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Monte Carlo Simulation for Energy Risk
            Management




Scotty Nelson




January 15, 2013


                                         1
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
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)
Background on
Deregulated Power
Markets



                    4
State of Deregulation




                        Source: Department of Energy



                                       5
Regulated vs. Deregulated Power Markets


   Regulated Setup                       Deregulated Setup

        Power (MWh)
                             Generator
                                                       Load


Generator             Load



        Payment ($)


                                             ISO




                                                   6
Risk Exposure to Power Price Movements




               Generator                           Load




                                   Payoff ($)
Payoff ($)




             Power Price ($/MWh)                Power Price ($/MWh)
Hedge Optimization




                     8
Decision Making
Under Uncertainty




                    9
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
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
     137
11

     141
     145
     149
     153
     157
     161
     165
           0
                                30
                                       40
                                              50
                                                     60
                                                           70
                                                                 80




               10
                          20
                                                                            90
                                                                                 100




                                     Power Price ($/MWh)
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
$/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
                            12/1/2012
13

                             2/1/2013
                             4/1/2013
                             6/1/2013
                             8/1/2013
                            10/1/2013
                            12/1/2013
$/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
     10/1/2012
14

     12/1/2012
      2/1/2013
      4/1/2013
      6/1/2013
      8/1/2013
     10/1/2013
     12/1/2013
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
     10/1/2012
15

     12/1/2012

      2/1/2013
      4/1/2013
      6/1/2013
      8/1/2013
     10/1/2013
     12/1/2013
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
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
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
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
     137
19

     141
     145
     149
     153
     157
     161
     165
           0
                                30
                                       40
                                              50
                                                     60
                                                           70
                                                                 80




               10
                          20
                                                                            90
                                                                                 100




                                     Power Price ($/MWh)
Monte Carlo
Simulation




              20
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)
Overview of PowerSimm Processes




   WX Sim               Load Sim




                       Spot Price Sim

                                        Calibrated Spot
                                                            Dispatch
                                          Price Data

                       Forward Price
                           Sim
                                                            Portfolio
                                                          Summarization




                                  22
Marginal Price of Electricity



                                         Demand


                                                                  Supply




     P2

                        Marginal price
  $/MWh




                        of electricity




      P1




                   Baseload (Coal)                Midmerit (CC)   Peakers (CTs)

                         MW
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
                                                       1/14/2012
USC Max DB


                                                       5/27/2012
             100
             150
                                                                                       CAMPUS

                                                                       AIRPORT
                                                                       INTERNATIONAL
                                                                                       DOWNTOWN L.A./USC
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)
Weather – simulated temperature – temporal
correlations
Weather – simulated temperature – benchmarking
Load – historical relationships


   Summer Load Profile                            Winter Load Profile




                            Load vs Temperature
Load – modelling – model specification




𝐿𝑜𝑎𝑑 𝑡
    = 𝑓 𝑀𝑜𝑛𝑡ℎ 𝑡 , 𝐷𝑂𝑊𝑡 , 𝐻𝑜𝐷 𝑡 , 𝑀𝑎𝑥𝐷𝐵 𝑡 + 𝜀 𝑡
Load – benchmarking simulations
Load – benchmarking simulations




                                  31
Spot Prices – historical relationships
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
Spot Prices – simulation results
Wrapup




         35
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)
What is My Portfolio Worth?




                Gross Margin At   Expected
                Risk              Value of
                                  Portfolio
                                              37
How Sensitive is My Portfolio To Prices?




                                              Sensitivity of gross
                                              margin = $19 million
                                                 per $/MWh




                        Optimal forward sale = ~1500 MW

                                                 38
Questions?

       Scotty Nelson
snelson@ascendanalytics.com




                      39

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Monte carlo simulation for energy risk management

  • 1. Monte Carlo Simulation for Energy Risk Management Scotty Nelson January 15, 2013 1
  • 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. 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)
  • 5. State of Deregulation Source: Department of Energy 5
  • 6. Regulated vs. Deregulated Power Markets Regulated Setup Deregulated Setup Power (MWh) Generator Load Generator Load Payment ($) ISO 6
  • 7. Risk Exposure to Power Price Movements Generator Load Payoff ($) Payoff ($) Power Price ($/MWh) Power Price ($/MWh)
  • 10. Decision Making Under Uncertainty • Risk Drivers  Deterministic scenario planning models  Sensitivity analysis  Monte Carlo simulation • Optimizing the Decision Making Process  Unconstrained Optimization  Constrained Optimization 10
  • 11. Generation (MW) 100 200 300 400 500 600 700 0 1 5 9 13 17 21 25 29 33 37 41 45 49 Dispatch Optimization 53 57 61 65 69 73 77 81 generation 85 89 93 97 eprice 101 105 109 113 117 121 125 129 133 137 11 141 145 149 153 157 161 165 0 30 40 50 60 70 80 10 20 90 100 Power Price ($/MWh)
  • 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. $/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 12/1/2012 13 2/1/2013 4/1/2013 6/1/2013 8/1/2013 10/1/2013 12/1/2013
  • 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 10/1/2012 14 12/1/2012 2/1/2013 4/1/2013 6/1/2013 8/1/2013 10/1/2013 12/1/2013
  • 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 10/1/2012 15 12/1/2012 2/1/2013 4/1/2013 6/1/2013 8/1/2013 10/1/2013 12/1/2013
  • 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. 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. 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. 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 101 105 109 113 117 121 125 129 133 137 19 141 145 149 153 157 161 165 0 30 40 50 60 70 80 10 20 90 100 Power Price ($/MWh)
  • 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. Overview of PowerSimm Processes WX Sim Load Sim Spot Price Sim Calibrated Spot Dispatch Price Data Forward Price Sim Portfolio Summarization 22
  • 23. Marginal Price of Electricity Demand Supply P2 Marginal price $/MWh of electricity P1 Baseload (Coal) Midmerit (CC) Peakers (CTs) MW
  • 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 1/14/2012 USC Max DB 5/27/2012 100 150 CAMPUS AIRPORT INTERNATIONAL DOWNTOWN L.A./USC
  • 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. Weather – simulated temperature – temporal correlations
  • 27. Weather – simulated temperature – benchmarking
  • 28. Load – historical relationships Summer Load Profile Winter Load Profile Load vs Temperature
  • 29. Load – modelling – model specification 𝐿𝑜𝑎𝑑 𝑡 = 𝑓 𝑀𝑜𝑛𝑡ℎ 𝑡 , 𝐷𝑂𝑊𝑡 , 𝐻𝑜𝐷 𝑡 , 𝑀𝑎𝑥𝐷𝐵 𝑡 + 𝜀 𝑡
  • 30. Load – benchmarking simulations
  • 31. Load – benchmarking simulations 31
  • 32. Spot Prices – historical relationships
  • 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. Spot Prices – simulation results
  • 35. Wrapup 35
  • 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. What is My Portfolio Worth? Gross Margin At Expected Risk Value of Portfolio 37
  • 38. How Sensitive is My Portfolio To Prices? Sensitivity of gross margin = $19 million per $/MWh Optimal forward sale = ~1500 MW 38
  • 39. Questions? Scotty Nelson snelson@ascendanalytics.com 39