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White Paper - Overview


Quantifying Natural Gas Storage Optionality: A Two-Factor Tree Model
Cliff Parsons*
Current Draft - August 3rd, 2011


*Cliff Parsons, Ph.D., is President of WTM Energy Software, LLC., 6422 Cottonwood Park Lane, Houston, TX 77041. Emails: Inquire@WTMenergy.com; cliff.parsons@sbcglobal.net}. The author gives special thanks to Dr. Stephen Figlewski, Charles Riedhauser, and Dr. Thanassis Tjavaras for many helpful comments and also thanks Dr. Rafael Mendible, Chris Richards, Avill Young, Dr. Wei Zhang, and Dayne Zimmerman for discussions and comments regarding this paper.}}


Abstract


We find evidence of strong mean-reversion in U.S. natural gas prices and proceed to test a valuation model of natural gas storage leases based on mean-reversion's effects. The model utilizes a two-factor tree in which both factors mean-revert, and the model calibrates to current market conditions, accounts for volume constraints, and can be applied to historical data. In applying the model to data on U.S. natural gas, we find that the model can consistently capture large amounts of optionality based on the premise of strongly mean-reverting prices: On historical price data spanning 1999 to 2006, simulated trading using our model obtained average values (not including the cost of the lease) of $1.244 per million British-thermal-units over intrinsic value for fast-cycle storage leases and $0.397 per million British-thermal-units over intrinsic for slow-cycle leases. Results relating stored inventory to storage lease optionality are also shown.


Introduction


In the U.S. natural gas industry, the modeling and valuation of leases on natural gas storage have been major concerns, especially since the U.S. has several trillion cubic feet of such storage. Firms in the industry recognize these leases possess vast optionality but do not believe they correctly understand and extract it. Heretofore, other authors on this subject have provided some basic understanding of lease optionality, but none has quantified this value using historical data. The goal of this paper is to quantify and better understand the optionality of U.S. natural gas storage leases, and we have two major findings: (a) The mean-reversion in U.S. natural gas spot prices, which is exploited by storage lease optionality, appears to be much greater than previously documented, and (b) the actual optionality that could have been extracted from leases for previous years appears to be large.


The U.S. currently has over four-trillion cubic feet of working natural gas storage on annual consumption of over 22-trillion cubic feet. Depleted oil and natural gas reservoirs, accounting for over 80% of U.S. storage, provide the slowest injection/withdrawal rates while the two other main types of storage, salt caverns and aquifers, provide faster rates. In short, depleted reservoirs, relative to the other types of storage, are filled with more sand or debris that inhibits the movement of natural gas stored within, thus slowing the rates of injection into and withdrawal from reservoirs. Thompson, Davison, and Rasmussen (2003) summarizes the main types of storage further.


Owners of storage facilities lease out space within, and a lease-holder has the right to inject into or withdraw from the facility only for a prespecified period of time, usually between each April 1st and the following March 31st, and within prespecified volume constraints, which are described through a ''ratchet schedule.'' A ratchet schedule is a schedule of all possible inventory levels and their associated daily maximum injection and withdrawal rates. As the lease-holder injects or withdraws, two types of transaction costs are typically incurred: a ''fuel'' charge, which is a percentage of injected or withdrawn gas, and a ''commodity'' charge, which is a dollar amount per unit of injected or withdrawn gas. These charges mostly exist to cover variable costs of operating the facility, with the chief cost being compressor operation for pushing more natural gas into or out of the facility.


Authors such as Manoliu (2004), Ludkovski and Carmona (2005), Chen and Forsyth (2006), and Boogert and De Jong (2008) posit, as do we, that storage lease optionality derives from the ability to exploit mean-reverting trends in natural gas spot prices: Only the opportunity to buy spot low, store it as prices mean-revert higher, then sell it high exists. And short-term, current forward prices on natural gas provide information regarding the expected spot price mean-reversion. We believe, as argued in Mastrangelo (2007), that such mean-reversion derives mainly from daily demand characteristics. Natural gas is a major U.S. heating source and colder (warmer) than expected days typically cause demand to increase (decrease). Such weather shocks mean-revert and carry through to demand and spot prices. Seasonality in these prices occurs since U.S. demand is predictably greater in winter than in summer, which typically leads to higher winter forward prices for U.S. natural gas.


If mean-reverting spot trends help create value in storage leases, a natural question concerns the persistence of these trends. Equilibrium arguments concerning convenience yields, e.g., Hull (1997), suggest costless and abundant natural gas storage should eliminate any trends causing excess expected profitability, but natural gas storage is neither costless nor abundant. The fixed costs to develop a storage field can be over $10 million per billion-cubic-feet of capacity, and most storage facilities in the U.S. possess the slowest, most constrained injection and withdrawal capabilities. Furthermore, storage facilities are often sited based on geology and regulation, not demand.


The hypothesis that mean-reversion affects storage lease optionality implies the magnitude of that reversion is important. Studies such as Pilipovic (1998), Clewlow and Strickland (2000), and Benth and Benth (2004) find statistical evidence of weak to moderate mean-reversion in U.S. natural gas prices while Eydeland and Wolyniec (2003) statistically rejects the mean-reversion hypothesis. Parsons (2008) explains why results like these may be biased downward and do not necessarily indicate weak mean-reversion in reality, they may just indicate that the price model used in the estimation is too simplistic regarding the long-run mean. Intuitively, evidence of strong spot mean-reversion in the U.S. market can be seen every day in its forward curve: Forward prices for adjacent months can be over 15% different from each other, which is too much difference for spot prices to overcome in too little time with only slight mean-reversion. In Section 4 we summarize our method of fitting mean-reversion speeds. In short, we find evidence that very strong mean-reversion exists in U.S. natural gas prices when the model accounts for a more generalized long-run mean process.


