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3 What’s so special about the energy markets?

3 What’s so special about the energy markets?

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energy derivatives Chapter 72



Energy

1800

1600

1400

1200

1000

800

600

400

200

0

10/01/1997



29/07/1997



14/02/1998



02/09/1998



21/03/1999



07/10/1999



21/03/1999



07/10/1999



Figure 72.2 Daily spot electricity prices.



Energy

10000



1000



100



10



1

10/01/1997



29/07/1997



14/02/1998



02/09/1998



Figure 72.3 Daily spot electricity prices, logarithmic vertical scale.



example. On August 11th 1999 there was a total solar eclipse in the Southern UK. Just before

the eclipse there was a drop in power demand as everyone went outside to ‘see’ the eclipse

and switched off lights, TVs etc. On returning a few minutes later, they switched everything

back on, leading to a surge in demand. If electricity could be easily stored the rapid fluctuations

in demand wouldn’t necessarily lead to rapid fluctuation in price. The same is true of natural



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Part Five advanced topics



Table 72.1 Spot electricity prices.

Time

0:00

1:00

2:00

3:00

4:00

5:00

6:00

7:00

8:00

9:00

10:00

11:00

12:00

13:00

14:00

15:00

16:00

17:00

18:00

19:00

20:00

21:00

22:00

23:00



$/MWh

14.6

13.7

14.3

14.1

13.7

14.3

15.8

34.2

42.8

47.7

55.2

89.9

468.0

900.0

900.0

900.0

709.1

189.4

92.8

31.3

58.1

51.5

31.3

19.7



gas, which can also rise many times in price quite suddenly. Other energy commodities are

relatively well behaved.

It’s not even obvious that we should use a continuous-price process as a model. Certainly,

the traditional lognormal asset price model is not going to be appropriate. Although the spikes

are extreme, prices do fall back to earlier levels equally dramatically, usually within a day or

two. We could model this as a jump process but it may have to be path-dependent to capture

the price falls. Maybe a mean-reverting process would be a reasonable approximation, which

would fit in well with our modeling experience so far. We’ll pursue this route later on.

In Table 72.2 are shown prices of US mid-continent electricity prices on July 28th 1999. These

prices, in $/MWh, are taken from Bloomberg whose headline was ‘Heat Boosts Next-Day Midwest Electricity Prices Near 1998 Highs.’ Two days later the headline was ‘Midwest Electricity

Prices Plummet on Cooler Monday Weather Forecast.’ Prices are shown in Table 72.3. What a

crazy market.

To summarize, energy prices have the following characteristics:











Basis risk due to location of delivery (difficulty in transportation);

Basis risk due to time of delivery (difficulty in storage);

Large jumps and mean reversion;

Seasonality effects.



energy derivatives Chapter 72



Table 72.2

Index

ECAR

East

AEP

West

Central

Cinergy

South

North

Main

Com-Ed

Lower

MAPP

North

Lower



Table 72.3

Index

ECAR

East

AEP

West

Central

Cinergy

South

North

Main

Com-Ed

Lower

MAPP

North

Lower



72.4



Bloomberg mid-continent electricity prices July 28th 1999.

$/MWh



Daily change %



Low



High



1780

1966

1544

1800

1972

1972

1700

1700

1981

1762

2200

1425

1850

1000



+1586

+1757

+1357

+1618

+1792

+1792

+1529

+1475

+1777

+1554

+2000

+1237

+1684

+792



600

1500

800

1800

600

600

1000

1400

1500

1500

2200

325

325

800



2500

2400

2100

1800

2500

2500

2100

2000

2200

2100

2200

2000

2000

1200



Bloomberg mid-continent electricity prices July 30th 1999.

$/MWh



Daily change %



Low



High



281

275

282

300

281

281

298

250

247

225

269

95

90

100



−1496

−1585

−1618

−1200

−1469

−1469

−1452

−1650

−1353

−1475

−1231

−1321

−1360

−1283



200

250

225

275

225

225

200

225

150

150

200

78

90

78



325

300

282

325

325

325

300

275

862

275

325

150

150

100



WHY CAN’T WE APPLY BLACK–SCHOLES THEORY

TO ENERGY DERIVATIVES?



The high volatility at the short end of the forward curve and the stability of the long end rule

out the use of the basic Black–Scholes model. The actual volatility of the spot price would

give unrealistically large option prices. In Figure 72.4 are shown the implied at-the-money

forward volatilities for Brent crude oil. This rapid decay of volatility is very typical of energy

underlyings, and represents the wild swings seen in spot prices and prices for early delivery.

We need something more sophisticated, not only because of this high volatility but also

because, as I’ve said before, but it can bear repeating, it’s hard to store electricity and virtually

impossible to hedge.



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Part Five advanced topics



45%

40%

35%

30%

Volatility



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25%

20%

15%

10%

5%

0%

Jul-98



Feb-99



Aug-99



Mar-00



Oct-00



Apr-01



Figure 72.4 Forward volatilities of at-the-money Brent crude oil options.



72.5 THE CONVENIENCE YIELD

The convenience yield is to energy what dividend yield is to stocks. Specifically, it measures

the net benefit less cost of holding the energy. Users of energy are willing to pay a premium

for the ability to get the energy they require, when they require it. On the other hand, there

is the cost of energy storage to take into account. The benefits minus the costs become the

convenience yield which can be quantified by examining the future prices of energy. If the

convenience yield were constant then we would expect the usual relationship between forward

and spot prices,

F = Se(r−q)(T −t) ,

where q is the convenience yield.

Because the convenience yield plays such an important role in shaping the forward price

curve, it is usual to use a much more sophisticated model for it than a simple constant.



´ TWO-FACTOR

72.6 THE PILOPOVIC

MODEL

The Pilopovi´c two-factor model takes the form

dS = α(L − S) dt + σ S dX1

and

dL = µL dt + ξ L dX2



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