modeling and hedging the risk in retail load contracts

1Hess Energy · 2010 All Rights Reserved

Modeling and Hedging the Risk in Retail Load Contracts

Eric Meerdink, Director of Structuring & Analytics

May 3, 2011


Background on Hess Corporation


Hess: Who We are Today

EXPLORATION Discovering oil and gas

PRODUCTION & DEVELOPMENT Getting crude oil out of the ground

SUPPLY, TRADING &TRANSPORTATIONBuying, selling and transporting crude oil and finished products

REFINING Processing the crude oil into finished products

ENERGY TRADINGHess Energy Trading Company, a joint venture buying and selling energy financial instruments

TERMINALSStoring products and distributing fuels to our customers

RETAIL MARKETINGSelling motor fuels and convenience products at retail stores

ENERGY MARKETINGMarketing petroleum products, natural gas and electricity to commercial, industrial and utility customers

A Totally Integrated Energy Company


One of the Largest Energy Suppliers on the East Coast


Hess Energy: Robust Product Suite

Fuel Oil

Delivery to Commercial & Industrial customers

Distributor sales from Hess terminals

110K BPD

Natural Gas

Marketing to Commercial & Industrial customers

Wholesale to LDCs

1.5 BCF/day

Electricity

Marketing to Commercial & Industrial customers

4,500 MWs/hr (RTC ) (enough electricity to power 4 million average homes)

#2 electric marketer on the east coast

Green Suite

Reducing electric usage during times of peak demand

Support renewable energy sources, such as wind, solar, biomass and hydropower

Balance your carbon impact from oil and natural gas with carbon offsets


Volumetric Risk in Retail Load Contracts


What is a Full Requirements Load Following Contract

• Full Requirements Load Following: A fixed price agreement to serve all the electricity load of a customer, and provide all products required to supply the electric load, for a pre-determined interval of time, without restrictions on volume. Typically served at a fixed rate per MWH.

• Also called Full Plant Requirements Contract.

• Typical key products to be supplied:○ Load Following Energy○ Capacity○ Transmission○ Ancillaries○ RECs


Volumetric or Swing Risk

• Volumetric or swing risk is defined as a cash flow risk caused by deviations in delivered volumes compared to expected volumes. The primary cause of these volumetric deviations is weather and economic conditions.

• Not enough that delivered volumes deviate from expected volumes.

○ These deviations in delivered volumes must be positively correlated with market prices.

○ The full requirements load following contract is delta hedged at some expected volume.

• Under these conditions the resulting expected cash flow position is negative and non-linear with respect to changes in market prices.

• Swing risk is similar to the gamma position of an option, as it is a second order price risk.


Figure 1. Correlation Between Price and Load

4,800

4,900

5,000

5,100

5,200

5,300

5,400

5,500

May-06 Sep-06 Jan-07 May-07 Sep-07 Jan-08 May-08 Sep-08 Jan-09 May-09 Sep-09 Jan-10 May-10 Sep-10

Month/Yr

MW

$0.00

$10.00

$20.00

$30.00

$40.00

$50.00

$60.00

$70.00

$80.00

$90.00

$/M

WH

MW

$/MWH

12-Month Rolling Average of Load and Price in PSE&G Zone


Figure 2: Retail Sale and Long Hedge

Long Hedge

Short Sale

$/MWH

Short Retail Sale

-

$

Net: Swing Risk “Gamma”

+


Figure 3. Change in Cash Flow when Power is Delta Hedged

Load less than expected load

Load equals expected load

Load greater than expected

load

Price less than expected price - 0 +

Price equals expected price 0 0 0

Price greater than expected

price+ 0 - Swing Risk

- - - - - -

LongPosition

Hedged ShortPosition

1

2

3

A B C


Expected Cost to Serve Load

and Swing Risk



• Model assumptions:○ Pi = Actual price in hour i (random variable)○ Li = Actual load in hour i (random variable)○ Covi = Covariance between P and L in hour i Cov(Pi,Li).○ i = hours in the month i = 1,…,N○ Averages will be denoted with a bar over the variable○ Expectations will be taken at time t given information available up to and

including time t. Referenced by a subscript t.

N

i

itt PowerofValueForwardP

NP

1

1

N

i

itt LoadExpectedofValueForwardL

NL

1

1



• Cost to serve load:

• Expected cost to serve load :

• Taking expectations and solving we get:

N

i

iiLP1

Cost

N

i

iitt LPECostE

1

N

i

N

iii

itt

itttt LPCovPLLLPNCostE

1 1

,)1(

Expected blockcost of power.

Expected loadshaping cost.

