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)

4

Background on Deregulated Power Markets

5

State of Deregulation

Source: Department of Energy

6

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)

Risk Exposure to Power Price MovementsPa

yoff

($)

Power Price ($/MWh)

Generator Load

Payoff

($)

Power Price ($/MWh)

Hedge Optimization

8

9

Decision Making Under Uncertainty

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

11

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)

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 uncertaintyo Can lead to biased decisions

13

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

14

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

15

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

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

17

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

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 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

19

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)

20

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

22

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

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

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

𝐿𝑜𝑎𝑑𝑡= 𝑓 (𝑀𝑜𝑛𝑡h𝑡 ,𝐷𝑂𝑊 𝑡 ,𝐻𝑜𝐷 𝑡 ,𝑀𝑎𝑥𝐷𝐵𝑡 )+𝜀𝑡

Load – benchmarking simulations

31

Load – benchmarking simulations

Spot Prices – historical relationships

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

Spot Prices – simulation results

35

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)

37

What is My Portfolio Worth?

Gross Margin At Risk

Expected Value of Portfolio

38

How Sensitive is My Portfolio To Prices?

Sensitivity of gross margin = $19 million

per $/MWh

Optimal forward sale = ~1500 MW

39

Questions?

Scotty Nelsonsnelson@ascendanalytics.com