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Valuation and Hedging of Natural Gas Storages

Ali SadeghiMarch 2011

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What are we going to talk about?• Storages contracts

• Capacity• Ratchets• Commodity charges• Demand charges• Fuel Charge• Cost of Carry

• Trading Strategies around Storage• Spot Trading• Rolling Intrinsic• Basket of Options• Virtual storages

• Hedging Strategies• Spot hedging• Intrinsic • Rolling Intrinsic• Basket of options

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Storage Contracts: Parameters Capacity: Maximum volume in GJ/MMBTU/BCF. Ratchet: Volume per day that can be injected or withdrawn.

Demand charge $/Capacity/month (fixed cost).

Commodity charges: $/GJ (applies only to the volumes injected or withdrawn, therefore a variable cost)

Fuel charge: $/GJ charge on injections and withdrawals (variable)

Cost of Carry: interest charge for the injection/withdrawal period.

Analogy with options: storages may be considered a basket of call option on the calendar spreads:

Premium = Demand charge Strike= fuel + Commodity + carrying costs Underlying asset = Summer-winter spread

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Trading Strategy: Spot Trading

Inject in summer Withdraw in winter

High year over year variance in net revenue Possibility of net negative revenue Still a useful approach since it can be implemented

along with other strategies.

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Spot hedging: negative spreads are not impossible

2008-2009 AECO Spot Prices

0

2

4

6

8

10

12

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Trading Strategy: Intrinsic

Intrinsic Value: The highest value that can be locked in today.

For a given forward curve, there are different ways for locking-in the injections and withdrawals. Usually a dynamic programming program is implemented to find the best combination.

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Trading Strategy: Intrinsic Pros

Returns are locked-in Negative returns impossible

Contras Intrinsic values change day by day, choosing the

best day to lock-in is not an easy task Therefore often hedgers forego the opportunity to benefit

from unexpected events in the market Similar situation to early exercise of an American

option

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When does Rolling Intrinsic Make Sense?

$6.60

$6.70

$6.80

$6.90

$7.00

Apr-08 May-08

Jun-08 Jul-08 Aug-08

Sep-08

Day One Day Two Day Three Day Four

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Trading Strategy: Rolling Intrinsic

$6.60

$6.70

$6.80

$6.90

$7.00

Apr-08 May-08

Jun-08 Jul-08 Aug-08

Sep-08

Day One Day Two Day Three Day Four

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Rolling Intrinsic: Summary

Starts from intrinsic value Gradually redo the hedges to capture the

extrinsic value as much as possible No guarantee for converging to the extrinsic

value or any where close to that At each instance of time the value is locked

in, no risk of downward MTM movements

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Why options

In theory, options realize the extrinsic value of the storage

Intrinsic: Buy Jun, sell Dec, Lock in the Dec-Jun spread

Options Sell a calendar spread option on Dec-Jun spread lock in the premium (always higher than the outright

spread) Costs are same in both cases

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How dose it settle

If spread settles in the money (wider than strike), than lock in the spread at expiry, pay the payoff, therefore no additional cost

If spread settles out of money, then no pay-off, there is still a chance to optimize in the spot and

spot to forward markets.

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Call/Put Hedging Strategy: Detailed Example

Example: September 11 2007 Oct futures: $5.934,Jan futures $7.871 Call price: $ 0.199, Put price: $0.136 (both at the strike price $2) Call is very often priced higher than put Intrinsic Spread = $1.94, Variable Cost=$0.25, Intrinsic Value $1.69

Hedging Strategy: Do not lock in, Sell a Call, Buy a Put

Call: Buyer receives/Seller pays: (Long dated future – close future) – StrikeSellers View: Short position in long dated future Long position in the close future

Put: Buyer receives/Seller pays: Strike - (Long dated future – close future) Sellers View: Long position in long dated future Short position in the close future

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Basket of Option

There are different combinations of options that might be sold for any given storage. The monthly volumes can not violate the ratchets

The combination with the maximum value is considered as basket of options.

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Problems with Options

Not always available Usually traded at NYMEX, therefore needs

additional locational hedging More difficult for non-liquid locations Many companies do not wish to trade options

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What if no option market is available: Delta Hedging Instead of selling the option, one can delta hedge

the storage to retain the value (intrinsic + extrinsic) up until the settlement.

The concept is same as hedging a long call option (instead of selling it).

There are few different ways to calculate the values and Greeks on a daily basis External soft-wares Proprietary models based on various option valuation

models: Bachelier formula Margrabe formula Monte Carlo simulation

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2010 NYMEX prices, implied volatilities and spreads Market Data

$-

$1.00

$2.00

$3.00

$4.00

$5.00

$6.00

$7.00

$8.00

25%

30%

35%

40%

45%

50%

55%

60%

65%

70%

75%

July Futures Jan Futres Spread July Implied Vol Jan Implied Vol

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Daily values and deltas of the storage with and without hedges Per Unit Option Analysis

$0.40

$0.60

$0.80

$1.00

$1.20

-100%

-50%

0%

50%

100%

Delta Hedged Total Value Intrinsic July Delta Jan Delta

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More Details:

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1687313