For modeling natural gas storage value, tree models, such as the one in Manoliu (2004), are only one of three prevalent methods. Another method is Monte Carlo simulation, which is outlined in Eydeland and Wolyniec (2003) and Boogert and De Jong (2008). Monte Carlo simulation appears to be the most used of the three at this time in the energy industry. The third, more recent method is the stochastic control approach as seen in Thompson, Davison, and Rasmussen (2003), Ludkovski and Carmona (2005), and Chen and Forsyth (2006). To our knowledge, none of these valuation models has been previously back-tested on historical data for quantifying storage lease optionality.


For building our valuation model, a tree model that we may successfully back-test, we concentrate our efforts in two parts: (a) developing a realistic price model of the (mean-reverting) spot price process, and (b) developing a methodology for capturing all of the optionality in storage leases, given all the constraints and the spot price process. Each part is complex to solve, especially for ensuring that the price model can be calibrated to all market conditions seen in back-testing. We succeed in creating a two-factor tree model of valuation that brings together both parts so that back-testing could commence. The two factors, described in more detail in Section 2, can be thought of as representing a short-term weather effect and a longer-term effect of changing supply and demand forecasts.


In back-testing our valuation model we find it is very successful at consistently capturing vast amounts of optionality based on historical data. We tested the model on two types of storage leases: fast-cycle (the daily injection and withdrawal rates are such that the lease's maximum capacity can be filled and depleted in six cycles per year) and slow-cycle (the cycle-rate is only 1.5 per year). Using historical price data from 1999 to 2006, our simulated daily trading captured average values (not including the cost of the lease) of $1.244 per million British-thermal-units (MMBtu) over intrinsic value for the fast-cycle storage lease and $0.397/MMBtu over intrinsic value for the slow-cycle lease. Corresponding forecasts of those values from the model, before any simulated trading commenced, were $1.149/MMBtu and $0.402/MMBtu, respectively. Further, all values from simulated trading over those years were strictly greater than corresponding initial intrinsic values. We note one caveat about out price data: A time-asynchronicity exists within it, and obtaining data without such asynchronicity is extremely challenging. Our results and the effects of this asynchronicity are explained further in Section 5.


An interesting aspect of our modeled lease optionality concerns its dependence on inventory level. Secomandi (2010) discusses this aspect for simple storage leases. Specifically, correctly positioning the gas inventory to capture spot trends adds to the optionality; this implies storage leases possess follow-on optionality. For example, having zero inventory disallows one from withdrawing now and buying back later should spot prices shock up then trend down; however, being partly filled allows for that trading. Further, inventories associated with higher maximum injection and withdrawal rates, as seen in the ratchet schedule, allow for trading more volume as trends emerge, thus increasing optionality. The preceding suggests that storage lease optionality is typically, but not necessarily, greatest for inventories strictly between full and empty and is optimally extracted by trading spot daily as opportunities arise.


Our valuation model shows that, at any given time, these optimal inventory levels tend to group together into a pocket. Below that pocket, the maximum allowed injection at the current spot price is a positive net present value trade; above, maximum withdrawal is positive net present value. Within the pocket, no injection or withdrawal is recommended. Secomandi (2010) Theorem 1 proves this result for simple storage leases having no ratchets. The pocket is where the change in lease value for a change in inventory, up or down, is close to zero net present value at the given spot price. As the spot price moves, the pocket moves. Thus, for an inventory in the pocket, both directions of spot price movement, up or down, are likely to move the pocket to no longer include that inventory, which then leads to either injection or withdrawal being a positive net present value trade for that inventory. Whereas for an inventory outside the pocket, only one direction of movement increases the corresponding positive net present value for the optimal trade associated with that inventory while the other direction decreases it. Optimal storage trading consists of constantly trading inventory in the direction of the pocket, which is not only a positive net present value trade itself, but also increases the probability that either direction of subsequent spot price movement generates another positive net present value trade.


An intriguing result of our model is that multiple pockets of high-optionality, caused by ratchets, may exist at any one time. This behavior occurs when advantages exist for being on either side of the ratchet. For example, having a higher daily withdrawal rate above a ratchet while having a higher daily injection rate below that ratchet allows for trading higher volumes on either side of the ratchet as particular trends emerge. We illustrate this behavior in Section 5.


The paper proceeds as follows. Section 2 gives the mean-reverting, two-factor spot process used in valuing storage leases, including the reasons for choosing such a process. We also detail the backward recursion methodology used for valuing storage leases, which captures lease optionality for an arbitrary pricing tree while accounting for various trading constraints. Section 3 summarizes the calibration and delta-hedging procedures for the model. Section 4 details our estimation of mean-reversion speeds used in the price model; the estimates give evidence of heavy mean-reversion in U.S. natural gas spot prices. Section 5 gives back-testing results that quantify how much optionality may actually exist in storage leases. The section also details an example from the model relating optionality and inventory. Section 6 concludes with a brief discussion of future research on this topic.


(See the white-paper pdf on the website for all other sections)




References





1 One can find this information on the Energy Information Administration and the Federal Energy Regulatory Commission websites.
2 Inventory levels for which these rates change from preceding levels are called ''ratchets.'' Ratchets typically exist since injection rates get slower as facilities fill while withdrawal rates get slower as facilities deplete, just like filling and emptying a balloon.
3 Kjaer and Ronn (2010) claims that trading only forward contracts with storage in some cases can capture values close to such a spot trading strategy.
4 One million British-thermal-units is approximately equal to 1,000 cubic feet of natural gas.
5 "Intrinsic value" for storage leases is merely the value that can be risklessly obtained by buying and selling natural gas in the current forward market and using storage to hold any forward-purchased gas through to its subsequent forward sale.

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