Monte carlo simulation for energy risk management

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Monte carlo simulation for energy risk management

  1. 1. Monte Carlo Simulation for Energy Risk ManagementScotty NelsonJanuary 15, 2013 1
  2. 2. Outline of Talk• Background on Deregulated Power Markets  Regulated vs. Deregulated Power markets  Market Structure and Participants  Risk Exposures• Decision Making Under Uncertainty  Deterministic Analysis  Sensitivity Analysis  Monte Carlo Simulation  Optimizing the Decision Making Process• Monte Carlo Simulation  Model Specification  Model Estimation  Model Simulation  Calibration  Benchmarking
  3. 3. Analytics for Deregulated Power Markets• Business questions:  What is my portfolio worth? (valuation)  How much of my expected dispatch output should I sell into the forward market? (hedging)  How much money can I lose? (risk management)  What trades should I enter into so I can maximize my profits and minimize my risk? (portfolio optimization)
  4. 4. Background onDeregulated PowerMarkets 4
  5. 5. State of Deregulation Source: Department of Energy 5
  6. 6. Regulated vs. Deregulated Power Markets Regulated Setup Deregulated Setup Power (MWh) Generator LoadGenerator Load Payment ($) ISO 6
  7. 7. Risk Exposure to Power Price Movements Generator Load Payoff ($)Payoff ($) Power Price ($/MWh) Power Price ($/MWh)
  8. 8. Hedge Optimization 8
  9. 9. Decision MakingUnder Uncertainty 9
  10. 10. Decision Making Under Uncertainty• Risk Drivers  Deterministic scenario planning models  Sensitivity analysis  Monte Carlo simulation• Optimizing the Decision Making Process  Unconstrained Optimization  Constrained Optimization 10
  11. 11. Generation (MW) 100 200 300 400 500 600 700 0 1 5 9 13 17 21 25 29 33 37 41 45 49 Dispatch Optimization 53 57 61 65 69 73 77 81 generation 85 89 93 97 eprice 101 105 109 113 117 121 125 129 133 13711 141 145 149 153 157 161 165 0 30 40 50 60 70 80 10 20 90 100 Power Price ($/MWh)
  12. 12. Deterministic Planning Models• Deterministic planning models  Pro: o Simple  Con: o How to come up with assumptions? o Are these assumptions realistic? o Doesn’t acknowledge uncertainty o Can lead to biased decisions 12
  13. 13. $/MMBtu 0 1 2 3 4 5 6 7 8 9 10/1/2008 12/1/2008 2/1/2009 4/1/2009 6/1/2009 8/1/2009 10/1/2009 12/1/2009 2/1/2010 4/1/2010 6/1/2010 8/1/2010 10/1/2010 12/1/2010 2/1/2011 Historical Henry Hub 4/1/2011 6/1/2011 8/1/2011 10/1/2011 Historical versus expected – Henry Hub 12/1/2011 2/1/2012 Expected Henry Hub 4/1/2012 6/1/2012 8/1/2012 10/1/2012 12/1/201213 2/1/2013 4/1/2013 6/1/2013 8/1/2013 10/1/2013 12/1/2013
  14. 14. $/MWh 100 150 200 250 300 350 400 450 50 0 10/1/2008 12/1/2008 2/1/2009 4/1/2009 6/1/2009 8/1/2009 10/1/2009 12/1/2009 2/1/2010 4/1/2010 6/1/2010 8/1/2010 10/1/2010 12/1/2010 2/1/2011 Historical West Hub 4/1/2011 6/1/2011 Historical versus expected – West Hub 8/1/2011 10/1/2011 12/1/2011 2/1/2012 Expected West Hub 4/1/2012 6/1/2012 8/1/2012 10/1/201214 12/1/2012 2/1/2013 4/1/2013 6/1/2013 8/1/2013 10/1/2013 12/1/2013
  15. 15. 100 120 20 40 60 80 0 10/1/2008 12/1/2008 2/1/2009 4/1/2009 heat rate 6/1/2009 8/1/2009 10/1/2009 12/1/2009 2/1/2010 4/1/2010 6/1/2010 8/1/2010 10/1/2010 12/1/2010 2/1/2011 Historical Implied Heat Rate 4/1/2011 6/1/2011 8/1/2011 10/1/2011 12/1/2011 2/1/2012 4/1/2012 Historical implied heat rate versus expected implied 6/1/2012 Expected Implied Heat Rate 8/1/2012 10/1/201215 12/1/2012 2/1/2013 4/1/2013 6/1/2013 8/1/2013 10/1/2013 12/1/2013
  16. 16. Sensitivity Analysis• Sensitivity analysis  Pro: o Simple  Con: o How to create sensitivity scenarios? o Are these scenarios realistic?• In general the following does not hold, especially for nonlinear functions E[𝑓 𝑋 ] ≠ 𝑓(𝐸 𝑋 ) 16