Expected covariancebetween price and load.

tttt LNPSFE 1Cost2SF = Shaping Factor. Ratio of the sum of the

expected load shaping cost and expected covariance

cost to the expected block cost.


Hedging the Expected Cost

• Start with the expected cost function, equation (1) and take a Taylor series expansion with respect to prices and loads.

• Where refers to higher order terms. Neglecting these terms we can write the change in expected cost as:

iti

t

iti

tit

iti

tit

N

i

it

itt L

LC

PPC

PLPLCost1

)3(

)3(11

tt

it

N

iit

iti

tt

N

i t

it

it

it

t

it

titt L

L

L

L

CPP

P

P

P

C

P

PLLLN

Price Hedge Load Hedge

The delta on a load followingcontract does not equal 1.0

After delta hedging the price riskwe are left with the first order load riskor Gamma risk.


Fair Value of a Load Following Contract

• A fair price or fair value contract has an expected value of zero.

• Fair value contracts require the inclusion of the expected value of the covariance between price and load, not just the expected hourly shaping cost. Excluding this cost component biases the distribution to the left.

• But inclusion of the expected covariance in the contract price does not guarantee that the swing risk has been minimized or removed. It only guarantees that the contract is priced fairly.

• We are still left with the negative tail risk from large positively correlated price and load movements – Cash Flow at Risk.


3020100-10-20-30-40-50-60

0.04

0.03

0.02

0.01

0.00

Cash Flow

De

nsi

ty

Figure 4. P&L Distribution: Swing Risk vs. Swing Cost

17

Negative Skew:

Swing Risk

Swing Cost

Excluding the expected covariance produces a distributionwith a negative expected value.

Mean


Option Hedge Development


P

Cha

nge

in P

&L

+

-

gamma

HedgeHow do we create this hedge?

Monthly Average

Price $/mwh

P

Figure 5. Short Gamma Hedge


Figure 6. Creating a Gamma Position from Options

P

Use vanilla calls and puts to construct the gamma position.

Cha

nge

in P

&L

+

-

Monthly Average

Price $/mwh

P ˆ


Solving for the Estimated Gamma Function

• Select a series of strikes, Ki , and quantities, , to create a portfolio of puts and calls.

• To estimate the gamma function we need to choose the amount of options for each strike, , so as to minimize the distance between the estimated gamma function and the true gamma function.

• Estimated gamma function equals:

• Choose the optimal quantities by minimizing the sum of the squared errors between the true and estimated gamma function over a set of Q prices.

i

i

i

M

iii

N

ii PKMaxKPMaxP

11

0,0,ˆ

2

1

ˆmin

Q

jjj PP


Theoretical Model

• It has been shown that a static hedge of plain vanilla options and forwards can be used to replicate any European derivative (Carr and Chou 2002, Carr and Madan 2001).

• Any twice continuously differentiable payoff function, , of the terminal price S can be written as:

• Our payoff function is the terminal profit. It can be decomposed into a static position in the day 1 P&L, initially costless forward contracts, and a continuum of out-of-the-money options. F0 is the initial forward price.

)(Sf

0

0

0000

F

FdKKSKfdKSKKfFSFfFfSf

InitialP&L

DeltaPosition Gamma Hedge: “Swing Risk”


Theoretical Model, Cont.

• The initial value of the payoff must be the cost of the replicating portfolio.

• Where P(K,T) and C(K,T) are the initial values of out-of-the-money puts and calls respectively.

• Interpretation of term within the integral: Second derivative of the payoff function representing the quantity of options bought or sold.

○ R = Fixed revenue rate○ SF = Shaping Factor○ L(S) = MWH, function of S (spot price of power)

0

0,,

0000

F

FrT dKTKCKfdKTKPKfeFfFV

SLSSFRSf 1

SLSFKf

12


Estimating the Gamma Function

• Need to estimate the relationship between load and price.

• Use historic data to estimate the following regression equation.

• The data for this equation is average load (peak, off-peak) and average price (peak, off-peak). LMP is the price, D is a monthly dummy variable, and DXLMP is an interactive dummy variable with price.

• Next set up a portfolio of a short load sale and a long hedge using monthly forwards. The fixed rate on the load sale equals the RTC cost of serving the load ($/MWH).

• Use the relationship estimated in the regression equation to vary the average monthly load with respect to a change in average monthly price. Use this to estimate the gamma function.

