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Monte Carlo Simulation for Energy Risk Management
Scotty Nelson
1
January 15, 2013
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)
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Background on Deregulated Power Markets
State of Deregulation
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Source: Department of Energy
Regulated vs. Deregulated Power Markets
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Power (MWh)
Load
Generator
Payment ($)
Regulated Setup
ISO
Generator Load
Deregulated Setup
Paym
ent (
$)
Power (M
Wh)
Payment ($)
Pow
er (
MW
h)
Risk Exposure to Power Price MovementsPa
yoff
($)
Power Price ($/MWh)
Generator Load
Payo
ff (
$)
Power Price ($/MWh)
Hedge Optimization
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Decision Making Under Uncertainty
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
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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
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Historical versus expected – West Hub
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Historical implied heat rate versus 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) à simple decision rule, if P>K then exercise, otherwise don’t
o Decisions today don’t impact decisions tomorrow
§ Power Plant
o Operational constaints à 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
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Monte Carlo Simulation
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
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WX Sim Load Sim
Spot Price Sim
Forward Price Sim
Calibrated Spot Price Data
Dispatch
Portfolio Summarization
Marginal Price of Electricity
$/M
Wh
MW
Supply
Demand
Baseload (Coal) Peakers (CTs)
Marginal price of electricity
Midmerit (CC)
P1
P2
Weather – historical relationships
Weather – modelling – vector autoregression
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 – benchmarking simulations
Load – benchmarking simulations
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Spot Prices – historical relationships
Spot Prices – modelling
Spot Prices – simulation results
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Wrapup
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?
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Gross Margin At Risk
Expected Value of Portfolio
How Sensitive is My Portfolio To Prices?
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Sensitivity of gross margin = $19 million
per $/MWh
Optimal forward sale = ~1500 MW
