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Topic Title: Heat Rate Options
Created On Fri Oct 12, 07 10:51 AM

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int1234
Junior Member

Posts: 6
Joined: Oct 2007

Fri Oct 12, 07 10:51 AM

Hi,
Can anyone suggest me how to price heat rate option ?
Also need product info. on window barriar heat rate swaption.

Thanks.

Edited: Fri Oct 12, 07 at 11:20 AM by int1234

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Eccdogg
Junior Member

Posts: 7
Joined: Apr 2004

Tue Oct 16, 07 07:26 PM

I assume by heat rate options you mean spark spread options. An option that pays off like Max(Power-Heat Rate*Natural Gas,0) not Max(Power/Natural Gas-Heat Rate,0). The value of the first depends on the absolute level of NG prices the second just the ratio of power to gas.

The simple answer is that You can price these using the Margrabe formula for the option to exchange one commodity for the other.

http://www.global-derivatives.com/index.php?id=38&option=com_content&task=view

The hard part is getting estimates for the parameters. Natural Gas Vol is easy enough, but a market quote for power Vol can be difficult to get and a market quote for correlation is very hard. So you must estimate the correlation of Gas and Power.

Other approaches whould be to

Value the option historically after scaling up power and gas to reflect current prices

Create a fundamentail model of the heat rate supply curve using power, gas, and weather data and simulate power and gas prices using this model.

I typically do all three to insure that I am not missing some key feature of the local market.

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int1234
Junior Member

Posts: 6
Joined: Oct 2007

Tue Oct 23, 07 09:46 AM

Thanks Eccdogg,
Heat rate option term sheet fixes Heat rate ( lets say 9.5 )
Then call option buyer gets power price which is lets say ERCOT north peak now call buyer exercise option when
ERCOT north peak > ( 9.5)*( Underlying index: for example GD waha gas price).
i.e. if spot market heat rate ( MHR ) > operating plant heat rate then it is profitable to buy gas & then sell electricity.
Now it is quite confusing here to distinguish Spark spread option from heat rate option

spark spread= Power price - ( Heat rate * Gas price)

if you take spark spread option term sheet
it says The holder of a European- spark spread call option
written on fuel G at a fixed heat rate HK has the right, but not the obligation, to pay at the
option's maturity HK times the fuel price at maturity time T and receive the price of one unit of
electricity. Thus, the payoff at maturity time T is
Payoff of a spark spread call= max(TS-HK*TG ,0) where TS and TG are the electricity and fuel prices at time T, respectively.

in case of heat rate option call buyer gets power price calculated from heat rate & observed gas price.

Can you suggest correct pricing method?

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mxt52
Junior Member

Posts: 3
Joined: Feb 2004

Thu Apr 10, 08 09:21 PM

I often hear from traders that heat rate options, especially for long tenors (Cal12 and longer) imply higher than 90% correlation between power and gas prices, for example in west power markets (sp15, etc). When we look at realized correlation using historical prices, it turns out to be much lower, somewhere in the range of 50-60%. Intuitively I feel that the two correlations (implied and realized) are not one and the same, but how are they different?

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terrorbyte
Senior Member

Posts: 255
Joined: Jul 2002

Thu Apr 10, 08 10:31 PM

You are right. They are not the same.

The forward heat rate is a proxy for forward power prices by assuming what HR plant is on the margin and what the gas price is for that month. This occurs in many markets where gas is on the margin in the generation bid stack.

Intra month correlations are being driven by the physical nature of the transmission grid, weather and therefore demand, supply constraints etc. If you are looking at the west, it is also being driven by the hydros in the north west.

This makes it a great challenge to value a daily spread option with the two correlation values and one that we have struggled with for a while ;-)

Good luck

Terror!

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mxt52
Junior Member

Posts: 3
Joined: Feb 2004

Fri Apr 11, 08 01:35 AM

Thanks. It makes sense the way you put it. But then does not high implied correlation implies that gas is on the margin for the most part of the duration of the contract? This seems unrealistic...

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terrorbyte
Senior Member

Posts: 255
Joined: Jul 2002

Fri Apr 11, 08 01:39 PM

That is the kicker.

When people are trading forward curves, using heat rates as the focal point to derive power prices means that the correlation is high and, putting aside intrinsic value, the options are not worth much.

Intra month though, the options are worth more. Assuming that you are modelling a fast start gas power plant, you may turn it on on the peak days 10 days out of the 20. So, there is value there and that will be represented by using a lower intra month correlation.

So, to model a daily heat rate option you must use a combination of the forward correlation and the intra month correlation.

Regards

Terror

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mxt52
Junior Member

Posts: 3
Joined: Feb 2004

Fri Apr 11, 08 04:06 PM

Thanks again - great explanation, great intuition. I always thought that even complex things can be explained on a "napkin". Those who refuse to do it usually do not completely understand the topic themselves

Posts: 30
Joined: Sep 2003

Wed Aug 27, 08 01:45 PM

Has anyone priced a barrier type Heat Rate option?

Edited: Wed Aug 27, 08 at 03:07 PM by rich7804

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terrorbyte
Senior Member

Posts: 255
Joined: Jul 2002

Wed Aug 27, 08 04:03 PM

Rich,

Can you please describe more clearly what you are asking? Does the Heat Rate option have a strike but a knock out above the strike?

