What Does the Model Consider as "Valuable" in Storage Leases?  (top)

As the user peruses this guide, it is worth noting what the WTM storage model considers as valuable in natural gas storage leases. This knowledge will help the user interpret the model results and recommendations much more clearly.

Purely and simply, the value in trading natural gas storage derives from being able to trade at same-day and next-day gas prices ("cash prices"). These prices possess very profitable trends (the most well-known trend is the winter/summer spread) and high volatility. Having access to a storage facility means that a trader can inject/buy when cash prices go too low and withdrawal/sell when prices go abnormally high. This ability to trade physical gas so as to exploit these trends is the optionality in storage.

Much optionality exists in storage, and that optionality is even greater when traders have the ability to either buy or sell gas from storage at any given time (by being partially filled). Further, if various gas storage inventory levels are associated with higher maximum daily injection/withdrawal quantities (MDIQs and MDWQs, respectively), then these levels become especially valuable! The trick for any storage trader is to (1) recognize the high-optionality inventory levels at any given time, (2) optimally trade toward those levels, (3) remain at those levels only for the term in which they are valuable, and (4) recognize and trade toward the next set of levels after that term. A lot of this so called follow-on optionality exists in storage leases, which makes the option value in storage very complex and not well-behaved relative to other American-type options.

The Storage Optimization Software (SOS^tm) from WTM Energy Software, LLC, gives values based on optimal trading/hedging, identifies the valuable inventory levels, recommends optimal trades each day for getting to those inventories, recommends optimal delta hedges each day for protecting total value (intrinsic plus extrinsic), and gives cash-to-prompt trading thresholds each day for buying and selling physical optimally.

In addition to these results, SOS also has a VaR (Value-at-Risk) Calculator that allows traders to ascertain how well total storage value is protected for any set of desired hedges. VaR minimizing hedges protect extrinsic value, not just intrinsic value! Thus, if traders prefer to use different hedges than the SOS recommended hedges, they can use the VaR Calculator to ascertain just how effective those hedges are. Relating storage hedges to extrinsic value protection is new and is just another valuable and unique feature of SOS.

 Overview of Worksheets Used to Run the Model  (top)

WTM's Storage Optimization Software (SOS^tm) is implemented through an Excel workbook containing 4 main worksheets, 1 calculator worksheet, 1 parameter sheet, and 1 reference sheet. The 4 main sheets and 1 parameter sheet are the ones from which the model extracts input or displays output. The 1 calculator sheet provides support in dynamic delta hedging. Note that copies of this workbook can be made for each storage lease, thus relieving traders from changing volume/ratchet inputs as different leases are valued. An overview of all sheets is now given.

The 4 Main Worksheets  (top)

Three of the 4 main sheets require the user to input a few values concerning the storage lease on each sheet. After such input, the user clicks a button to run the storage model. The model may take several minutes to run, depending upon the storage lease term and winter/summer spreads in prices and volatilities, but upon completion the output will appear on the fourth main worksheet, "4-Output." The specific outputs shown are

• 1. Total dollar storage value for the amount of gas inventory currently stored
• 2. Dollar storage value per unit of maximum capacity
• 3. Recommended physical trade for the current day
• 4. Recommended forward price deltas assuming the current inventory is held over until the next trading day
• 5. One-day-95% VaR of the delta-hedged storage value
• 6. Intrinsic Values and corresponding intrinsic hedges
• 7. Threshold cash-to-prompt spreads for optimal injection/withdrawal
• 8. A table of storage values, recommended physical trades, futures deltas, and VaRs for the whole range of inventory levels

Note that the values are given for the current inventory and do not include the average cost of gas for obtaining that inventory: Adding the average cost of gas to the model value gives one an idea of performance-to-date.

A sample and partial screen shot of these results is given below.



Only a partial screen shot is shown above, where some of the results in (1) through (4) and (6) are shown, and part of the results table in (8) is shown just below that. The rest of the results table's storage values, hedging deltas, and VaRs are not shown.

The threshold cash-to-prompt spreads give the spread to the prompt price that the cash price must pass in order to inject or withdrawal optimally. Note that this spread could be positive for injections (usually for very low inventories) or negative for withdrawals (usually for very high inventories). The results table discussed is output from the model to give the trader an idea of which inventory levels possess the most optionality for cash-price plays. Specifically, the inventories where the recommended physical trade is zero are typically the levels possessing the most optionality. These levels typically coincide with the highest VaRs. ¹ Also, if the trader subsequently injects or withdrawals on the current day, then the trader should consult the results table for the correct hedging deltas associated with the new inventory.

