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Dynamic Risk Management of Electricity Contracts with Contingent Portfolio Programming

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.

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Dynamic Risk Management of Electricity Contracts with Contingent Portfolio Programming

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  1. Dynamic Risk Management of Electricity Contracts withContingent Portfolio Programming Janne Kettunen, Ahti Salo, and Derek Bunn Systems Analysis Laboratory Helsinki University of Technology Management Science and Operations London Business School

  2. 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

  3. Time 0 1 2 Scenario Tree with Two Example Paths Highlighted sp = spot price sl = load Ho, Stapleton, Subrahmanyam (1995), Peterson Stapleton (2002)

  4. Probability Probability 1-β Portfolio loss VAR CVAR Maximum Loss Conditional Value-At-Risk (Rockafeller and Uryasev, 2000) f(x,y) = loss function y = uncertainty p(y) = probability density function β = confidence level x = portfolio decision strategy  = threshold value (=VAR)

  5. Conditional-Cash-Flow-At-Risk (CCFAR) • CCFAR can be derived from CVAR • A discrete CVAR • Portfolio loss framed using cash position beyond the threshold level Computation Definitions s.t. (Kettunen and Salo, 2006)

  6. Electricity Contract Portfolio Optimization Maximize expected terminal cash position such that, Risk management constraints for conditional cash flow at risk (CCFAR) … cash position and trading constraints

  7. Computational Experiments • 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

  8. 5,6% cost reduction Comparison of Contingent Optimization, Periodic Optimization and Fixed Allocation Methods Figures in million euros

  9. Risk averse player Competitive player Uncertainty in Premium and Correlation Figures in million euros

  10. Uncertainty in Premium and Correlation No correlation vs. correlation Risk averse player Competitive player Figures in million euros

  11. Risk averse player Competitive player Uncertainty in Mean Reversion and Volatility of Load Figures in million euros

  12. Risk averse player Competitive player Uncertainty in Mean Reversion and Volatility of Spot Price Figures in million euros

  13. CCFAR6wks,95%<€0.6M Risk averse player B Competitive player Expected Cost with 6 Weeks and 4 Weeks 95% CCFAR Constraints Figures in million euros

  14. Conclusions 1/2 • 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)

  15. Conclusions 2/2 • 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

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