Natural gas storage allows the operator to store (inject) a volume of gas for sale (withdraw) at a later date. Physically “Storage” is a gas reservoir with pipes and compressors attached to it. The physical characteristics that dictate operations are: total working gas capacity (volume of gas that can be injected and withdrawn), rates of injection and rates of withdrawal. Injection and withdrawal rates can change depending on how much gas is in the reservoir.

A storage owner/operator often sells capacity as storage contracts. These contracts express physical properties and actual operating costs of the storage in terms of constraints and costs imposed on the counterparty. There are many different combinations of these parameters within contracts reflecting physical and operational diversity of storage reservoirs. The AdaptiveRisk Storage Model has sufficient flexibility to price most such contracts.

The suggested way to read this document is with the Storage Model page opened up, so that one can see examples of inputs.

Data Required for Pricing Storage Contracts

Conversion Factors

There are several ways to specify a unit of natural gas that is used in describing and pricing storage contracts. The intent of this subsection is to list all of them for reference:

Btu - British thermal unit
Therm - one therm equals 100,000 Btu
cf - cubic foot

Even though the first two units describe heat content and the third is a unit of volume, the following standard conversion between volume and heat content is accepted:

1 cf = 1,036 Btu

These units are often prefixed by power of tens indicators:

M - one thousand (1,000)
MM - one million (1,000,000)
B - one billion (1,000,000,000)

The AdaptiveRisk Storage Model uses only MMBtu to describe gas volume.

Physical Storage Constraints

Capacity (MMBtu)

“Capacity” is the total amount of working gas of the storage. Usually contracts specify this value in Bcf (billions of cubic feet). 1 Bcf = 1,036,000 MMBtu

Rate Constraints (MMBtu/Day)

In the simplest form, the injection and withdrawal rates are constant numbers independent of the amount of gas in storage, specifying how much gas we can inject or withdraw in one day. Often these rates are specified in terms of percentages of the Capacity. In some contracts the injection and withdrawal rates might differ from month to month.

In actuality, the injection and withdrawal rates do depend on the level of storage, and therefore contracts often specify different rates for different intervals of storage levels (described in % of Capacity). Such specifications are called ratchets.

In yet more complex contracts the ratchets can be different in different months.

Rated Constraints

When there are ratchets, the optimal monthly injection/withdrawal volumes often require rates to change throughout the month. In this case it would be impossible to set up a hedge using forward contracts, since these contracts specify constant (rated) delivery of gas over the month.

The AdaptiveRisk Storage Model’s flag Rated ensures that optimization is performed only over policies that result in constant injection/withdrawal rates over each month.

Level Constraints

A storage contract starts and ends with specific natural gas storage levels. Most contracts spell out what these levels should be: empty-empty (most common), full-full or any other. Sometimes the storage owner specifies that at the end of a particular month the storage level should be within a specified interval (usually to ensure reliability of gas supply).

Volume Constraints

Sometimes storage owners require minimal injection or withdrawal volumes in particular months.

Costs

Injecting and withdrawing gas to/from storage is done by running compressors. The cost of operating compressors is passed to the storage contract buyer through a fixed cost per MMBtu injected/withdrawn and a percentage of gas used to run the compressors.

There are several ways to assign these costs. The AdaptiveRisk Storage Model assumes that all costs are applied to volume in storage. I.e. to inject x MMBtu’s of gas into storage one needs to buy (1 + InjectionFuel)x MMBtu’s. In this convention, the fixed cost is applied to the gas that ends up in the storage, i.e. it will be InjectionCost x. Similarly for withdrawal: when withdrawing x MMBtu’s from the storage, only (1 - InjectionFuel)x will be available for sale once the fuel cost is used by the compressors, but the fixed cost will apply to the full withdrawal amount x.

Another convention is to apply all costs to gas outside of the storage. Comparing volumes bought/sold to volumes that ended up in the storage, one can derive the conversion formulas to adjust these costs to the AdaptiveRisk Storage values (this outside storage gas convention values are prefixed by Out, e.g. OutInjectionFuel):

InjectionFuel = OutInjectionFuel/(1 - OutInjectionFuel)
InjectionCost = OutInjectionCost/(1 - OutInjectionFuel)
WithdrawalFuel = OutWithdrawalFuel/(1 + OutWithdrawalFuel)
WithdrawalCost = OutWithdrawalCost/(1 + OutWithdrawalFuel)

Valuation Day Data

The valuation date data consists of market information, as well as the initial level of storage.

The market data consists of bid/ask prices of relevant monthly contracts, as well as the discount factor to the middle of each month.

If storage is managed using intrinsic positions, it is possible to specify existing intrinsic position, then the optimization will produce incremental benefit of adjusting this position. This feature is handy if a trader hedges storage using rolling intrinsic method.

Extrinsic Valuation

Since a buyer does not need to commit to injection or withdrawal at the time of contract initiation and can postpone that decision to the day of actual operation, there is value in the storage contract due to availability of a delayed decision. This extra value is called extrinsic. Often it is possible to capture total value (intrinsic+extrinsic) using delta hedging.

To be able to accurately calculate the extrinsic value of the storage contract in addition to forward prices, one needs to know statistic properties of these prices. The most common statistical model used for this purpose is the Joint Geometric Brownian Motion. The parameters that specify a Geometric Brownian Motion are volatilities and correlations between contracts. These parameters can exhibit term structure: they can change as the valuation time approaches the contract expiration times. The AdaptiveRisk Storage Model can take this term structure into account by using two HJM type models.

To fully specify forward price dynamics, the storage model requires term volatilities (volatility of vanilla option from valuation date to its expiration before start of the delivery month) for each monthly contract in the delivery period. This data is often readily available from the natural gas option market. On the other hand, the market information about correlations or term structure is very limited. In such cases the common approach is to use historical data to calibrate required parameters. The AdaptiveRisk Storage Model adopts a specific functional form that uses five parameters to describe the term structure of volatilities and correlations. It provides a tool that allows for fast and robust calibration of these parameters if historical data is available.

For testing purposes it is possible to assume that there is no term structure of volatility or correlation. This way each contract’s volatility is constant from valuation day to expiration and is equal to the term volatility. The user can then specify a constant correlation matrix between all contracts. The AdaptiveRisk Storage model allows for such specification.

Storage Model Outputs

Intrinsic

If only intrinsic calculation is requested, the results page has the following information:

Intrinsic - dollar value produced by intrinsic valuation
Intrinsic Hedge - volume of forwards needed to buy/sell in each month to hedge intrinsic value
Intrinsic Inventory - level of storage at the beginning of each month if injection/withdrawal follows the schedule produced by intrinsic valuation (i.e. if forward in intrinsic hedge are held for the physical delivery and all gas received is put into storage and all gas sent is obtained from storage).

This information is provided in tabular form as well as on a plot. The user can click on the plot legend to remove or add back some of the described data series.

Extrinsic

If extrinsic calculation is requested, the results page has the following information:

Premium (intrinsic+extrinsic) - total dollar value of the storage contract
Extrinsic - dollar value of extrinsic part
Intrinsic - dollar value of intrinsic part
Delta - delta position for each monthly forward contract
Intrinsic Hedge, Intrinsic Inventory - same as in the case of just intrinsic calculations
Vega - sensitivity of premium to 1% variation of each term volatility