  17. 17. Monte Carlo Simulation• Monte Carlo simulation  Pro: o Realistic representations of possible states of the world (this could actually happen) o Correlations are maintained o Can benchmark against actual price distributions  Cons: o Complex, slow 17
  18. 18. Optimizing the Decision Process• Given the prices, we want to optimize a decision process• Example:  European Call Option o Value a call option, value=max(P-K,0)  simple decision rule, if P>K then exercise, otherwise don’t o Decisions today don’t impact decisions tomorrow  Power Plant o Operational constraints  can’t turn on and off instantly o How to optimize the decision process, given that decisions today impact possible decisions tomorrow? o Answer is provided through dynamic programming 18
  19. 19. Generation (MW) 100 200 300 400 500 600 700 0 1 5 9 13 17 21 25 29 33 37 41 45 49 Dispatch Optimization 53 57 61 65 69 73 77 81 generation 85 89 93 97 eprice 101 105 109 113 117 121 125 129 133 13719 141 145 149 153 157 161 165 0 30 40 50 60 70 80 10 20 90 100 Power Price ($/MWh)
  20. 20. Monte CarloSimulation 20
  21. 21. Monte Carlo Framework- Model Specification - Specify a model of the fundamental risk drivers- Model Estimation - Estimate the unknown parameters of the model- Simulation - Simulate the risk drivers- Calibration - Use any known information to calibrate the simulations, to match observed real world quantities- Decision Making - Optimize the decision process- Summarize - Summarize the outcomes (e.g. using probability distributions)
  22. 22. Overview of PowerSimm Processes WX Sim Load Sim Spot Price Sim Calibrated Spot Dispatch Price Data Forward Price Sim Portfolio Summarization 22
  23. 23. Marginal Price of Electricity Demand Supply P2 Marginal price $/MWh of electricity P1 Baseload (Coal) Midmerit (CC) Peakers (CTs) MW
  24. 24. 100 20 40 80 120 60 0 1/1/2007 Weather – historical relationships 5/19/2007 10/1/2007 2/12/2008 LAX Max DB 6/25/2008 11/6/2008 100 120 20 40 60 80 0 3/20/2009 0 9/1/2009 1/13/2010 7/27/2010 50 12/8/2010 4/21/2011 9/2/2011 1/14/2012USC Max DB 5/27/2012 100 150 CAMPUS AIRPORT INTERNATIONAL DOWNTOWN L.A./USC
  25. 25. Weather – modelling – vector autoregression 𝑈𝑆𝐶 𝐷𝐵 𝑡 = 𝑓(𝑈𝑆𝐶 𝐷𝐵 𝑡−1 , … , 𝑈𝑆𝐶 𝑀𝑎𝑥𝐷𝐵 𝑡−𝑙 , 𝐿𝐴𝑋 𝐷𝐵 𝑡 , … , 𝐿𝐴𝑋 𝐷𝐵 𝑡−𝑙 ) +𝜀 𝑡,1 𝐿𝐴𝑋 𝐷𝐵 𝑡 = 𝑓(𝑈𝑆𝐶 𝐷𝐵 𝑡−1 , … , 𝑈𝑆𝐶 𝑀𝑎𝑥𝐷𝐵 𝑡−𝑙 , 𝐿𝐴𝑋 𝐷𝐵 𝑡 , … , 𝐿𝐴𝑋 𝐷𝐵 𝑡−𝑙 ) +𝜀 𝑡,2 𝜺~𝑁(0,Ω)
  26. 26. Weather – simulated temperature – temporalcorrelations
  27. 27. Weather – simulated temperature – benchmarking
  28. 28. Load – historical relationships Summer Load Profile Winter Load Profile Load vs Temperature
  29. 29. Load – modelling – model specification𝐿𝑜𝑎𝑑 𝑡 = 𝑓 𝑀𝑜𝑛𝑡ℎ 𝑡 , 𝐷𝑂𝑊𝑡 , 𝐻𝑜𝐷 𝑡 , 𝑀𝑎𝑥𝐷𝐵 𝑡 + 𝜀 𝑡
  30. 30. Load – benchmarking simulations
  31. 31. Load – benchmarking simulations 31
  32. 32. Spot Prices – historical relationships
  33. 33. Spot Prices – modelling 𝑃𝑜𝑤𝑒𝑟 𝑡 = 𝑓 𝐿𝑜𝑎𝑑 𝑡−1 , 𝑃𝑜𝑤𝑒𝑟 𝑡−1 , 𝐺𝑎𝑠 𝑡−1 + 𝜀 𝑡,1 𝐺𝑎𝑠 𝑡 = 𝑓 𝐿𝑜𝑎𝑑 𝑡−1 , 𝑃𝑜𝑤𝑒𝑟 𝑡−1 , 𝐺𝑎𝑠 𝑡−1 + 𝜀 𝑡,2
  34. 34. Spot Prices – simulation results
  35. 35. Wrapup 35
  36. 36. Analytics for Deregulated Power Markets• Business questions:  What is my portfolio worth? (valuation)  How much of my expected output should I sell into the forward market? (hedging)  How much money can I lose? (risk management)  What trades should I enter into so I can maximize my profits and minimize my risk? (portfolio optimization)
  37. 37. What is My Portfolio Worth? Gross Margin At Expected Risk Value of Portfolio 37
  38. 38. How Sensitive is My Portfolio To Prices? Sensitivity of gross margin = $19 million per $/MWh Optimal forward sale = ~1500 MW 38
  39. 39. Questions? Scotty Nelsonsnelson@ascendanalytics.com 39

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