraints
such that,
Maximize expected terminal cash position
Helsinki University of Technology Systems Analysis Laboratory
7
London Business SchoolManagement Science and Operations
Electricity distributor: uncertain load and price and can use futures to hedge risks Price data (€/MWh) from Nordpool 1999-2005 and futures seen on 24.3.2006 Load data (GWh) from Finnish Energy Industries 1999-2005 (used 1% of actual)
– Conditional volatilities (fitting GARCH(1,1) for filtered data)
– Premiums (fitting linear equation)
– Mean reversions cP=0.2 and cL=0.4 (fitting linear equation)
– Correlation: N=0.08 and λ=0.1 (fitting linearized version of )
– Risk free interest rate 2%
– Trade fee 0,03€/MWh
Computational ExperimentsComputational Experiments
Helsinki University of Technology Systems Analysis Laboratory
8
London Business SchoolManagement Science and Operations
Comparison of Contingent Optimization, Periodic Comparison of Contingent Optimization, Periodic Optimization and Fixed Allocation Methods Optimization and Fixed Allocation Methods
5,6% cost reduction
Figures in million euros
Helsinki University of Technology Systems Analysis Laboratory
9
London Business SchoolManagement Science and Operations
Uncertainty in Premium and CorrelationUncertainty in Premium and Correlation
Risk averse player
Competitive player Figures in million euros
Helsinki University of Technology Systems Analysis Laboratory
10
London Business SchoolManagement Science and Operations
Uncertainty in Premium and CorrelationUncertainty in Premium and CorrelationNo correlation vs. correlation
Risk averse player
Competitive player Figures in million euros
Helsinki University of Technology Systems Analysis Laboratory
11
London Business SchoolManagement Science and Operations
Uncertainty in Mean Reversion and Volatility of LoadUncertainty in Mean Reversion and Volatility of Load
Risk averse player
Competitive player Figures in million euros
Helsinki University of Technology Systems Analysis Laboratory
12
London Business SchoolManagement Science and Operations
Uncertainty in Mean Reversion and Volatility of Spot PriceUncertainty in Mean Reversion and Volatility of Spot Price
Risk averse player
Competitive player Figures in million euros
Helsinki University of Technology Systems Analysis Laboratory
13
London Business SchoolManagement Science and Operations
Expected Cost with 6 Weeks and 4 Weeks 95% Expected Cost with 6 Weeks and 4 Weeks 95% CCFAR ConstraintsCCFAR Constraints
Competitive playerRisk averse player
B
CCFAR6wks,95%<€0.6M
Figures in million euros
Helsinki University of Technology Systems Analysis Laboratory
14
London Business SchoolManagement Science and Operations
Model– Correlation important to include
– Optimal strategies robust (remain close to efficient frontiers)
– Contingent optimization consistently more efficient than periodic optimization or fixed
allocation methods
Risk management perspective– Competitive player: most concern about price related uncertainties
– Risk averse player: most concern about premiums
– Both players bear load related risk (swing-option contracts)
Conclusions 1/2Conclusions 1/2
Helsinki University of Technology Systems Analysis Laboratory
15
London Business SchoolManagement Science and Operations
Standard risk management intuitions supported– Increase in volatilities increase risks
– Decrease in mean reversions increase risks
– Increase in premiums increase cost
Risk constraint matrix for concurrent time periods and confidence levels– Re-run model when new information arrives (rolling horizon)
– Regulatory requirements
– Financially tight situation
Conclusions 2/2Conclusions 2/2