Regards

Terror

Posts: 30
Joined: Sep 2003

Wed Aug 27, 08 05:51 PM

It is Asian in Strike and it knocks out at given barrier level

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terrorbyte
Senior Member

Posts: 255
Joined: Jul 2002

Sat Sep 06, 08 07:36 PM

Rich,

I am sorry I let this one drop. OK. I don't know of a closed form solution. If I had to value this, I would be building a price process and doing a Monte Carlo.

If this is a monthly heat rate option, it will be relatively easy to build the price process.

If this is a daily heat rate option, the Monte Carlo should NOT use a lognormal price distribution as daily power and gas prices rarely fit this distribution. When I model daily power or gas prices, I fit an individual distribution to the underlying prices based on monthly history (eg a logistic distribution) and incorporate jumps. This will provide you with a more accurate portrayal of price behaviour.

Finally, for daily a option, I would also give the extrinsic value of the option a haircut (generally 10 to 25%). Due to timing issues in the market, the purchaser will know the power price for the next day hours after the gas price is published. This delay means that the option may end up dispatched and losing money due to a poor exercise. This will not effect you if it is a true Asian option and auto settles after the fact but it is an issue for European style Heat Rate options.

I hope this helps.

cheers

Terror

Posts: 189
Joined: May 2005

Fri Oct 24, 08 04:14 AM

Well, pricing is one challenge, but how about hedging? Forgetting illiquidity for a minute, do you trust the greeks from the margrabe formula? If not, what do you do?

Posts: 137
Joined: Nov 2006

Fri Oct 24, 08 08:57 PM

Quote
Originally posted by: jd1123
Well, pricing is one challenge, but how about hedging? Forgetting illiquidity for a minute, do you trust the greeks from the margrabe formula? If not, what do you do?

No. This is the area the money is made. An interesting idea is a full blown SDP method and go from there.

Edited: Fri Oct 24, 08 at 08:59 PM by diogenes

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mdixon2005uk
Junior Member

Posts: 1
Joined: Oct 2005

Sat Oct 25, 08 09:51 PM

I would take a look at Valdo Durrleman's paper with Rene Carmona on pricing and hedging spread options - you will find this to be quite comprehensive although there isn't much information on historical calibration....

www.cmap.polytechnique.fr/~valdo/papers/siam.pdf

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kvgg6
Junior Member

Posts: 2
Joined: Jul 2009

Fri Jul 24, 09 05:41 PM

I have a question on pricing heat-rate options with daily strike capacility. Say for e.g. the option is active from Jan-10 onwards.

From now till Jan-10, I use forward volatilities for power and gas to simulate price paths. Once I enter the month in which the option is active, I use spot volatilities for power and gas and spot correlation in order to simulate the intra-month power and gas prices. If I use this approach, the option price that I get after discounting to the present day is significantly higher than the price quoted in the market.

However if I use a weighted average of forward and spot volatilities for power and gas in simulating the intra-month price paths, the resulting option price is much closer to the market quotes.

Is anything wrong with the first approach? To me, the first approach seems to be correct theoritically.
I would like to know how the market is valuing such daily options based on your perceptions?

Thanks
Karthik

-------------------------
VKarthik

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Beachcomber
Member

Posts: 122
Joined: May 2004

Sat Jul 25, 09 11:13 PM

Hi,

Just saw this post, a couple of comments.

Margrabe's formula works when there are 0 fixed costs; often times a spark spread or heat rate option will trade with Variable Operating and Maintanence (VOM) as a fixed cost. In this case, Kirk's approximation works fairly well; We have also programmed the Carmona/Durrleman method and it seems to work pretty well.

For more information on pricing spark spread options, Energy and Power Risk Management by Eydeland and Wolyniec is an excellent resource.

As far as pricing heat rate options with daily calls, pay attention to the Eydeland and Wolyniec sections on correlation.

Posts: 137
Joined: Nov 2006

Sun Jul 26, 09 10:07 PM

Well, how much trust do you have in the spot vols?
Generally, either blended or forward vols are good estimates, since spot quotes are going to be very nosiy.
Also, pay attention to the impact of correlation, which might lead to a break down in your valuation model.

Aside from a Real Option Approach, I think what you have seems reasonable (for what it is worth).

Edited: Sun Jul 26, 09 at 10:10 PM by diogenes

Posts: 30
Joined: Sep 2003

Mon Jul 27, 09 02:16 AM

Where do you even get Spot Vols? Are these historical estimates?
" if I use a weighted average of forward and spot volatilities for power and gas in simulating the intra-month price paths, the resulting option price is much closer to the market quotes" What kind of correlation is getting your Vols to price near market quotes.

Posts: 137
Joined: Nov 2006

Wed Jul 29, 09 01:16 AM

Quote
Originally posted by: rich7804
Where do you even get Spot Vols? Are these historical estimates?
" if I use a weighted average of forward and spot volatilities for power and gas in simulating the intra-month price paths, the resulting option price is much closer to the market quotes" What kind of correlation is getting your Vols to price near market quotes.

ICAP has some quotes, then do some mapping if needed.

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