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Monte Carlo Simulation for Energy Risk Management
Scotty Nelson
1
January 15, 2013
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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
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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)
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4
Background on Deregulated Power Markets
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State of Deregulation
Source: Department of Energy
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Regulated vs. Deregulated Power Markets
Power (MWh)
LoadGenerator
Payment ($)
Regulated Setup
ISO
GeneratorLoad
Deregulated Setup
Paym
ent ($
)
Power (M
Wh)
Payment ($)Po
wer
(M
Wh)
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Risk Exposure to Power Price MovementsPa
yoff
($)
Power Price ($/MWh)
Generator Load
Payoff
($)
Power Price ($/MWh)
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Hedge Optimization
8
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Decision Making Under Uncertainty
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Decision Making Under Uncertainty
•Risk Drivers Deterministic scenario planning models Sensitivity analysis Monte Carlo simulation
•Optimizing the Decision Making Process Unconstrained Optimization Constrained Optimization
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Dispatch Optimization
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 1011061111161211261311361411461511561611660
100
200
300
400
500
600
700
0
10
20
30
40
50
60
70
80
90
100
generation eprice
Gene
ratio
n (M
W)
Pow
er P
rice
($/M
Wh)
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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 uncertaintyo Can lead to biased decisions
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Historical versus expected – Henry Hub
10/1/2
008
11/19/2
008
1/7/2
009
2/25/2
009
4/15/2
009
6/3/2
009
7/22/2
009
9/9/2
009
10/28/2
009
12/16/2
009
2/3/2
010
3/24/2
010
5/12/2
010
6/30/2
010
8/18/2
010
10/6/2
010
11/24/2
010
1/12/2
011
3/2/2
011
4/20/2
011
6/8/2
011
7/27/2
011
9/14/2
011
11/2/2
011
12/21/2
011
2/8/2
012
3/28/2
012
5/16/2
012
7/4/2
012
8/22/2
012
10/10/2
012
11/28/2
012
1/16/2
013
3/6/2
013
4/24/2
013
6/12/2
013
7/31/2
013
9/18/2
013
11/6/2
013
12/25/2
0130
1
2
3
4
5
6
7
8
9
Historical Henry Hub Expected Henry Hub
$/M
MBt
u
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Historical versus expected – West Hub
10/1/2
008
11/19/2
008
1/7/2
009
2/25/2
009
4/15/2
009
6/3/2
009
7/22/2
009
9/9/2
009
10/28/2
009
12/16/2
009
2/3/2
010
3/24/2
010
5/12/2
010
6/30/2
010
8/18/2
010
10/6/2
010
11/24/2
010
1/12/2
011
3/2/2
011
4/20/2
011
6/8/2
011
7/27/2
011
9/14/2
011
11/2/2
011
12/21/2
011
2/8/2
012
3/28/2
012
5/16/2
012
7/4/2
012
8/22/2
012
10/10/2
012
11/28/2
012
1/16/2
013
3/6/2
013
4/24/2
013
6/12/2
013
7/31/2
013
9/18/2
013
11/6/2
013
12/25/2
0130
50
100
150
200
250
300
350
400
450
Historical West Hub Expected West Hub
$/M
Wh
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Historical implied heat rate versus expected implied heat rate
10/1/2
008
11/19/2
008
1/7/2
009
2/25/2
009
4/15/2
009
6/3/2
009
7/22/2
009
9/9/2
009
10/28/2
009
12/16/2
009
2/3/2
010
3/24/2
010
5/12/2
010
6/30/2
010
8/18/2
010
10/6/2
010
11/24/2
010
1/12/2
011
3/2/2
011
4/20/2
011
6/8/2
011
7/27/2
011
9/14/2
011
11/2/2
011
12/21/2
011
2/8/2
012
3/28/2
012
5/16/2
012
7/4/2
012
8/22/2
012
10/10/2
012
11/28/2
012
1/16/2
013
3/6/2
013
4/24/2
013
6/12/2
013
7/31/2
013
9/18/2
013
11/6/2
013
12/25/2
0130
20
40
60
80
100
120
Historical Implied Heat Rate Expected Implied Heat Rate
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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
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Monte Carlo Simulation
•Monte Carlo simulation Pro:
o Realistic representations of possible states of the world (this could actually happen)o Correlations are maintainedo Can benchmark against actual price distributions
Cons:o Complex, slow
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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 constaints can’t turn on and off instantlyo How to optimize the decision process, given that decisions today impact possible
decisions tomorrow?o Answer is provided through dynamic programming
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Dispatch Optimization
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 1011061111161211261311361411461511561611660
100
200
300
400
500
600
700
0
10
20
30
40
50
60
70
80
90
100
generation eprice
Gene
ratio
n (M
W)
Pow
er P
rice
($/M
Wh)
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Monte Carlo Simulation
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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)
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Overview of PowerSimm Processes
22
WX Sim Load Sim
Spot Price Sim
Forward Price Sim
Calibrated Spot Price Data Dispatch
Portfolio Summarization
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Marginal Price of Electricity
$/M
Wh
MW
Supply
Demand
Baseload (Coal) Peakers (CTs)
Marginal price of electricity
Midmerit (CC)
P1
P2
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Weather – historical relationships
1/2/2007 4/6/2008 8/5/2009 1/3/2011 4/2/20120
20
40
60
80
100
120
DOWNTOWN L.A./USC CAMPUSINTERNATIONAL AIRPORT
0 20 40 60 80 100 1200
20
40
60
80
100
120
USC Max DB
LAX
Max
DB
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Weather – modelling – vector autoregression
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Weather – simulated temperature – temporal correlations
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Weather – simulated temperature – benchmarking
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Load – historical relationships
Summer Load Profile Winter Load Profile
Load vs Temperature
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Load – modelling – model specification
𝐿𝑜𝑎𝑑𝑡= 𝑓 (𝑀𝑜𝑛𝑡h𝑡 ,𝐷𝑂𝑊 𝑡 ,𝐻𝑜𝐷 𝑡 ,𝑀𝑎𝑥𝐷𝐵𝑡 )+𝜀𝑡
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Load – benchmarking simulations
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Load – benchmarking simulations
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Spot Prices – historical relationships
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Spot Prices – modelling
𝑃𝑜𝑤𝑒𝑟 𝑡= 𝑓 (𝐿𝑜𝑎𝑑𝑡 −1 ,𝑃𝑜𝑤𝑒𝑟 𝑡 −1 ,𝐺𝑎𝑠𝑡− 1 )+𝜀𝑡 ,1
𝐺𝑎𝑠𝑡= 𝑓 (𝐿𝑜𝑎𝑑𝑡 −1 ,𝑃𝑜𝑤𝑒𝑟 𝑡 −1 ,𝐺𝑎𝑠𝑡− 1 )+𝜀𝑡 ,2
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Spot Prices – simulation results
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Wrapup
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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)
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What is My Portfolio Worth?
Gross Margin At Risk
Expected Value of Portfolio
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How Sensitive is My Portfolio To Prices?
Sensitivity of gross margin = $19 million
per $/MWh
Optimal forward sale = ~1500 MW