This post presents a detailed examination of the pricing and optimisation of natural gas storage in competitive natural gas market. Over the past decade valuation approaches have been suggested. Of those approaches, the most general ones are based on Monte Carlo price simulations, allowing the evaluation of different market trading strategies and different assumptions about the underlying price process.
A number valuation techniques are discussed and a short literature review is given which concludes that on average, the highest estimated storage value is realised with a combination of spot optimisation and dynamic delta hedging in the forward market.
Gas storage assets role in the gas value chain
Storage plays a vital role in competitive natural-gas markets, because the average variability in the consumption of natural gas is much greater than the average variability in production. Demand is not only fluctuating, but often also at a considerable distance from the production sources. In both North America and Europe natural gas storage capacity measured by working volume is around 18% of total consumption.
Flexibility in the gas supply is also provided by production variations, pipeline and LNG transportation, but gas storage takes a large share of flexibility in many demand areas. For example, the US natural gas production has sharply increased due to the shale gas revolution in the past 5 years. The locations of production were not always well connected to the traditional demand areas, which has boosted investments in both transportation and storage.
A gas storage (asset or product) has three main operating characteristics; (1) working gas volume, (2) withdrawal rate and (3) injection rate. The working gas volume is the capacity that can be actively used in cycling the gas through the storage in several days, weeks or months. Another part of the storage volume, the cushion gas volume, is needed to maintain enough pressure, but is not used operationally; it may be a big portion of the initial investment though. The withdrawal or send-out rate defines the volume that can be withdrawn, often expressed per day or hour. It may be volume-dependent with lower rates when there is relatively little gas in the storage asset. Likewise, the send-out rate, the third primary storage parameter is often decreasing when the storage is almost full. Other important storage parameters are the variable costs for injection and withdrawal, the maintenance and support costs for operating the facility, and of course the location of the storage.
Natural gas storage assets have been constructed in different geological structures, which are often categorised in the following three groups: empty oil and gas fields, salt caverns and aquifers.
Empty oil and gas fields generally provide the largest working volume, i.e. the volume that can effectively be used for making cycles of injection and withdrawal in a year. Albeit being large in working volume, the deliverability, measured by the withdrawal or send-out rate, is often comparatively low. This means that former oil and gas fields are mostly used for providing seasonal flexibility, having the ability to cycle once or at most twice a year. Aquifers and salt caverns tend to have smaller working volumes but much higher deliverability. The right mix of seasonal and high-cycle storage assets, in combination with other sources of supply flexibility, is important for demand areas to absorb fluctuations in natural gas demand in a variety of market conditions. The larger and slower storage assets help to bridge the demand differences between seasons, for example fill up in summer and deliver in winter (heating). In turn, high-cycle storage assets, often in combination with LNG storage tanks, provide quick short-term security of supply, needed during a series of cold winter days (heating) or hot summer days (air conditioning creating high power demand).
In liberalised markets, the natural-gas storage service is unbundled from the production, sales and transportation services. This means that storage is offered as a distinct, separately charged service under different regulations of third-party access. When there is a sufficiently liquid market for spot and forward or futures trading, market players can adjust their trading and operating decisions to the price signals. This allows them to benefit from price spreads and price movements (volatility).
Market players tend to own or contract natural gas storage flexibility primarily for managing the fluctuations in their own portfolio. In areas with limited or no trading possibilities, storage capacity is inefficiently used, because every player has to secure sufficient flexibility in his own portfolio. Thanks to liberalisation, market players may not have to find the perfect balancing within their own portfolio. They may be net short or long flexibility and make their ultimate operational decisions based on a combination of internal flexibility sources and market prices. This leads to amore efficient use of available capacities for the market as a whole. The ongoing liberalization process in the European markets, and the improved decision making processes within the energy companies, is therefore one of the explanations of the lower price volatility and lower winter-summer spreads, especially on the continental markets. This has gone hand in hand with larger trade volumes and lower profitability of storage assets.
