Valuation and Hedging of
Natural Gas Storages
Ali Sadeghi
March 2011
1
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
2
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Ratchet: Volume per day that can be injected or withdrawn.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withdrawn, therefore a variable cost)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
3
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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4/
1/
4/ 200
15 8
/
4/ 20 0
29 8
/
5/ 20 0
13 8
/
5/ 20 0
27 8
/
6/ 20 0
10 8
/
6/ 20 0
24 8
/2
7/ 0 08
8/
7/ 200
22 8
/2
8/ 0 08
5/
8/ 200
19 8
/2
9/ 0 08
2/
9/ 200
16 8
/
9/ 20 0
30 8
10 /20
/1 08
4
10 /2 0
/2 08
8
11 /2 0
/1 08
1
11 /2 0
/2 08
5/
12 2 00
/9 8
12 /20
/2 08
3/
2
1/ 008
6/
1/ 200
20 9
/2
2/ 0 09
3/
2/ 200
17 9
/2
3/ 0 09
3/
3/ 200
17 9
/
3/ 20 0
31 9
/2
00
9
Spot hedging:
negative spreads are not impossible
2008-2009 AECO Spot Prices
12
10
8
6
4
2
0
5
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.
6
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
7
When does Rolling Intrinsic Make
Sense?
$7.00
$6.90
$6.80
$6.70
$6.60
Apr-08 May- Jun-08 Jul-08 Aug08
08
Day One
Day Two
Sep08
Day Three
Day Four
8
Trading Strategy: Rolling Intrinsic
$7.00
$6.90
$6.80
$6.70
$6.60
Apr-08
May08
Day One
Jun-08
Jul-08
Day Two
Aug08
Sep08
Day Three
Day Four
9
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
10
Why options


In theory, options realize the extrinsic value of the
storage
Intrinsic:



Options



Buy Jun, sell Dec,
Lock in the Dec-Jun spread
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
11
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 payoff,

there is still a chance to optimize in the spot and
spot to forward markets.
12
Call/Put Hedging Strategy: Detailed Example
Call: Buyer receives/Seller pays:
(Long dated future – close future) – Strike
Sellers 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
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
13
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.
14
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
15
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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1/
4/
1/ 2 0
11 10
/
1/ 201
18 0
/
1/ 201
25 0
/2
2/ 010
1/
2
2/ 010
8/
2/ 2 01
15 0
/
2/ 201
22 0
/2
3/ 010
1/
2
3/ 010
8/
3/ 2 01
15 0
/
3/ 201
22 0
/
3/ 201
29 0
/2
4/ 010
5/
4/ 2 01
12 0
/
4/ 201
19 0
/
4/ 201
26 0
/2
5/ 010
3/
5/ 2 01
10 0
/
5/ 201
17 0
/
5/ 201
24 0
/
5/ 201
31 0
/2
6/ 010
7/
6/ 2 01
14 0
/
6/ 201
21 0
/
6/ 20
28 10
/2
01
0
2010 NYMEX prices, implied
volatilities and spreads
Market Data
$8.00
75%
$7.00
70%
$6.00
65%
$5.00
60%
55%
$4.00
50%
$3.00
45%
$2.00
40%
$1.00
35%
30%
$25%
July Futures
Jan Futres
Spread
July Implied Vol
Jan Implied Vol
17
1/
4/
1/ 2 01
11
/ 0
1/ 201
18
0
1/ / 201
25
/2 0
2/ 010
1/
2
2/ 010
8/
2/ 2 01
15
0
/
2/ 201
22
0
/2
0
3/ 10
1/
2
3/ 010
8/
3/ 2 01
15
/ 0
3/ 201
22
0
3/ / 201
29
/2 0
4/ 010
5/
4/ 2 01
12
/ 0
4/ 201
19
0
/
4/ 201
26
0
/2
5/ 010
3/
5/ 2 01
10
0
5/ / 201
17
/ 0
5/ 201
24
0
5/ / 201
31
/2 0
6/ 010
7/
6/ 2 01
14
0
6/ / 201
21
/2 0
01
0
Daily values and deltas of the storage
with and without hedges
Per Unit Option Analysis
$1.20
100%
$1.00
50%
$0.80
0%
$0.60
-50%
$0.40
-100%
Delta Hedged
Total Value
Intrinsic
July Delta
Jan Delta
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More Details:
http://papers.ssrn.com/sol3/papers.cfm?abstr
act_id=1687313
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