The table also shows which value is more important that day: intrinsic or extrinsic. If the region of high-optionality inventories is in the middle, extrinsic is more the focus; if the region is near full or empty, intrinsic is more the focus.

The 1 Calculator Worksheet  (top)

The 1 previously mentioned calculator worksheet supports the trader in dynamic hedging. It allows for the trader to perform what-if scenarios for hedging total storage value, both intrinsic and extrinsic! Specifically, the trader can enter a set of proposed hedges into the VaR Calculator, click a button, and the VaR of the storage value hedged with those proposed hedges appears. The VaR of the storage value hedged with optimal hedges is also shown for comparison. If the two VaRs are close, the trader can be confident that the set of proposed hedges will protect total storage value well. Thus, traders may now assess tradeoffs of locking-in intrinsic versus the effect on protecting extrinsic.

The 1 Parameter Worksheets  (top)

The 1 parameter sheet allows for three pieces of input: the short-term mean-reversion speed, the long-term mean-reversion speed, and capacity constraint on the net-delta. This last parameter is a percentage of tolerance (i.e., enter 10% as 10.0), relative to the lease's maximum capacity, of how far off the calculated optimal delta hedges are allowed to be from fully hedged. For example, both a value of 10.0 (meaning 10%) for this parameter and a value of 1 million MMBtus for the maximum capacity mean that the current inventory plus calculated injection delta hedges must be within 100,000 MMBtus of the calculated withdrawal delta hedges (but the total capacity hedged may be under the maximum capacity by more than 100,000 units, i.e., the parameter does not constrain this from happening). Thus, the optimal delta hedges calculated are calculated under the constraint implied by this parameter.

The two mean-reversion speeds are referenced in the white-paper as a and b, respectively. This paper is on our website and may be downloaded and printed.

The model has default estimated values for the mean-reversion speeds but allows for input of them since different mean-reversion speeds may apply for different storage locations. If the user wishes to override the default values, then the user must estimate these parameters outside the model and input them on the parameter worksheet. Within the model, these parameters are considered constants during valuations.

Note that the default values are a = 9.0 and b = 0.1. These values were estimated using data on different storage years, cycle-rates, and gas hubs around North America, so one may use these values if one cannot estimate them for the time being.

The 1 Reference Worksheets  (top)

The 1 previously mentioned reference sheet contains data and results that allow (1) for various other worksheets in the workbook to operate, (2) for your company to run the model (the model only works for certain company codes), and (3) for easier support from WTM if the calculation module should somehow fail. This sheet should not be deleted or modified in any way!

We now discuss the individual worksheets in detail.

The Worksheets in Detail  (top)

The storage model runs on the input of the four following worksheets: The sheets are named "1-StartHere," "2-PriceInputData," "3-VolumeInputData," and "Parameters." Not much input is entered on each sheet, but once the data is properly input, the user may click the button "Get Results" on sheet "4-Output" to run the storage model and get results.

The 1 calculator sheet and 1 reference sheet are explained further below.

Worksheet "1 - StartHere"  (top)

Upon opening the workbook (under "Enable Macros"), the cursor will be placed immediately on the sheet labeled "1-StartHere." Only 3 dates are to be entered on this sheet: the beginning storage lease date, the ending storage lease date, and the date for which the valuation is run, which is usually the current date (all in mm/dd/yyyy format).

Two click-buttons appear on the sheet. The "Erase and Rebuild This Sheet" button is used to clear the sheet and reload various cells with proper labeling and formatting for data entry. The dates are to be entered in the light-blue highlighted cells in "mm/dd/yyyy" format.

When all 3 dates are entered, the user clicks the other button, "Enter Dates and Click Here." The input dates are immediately checked for correctness, other sheets are updated based on the entered dates, and the next worksheet is shown. However, if an error exists with the dates, then an error message appears that tells the user about the problem. A screen shot of this sheet is shown below.

Worksheet "2 - Price Input Data"  (top)

This second worksheet is for input of market data: forward prices, physical premiums, contract volatilities, and interest rate data. On this sheet, 4 click buttons are present.

The button labeled "Get Prices, Vols, Rates" is used to load all values from row 12 downward (the values in cells B4 and B5 are always entered manually, and cell B7 is calculated). Note that since WTM does not know how you store this data currently, your IT department will have to modify the VBA code connected with this button in the back of this workbook in order to collect this data automatically. Until then, prices, vols, and rates will have to be entered manually.