11

1

11

1i itiiiitt lmpDDlmpLoad


Example Regression Output On-Peak PSE&G FP

Regression StatisticsMultiple R 87.27%R Square 76.16%Adjusted R Square 75.61%Standard Error 417.5841127Observations 445

ANOVAdf SS MS F Significance F

Regression 10 241771008.8 24177100.88 138.6488552 2.4513E-128Residual 434 75679397.18 174376.4912Total 444 317450406

Coefficients Standard Error t Stat P-valueIntercept 3,698.5486 64.27 57.55 0.00%LMP 7.1820 0.83 8.64 0.00%Mar_P -4.9284 1.02 -4.81 0.00%Apr_P -6.7488 1.01 -6.68 0.00%May_P -5.8316 0.96 -6.08 0.00%Jun_P 6.4907 0.73 8.94 0.00%Jul_P 11.8957 0.73 16.30 0.00%Aug_P 10.2282 0.77 13.28 0.00%Sep_P 4.6888 0.84 5.61 0.00%Oct_P -2.2002 0.92 -2.38 1.77%Nov_P -3.5755 0.99 -3.62 0.03%

Adjusted R2 = 75 %.

Interactive dummy variables

StatisticallySignificant

A $1 change is prices equals a 7 MW change in average daily peak load.For July the change equals 19 = 7 + 12.


-$2,000

$0

$2,000

$4,000

$6,000

$8,000

$10,000

$12,000

$14,000

$16,000

$18,000

$20,000

$0.00 $20.00 $40.00 $60.00 $80.00 $100.00 $120.00 $140.00

Market Price

Ch

an

ge

in P

&L

($

00

0)

-Gamma

Estimate

Cost as of February 9, 2009.

Estimated gamma function for July 2010 PSE&G FP load.The option cost equals $1.89/MWH per MWH served.

Figure 7: Example of a Gamma Function Estimate


Mitigating Swing Risk in Practice

“In theory there is no difference between theory and practice.

In practice there is” Yogi Berra


Minimizing Cash Flow at Risk

• In practice we cannot purchase options in such a way as to create the smooth curves depicted earlier. Instead we need to find discrete strikes so as to minimize the “swing risk”.

• Swing risk is here defined as Cash Flow at Risk (CF@R). CF@R is the expected loss assuming that all contracts are taken to delivery. I am defining CF@R as the difference between the mean of the distribution and the 5th percentile.

• Since we cannot perfectly hedge the swing risk by purchasing a continuum of options we need another objective risk minimization strategy.

• Use as a strategy the minimization of the CF@R or an objective level for the CF@R. An example would be to reduce the CF@R by 50%.


Reduce Cash Flow at Risk

3020100-10-20-30-40-50

0.06

0.05

0.04

0.03

0.02

0.01

0.00

X

Density

Accountnig or Actuarial w ith Options

Accounting Model

Cash Flow

Swing RiskReduced

Delta Hedged

Hedged with

Options


Methodology

• Use Monte Carlo simulation to model the load following contract and all hedges.

• Model takes into account the relationship between price and load, volatilities and correlations.

• Run the model to estimate the expected cost to serve the load and establish the fair price of the contract.

• Layer in delta hedges to estimate the cash flow distribution and estimate the CF@R.

• Determine the amount of risk to be minimized. This is a management decision. Cut the CF@R by 50%.

• Determine the portfolio of available options in the market.• Use an available optimization routine to determine the optimal option

portfolio that meets the required risk criteria.


Simulated Gamma Position

($1,600,000)

($1,400,000)

($1,200,000)

($1,000,000)

($800,000)

($600,000)

($400,000)

($200,000)

$0

$200,000

$400,000

$0 $50 $100 $150 $200 $250 $300 $350

Average On-Peak LMP

To

tal P

&L

Example uses NJ BGS CIEP Load for July.

Approximately 80 MWs average load on-peak.


Cash Flow Distribution

Swing Risk

NJ BGS CIEP Load for July


Cash Flow Distribution with Swing Hedge

Swing Risk Removed

NJ BGS CIEP Load for July.

Objective was to reduce CF@R by 50%.


Efficient Frontier Analysis

($1,200,000)

($1,000,000)

($800,000)

($600,000)

($400,000)

($200,000)

$0

$0 $200,000 $400,000 $600,000 $800,000 $1,000,000 $1,200,000

Option Cost

5th

Pe

rce

nti

le

+/- 10% Strangle

+/- 30% Strangle

The efficient frontier tells what the minimum option cost would be toachieve a particular level of the 5th percentile.


Contact

Eric Meerdink

Director of Structuring & Analytics

Hess Corporation

One Hess Plaza

Woodbridge, NJ 07095

Office: 732-750-6591

Cell: 732-425-4655

Email: [email protected]

modeling and hedging the risk in retail load contracts

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