1. 1 Valuation and Hedging of Natural Gas Storages Ali Sadeghi March 2011

2. 2 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

3. 3 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 Ratchet: Volume per day that can be injected or withdrawn.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 Commodity charges: $/GJ (applies only to the volumes injected or withdrawn, therefore a variable cost) Fuel charge: $/GJ charge on injections and withdrawals (variable) Cost of Carry: interest charge for the injection/withdrawal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

4. 4 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.

5. 5 Spot hedging: negative spreads are not impossible

6. 6 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.

7. 7 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

8. 8 When does Rolling Intrinsic Make Sense?

9. 9 Trading Strategy: Rolling Intrinsic

10. 10 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

11. 11 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

12. 12 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.

13. 13 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) – 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

14. 14 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.

15. 15 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

16. 16 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

17. 17 2010 NYMEX prices, implied volatilities and spreads

18. 18 Daily values and deltas of the storage with and without hedges

19. 19 More Details: http://papers.ssrn.com/sol3/papers.cfm?abstr act_id=1687313