The button labeled "Erase and Rebuild This Sheet" is used to clear the sheet and reload various cells with proper labeling and formatting for data entry. All input is entered in the light-blue highlighted cells, and the forward contract months (e.g. Apr-2005) and option expirations (e.g. mm/dd/yyyy format) that can be input are filled into the sheet automatically into their respective columns. Also, those contract months and expirations that are required entry are so marked (more on what is and is not required is given later).

The button labeled "Click to Fill in Dates" is just like the "Erase and Rebuild This Sheet" button with one major exception: All prices, rates, and volatilities that were on the sheet previously will not be erased; only contract months, option expirations, and which of them is required input are modified. Such a feature reduces redundant price/rate/volatility input.

Clicking the button labeled "Enter Data and Click Here" immediately causes all data to be checked for correctness, and the next worksheet is shown if all data are validated. If, on the other hand, a problem exists with the data, then an error message appears that tells the user about the problem.

The data entered on this worksheet consist of 3 groups: (1) - cash and BalMo-to-prompt spreads, forward prices, and physical premium data, (2) - volatility data, and (3) - interest rate data. A screen shot of this worksheet is now given.

Cash and BalMo-to-Prompt Spreads, Forward Prices and Physical Premium Data  (top)

The current cash and BalMo-to-prompt spreads per MMBtu are entered into the light-blue highlighted cells marked accordingly. They are required input and must be a number that makes sense. These numbers come from the traders around 8am as the cash market trades.

Forward price data is entered into four columns just below, and the cells are shaded in light-blue. The first of the columns should already have contract months, such as "Apr-2005," filled in. If not, or if you are unsure about which contract months to input and where, then click either the button "Click to Fill in Dates" or "Erase and Rebuild This Sheet," and the correct contract months will be shown.

The second column of the forward price data is for NYMEX prices per MMBtu. If the price's spreadsheet row is marked as required (the mark is to the right of the cell containing the price), then a number strictly greater than zero must be entered. If the price is not marked as required, then a price may or may not be entered at the user's choice, but no gaps must exist between expirations. Any contract months in the first column not required and not having prices entered next to them must be erased; otherwise, the model will prompt the user with an error message to supply prices.

The third and fourth columns are for location basis and physical premium per MMBtu, respectively. Both must be entered, even if zero, next to every entered NYMEX price, and these numbers can be positive or negative. However, any NYMEX price, its basis, and its physical premium must sum (the sum is the physical price) to be strictly greater than zero.

Volatility Data  (top)

Two columns of data (shaded in light-blue) are available for data entry: option expiration in mm/dd/yyyy format and percentage volatility. The required option expirations should be automatically filled on the sheet and correspond to NYMEX expirations. If the expirations are not filled, or if you are unsure about which contract months to input (and where to input), then click either the button "Click to Fill in Dates" or "Erase and Rebuild This Sheet," and the expirations will be shown in their correct placement.

For each option expiration, a single percentage volatility is entered (i.e., 50% is entered as 50.0). This volatility is merely the implied volatility of the contract corresponding to the option expiration. For example, if the prices are for a location very near Henry Hub, then the NYMEX implied volatilities will do. For a location far from Henry Hub, scaling the NYMEX implied volatilities will do.

Interest Rate Data  (top)

A set of two columns on the right of the worksheet, highlighted in light-blue, are used to input this data. Zero-coupon instruments on either LIBOR or Treasury strips can be used, but the company's WACC is more conservative. The data are entered starting from top to bottom and in ascending expiration order (no empty rows in the midst of the data should appear).

The first column is the maturity in mm/dd/yyyy format. The second column is for the continuously compounded yield-to-maturity, which must be entered as a percentage strictly greater than zero (i.e., enter 10% as 10.0). The longest maturity must be greater than or equal to the lease end-date.

Worksheet "3 - Volume Input Data"  (top)

This third worksheet is for input of operational data: maximum capacity, current capacity, fuel charges (both injection and withdrawal), commodity charges (both injection and withdrawal), ratchets, minimum requirements, and ad-valorem taxes. On this sheet, 2 click buttons are present.

The button labeled "Erase and Rebuild This Sheet" is used to clear the sheet and reload various cells with proper labeling and formatting for data entry. All input is entered in the light-blue highlighted cells.

Clicking the button labeled "Enter Data and Click Here" immediately causes all data to be checked for correctness, and the next worksheet is shown if all data are validated. If, on the other hand, a problem exists with the data, then an error message appears that tells the user about the problem.