From the viewpoint of system security of supply this may be a dangerous equilibrium as under normal market conditions the available storage capacity is efficiently used and available at relatively low cost. However, over longer horizons (and in unusual market conditions) there may be a shortage of storage flexibility in the system. This is a general policy maker’s concern in liberalised markets which require long-term investments. The perfect policy mechanism for dealing with such potential under investments does not exist and individual countries have adopted a variety of approaches, ranging from holding ‘strategic’ reserves to investment subsidies or obligations on supply companies to contract a minimum level of storage capacity. All such mechanisms may increase security of supply, but introduce other market inefficiencies, both in the operational use of capacities and in new investments.
Pricing and valuation approaches to gas storage
There are basically four valuation approaches to natural gas storage; (1) intrinsic, (2) rolling intrinsic, (3) basket of spreads and (4) spot trading
It takes the current forward curve, calculates the optimal trades in the forward market and the corresponding cash-flows. The search for the optimal trades in the forward market includes all trades whose flows can be backed by the storage. This is the asset-backed trading principle. When the storage has volume-dependent injection or withdrawal rates, there may actually be no trades which can be exactly absorbed by the storage and at the same time use the storage capacities fully. In such situations it is common practice to calculate the optimal trades on a daily basis and then to spread the volumes over the products that are actually traded, such as months, quarters and seasons. In general, the intrinsic value, if it can be traded in the market, provides an immediate value and forms the lower bound to what can be actually achieved. The optimisation for the intrinsic calculation can be based on linear-programming (possibly with integers) or on dynamic programming.
The rolling intrinsic approach is very similar to the intrinsic, but also considers profits of rebalancing the portfolio over time. At every re-hedge date a new intrinsic optimization is executed, but including an initial position. This initial position is taken from the intrinsic optimization and any subsequent rebalancing trades.
The rolling intrinsic trading strategy is relatively popular among traders, because it is a safe strategy (the profit cannot go below intrinsic) which can be easily explained to others. In order to judge the potential future value of the rolling intrinsic approach, a representative set of potential future market price developments has to be simulated. For each simulation and each re-hedge date the rolling intrinsic approach requires a separate intrinsic optimisation, which may make it somewhat slow to calculate. The estimated future roll profits, averaged over the simulations, largely depend on the methodology to describe the forward price dynamics.
Roll trades are only profitable if the portfolio can be rebalanced, which is typically when a forward spread changes sign. Such spread sign reversals tend to happen in the shorter end of the forward curve. In any case, a fair rolling intrinsic valuation depends heavily on a realistic price process. Hence, a multi-factor price model, with multiple stochastic factors, is needed. The first (known) description of rolling intrinsic for gas storage is in Gray and Khandelwal (2004). Another article describing this approach is from Bjerksund et al. (2011). It should be noted though that they overestimate the benefits of this approach, mainly because they ignore the requirement that forward contracts should be actually traded.
Basket of Spreads
The basket of spreads approach treats a gas storage as a set of time spread options. As a simple example, suppose four quarters ahead can be traded and the intrinsic strategy is to buy the Jul-Sep forward and sell the same volume in the Jane-Mar forward of the following year. Then at any future date until end of June, whenever the Oct-Dec forward becomes cheaper than the Jul-Sep forward, a trader can roll the two products (sell Jul-Sep, then buy Oct-Dec). This is also the essence of the rolling intrinsic strategy. Whereas the rolling intrinsic strategy evaluates many potential scenarios to find out if a roll (and other rolls) are profitable, the basket of spreads values the optionality of a roll directly. Under certain assumptions similar to the ones underlying the Black-Scholes formula the spread options can be valued with the Margrabe’s formula or variations of it (Margrabe, 1978; Kirk, 1995; Li et al., 2008; Lo, 2014). The basket of spreads approach can be regarded as a simplification of the rolling intrinsic.
It has a number of important restrictions, in particular that the storage asset should be described as a set of non-path-dependent options., There are potentially more options to be exercised, but the potential exercise of one option may hinder (or allow) the exercise of another option. As a result, only few spread options can be considered and the approach undervalues the true storage value.
Eventually, traders can take operating decisions on at least a daily basis. In the presence of spot trading markets, this is why the true storage value should include a spot trading component.
Within the spot trading valuation approaches, three solution approaches can be distinguished: tree building, stochastic control and least-squares Monte Carlo.
Each has its own advantages and disadvantages, but essentially rely on the same principles. That is, all approaches model the dynamics of the underlying gas prices and find the optimal spot trading actions while taking into account future optionality. In general, the real option principle for storage assets is to find the right balance between immediate cash-flows and the creation of flexibility for higher future cash-flows.
Spot valuation – a simple example
Suppose that we have a gas storage with 100 therm working volume and 1 therm withdrawal rate per day; it is filled with 1 therm and the forward curve is flat at a price of 50 p/th. When the spot price is 50.5 p/th, an intrinsic strategy will advise to withdraw spot and sell at the forward price, thus locking in 0.5 pence profit (ignoring costs and discounting issues). However, releasing the gas today means the lost option- ality to inject the next day and later (unless we inject again). Therefore, depending on price volatility, it may be optimal to keep the single therm in store, thereby creating more flexibility for the future.
In a tree based approach (Manoliu, 2004; Felix and Weber,2012; Parsons, 2013) the spot price is described by upward and downward movements, each of which has a (possibly time-varying) magnitude and probability. In order to capture the mean-reversion and possibly other spot price dynamics, the tree should be constructed differently than in a standard binomial recombining tree used for many stock options (Cox et al., 1979). To capture the mean-reversion, there are typically three possible movements from a node to another node (a node is a price on a specific day) required. In each node of the price tree, the expected continuation value is stored for a discrete set of possible gas storage volumes. Then at any node a backward procedure determines which is the optimal storage action (injection, withdrawal, no action) which yields the highest sum of expected continuation value and immediate cash-flow. This backward procedure can be relatively fast. The main drawback is the limited flexibility to model prices in a tree.
Another optimisation approach to the spot trading decisions can be grouped under the name stochastic control. This type of approach is described in Thompson et al. (2009), Carmona and Ludkovski (2010), and Chen and Forsyth (2010). For example, Chen and Forsyth solve Hamilton-Jacobi-Bellman equation defining the stochastic control problem of the gas storage. The stochastic control approach is rather elegant, but does not (yet) seem to be widely adapted.
In contrast, the least-squares Monte Carlo (LSMC) approach has become a popular approach in the field of derivatives, with gas storage as a special application.
It is actually rather similar to the tree based approaches, with the advantage that there is complete flexibility in defining the gas price model. As long as the gas price model can be discretised and able to generate Monte Carlo simulations, the LSMC can be implemented. The LSMC approach has been popularised by Longstaff and Schwartz (2001), who actually give the main credits of the method to Carriere (1996). These early papers describe the valuation of American (financial) options with typically a single exercise. De Jong and Walet (2003) were the first to show how the LSMC can be applied to the problem of gas storage valuation.
The methodology bears great similarity to the tree building approach, with the main difference that the expected continuation values are not derived from nodes in the price tree. Instead, the storage LSMC performs a linear regression on each day, bundling the information from the cross-section of the simulated paths. All of the spot trading approaches can essentially be combined with a multi-factor price process, but the flexibility of Least-squares Monte Carlo makes this especially easy.
“…changes in volatility and
mean-reversion have a significant impact on the estimated storage
The valuation and optimal operation of gas storage assets in liberalised gas markets relies on a model, a gas forward curve and market parameter assumptions. So far, the literature has mainly focused on the modelling aspect.
With different assumed forward curves and market parameters, such as winter-summer spread in the forward curve and volatility of the spot prices, inevitably leading to different estimated and realised storage values.
Most value can be generated with a gas storage if the daily injections and withdrawals are adjusted to spot prices, for example based on the daily trading signals of the least-squares Monte Carlo method. However, realised values can fluctuate dramatically from year to year. Part of the fluctuations have to be accepted and are due to fundamental changes in the supply-demand balance resulting in different levels of price seasonality and price volatility. Another part of the fluctuations are more short-lived and can be effectively hedged in the forward market.