The data entered on this worksheet consist of 5 groups: (1) - inventory data such as maximum capacity, current inventory, (2) - transaction costs, (3) - ratchet information, (4) - minimum requirement data, and (5) - ad-valorem taxes. A partial screen shot of this worksheet is now given.

Inventory Data  (top)

The "Capacity in MMBtus" is the maximum capacity of the storage lease and must be a number strictly greater than zero. The "Current MMBtu Inventory" is the amount of MMBtus currently in storage and must be a number greater than or equal to zero, but less than or equal to the maximum capacity.

Fuel and Commodity Charge  (top)

Two fuel charges per calendar month must be entered: one for injection and one for withdrawal. These are to be entered as percentages greater than or equal to zero (i.e., 1.5% is entered as 1.50). These fuel charges are applied in the same way that fuel charges are applied in gas transportation: The percentage is applied to a grossed-up volume such that the delivered volume is left remaining after applying the charge.

Two commodity charges per calendar month must be entered: one for injection and one for withdrawal. These are to be entered as numbers greater than or equal to zero and are in dollars per MMBtu.

If bid/ask spreads or transportation costs to/from the storage facility are involved, one may adjust these fuel and commodity charges accordingly (bid/ask spreads are just like extra commodity charges; transport may add both extra fuel and commodity charges).

Ratchet Information  (top)

The ratchet information consists of 25 columns highlighted in light-blue. The first column, "Level in MMBtus," is the starting-volume of the ratchet. The second and third columns, respectively, are for the MDIQs and MDWQs for each January of the lease term for that starting-volume. Both the MDIQs and MDWQs are entered in MMBtus, and they apply to volumes greater than or equal to the starting-volume but strictly less than the next ratchet starting-volume, and only for each January of the lease term. The fourth and fifth columns, respectively, are the MDIQs and MDWQs for each February of the lease term, etc. The last two columns, respectively, are the MDIQs and MDWQs for each December of the lease term.

The ratchet starting-volumes must be entered in strictly ascending order, starting from zero, and with no gaps in the data. Except for the first starting-volume, which is always zero, all volumes must be strictly greater than zero. The MDIQs and MDWQs must be numbers greater than or equal to zero. Only data entered in the light-blue cells are considered by the model.

The ratchet data presented to the storage trader are usually not given in a way that can be directly input on this worksheet. The proper way to create the ratchet lines to be filled on the worksheet is as follows:

• 1. start from 0 inventory and enter 0, its MDIQs, and its MDWQs on the first line of the ratchet section, respectively, for each calendar month;
• 2. going from 0 inventory, determine the next inventory level for which either an MDIQ or an MDWQ changes due to a ratchet or month; enter that level value, the MDIQs, and the MDWQs on the next line of the ratchet section, respectively (if either the MDIQ or the MDWQ changed at that inventory level or month, but not both, then the value for the one that didn't change is still entered on the line, and its value is equal to its value on the previous line);
• 3. continue performing step 2 until you reach the final inventory level for which the MDIQs and MDWQs no longer change up to the maximum capacity (therefore, the volume level of the last line in the ratchet section is a number strictly less than the maximum capacity).

For example, if a ratchet schedule is presented as follows . . .

• 0 inventory up to 499,999 the MDIQ is 10,000,
• 500,000 and over the MDIQ is 20,000,
• the MDWQ is always 15,000,
• no injection in January is permitted,

then two lines are input on the ratchet schedule as follows:

		Jan		Feb
	Start Volume	Inj	Wth	Inj	Wth
1.	0	0	15,000	10,000	15,000
2.	500,000	0	15,000	20,000	15,000

Minimum Requirement Data  (top)

Three columns of data, highlighted in light-blue, are entered. The first column is the minimum requirement volume in MMBtus, while the second and third columns are the beginning and ending dates for which the requirement applies. The volumes are entered in MMBtus and must be numbers greater than or equal to zero. The dates are entered in mm/dd/yyyy format, the beginning and ending dates may be the same, and those dates can be any date in the remaining lease term, including the current date or the end-date of the lease.

Note that no data whatsoever has to be entered in the minimum requirements section for the model to run. Also note that the requirements must start from the top and work down with no gaps in the data (but do not have to be in any date order). Lastly, only data entered in the light-blue cells are considered by the model.

Ad-Valorem Data  (top)

Three columns of data, highlighted in light-blue, are entered. The first column is the date the tax is figured on any working gas inventory, the second is the percentage tax (i.e., 1% is entered as 1.0), the third is the dollar per MMBtu tax. The model allows for both types of taxes to be entered at once.

Worksheet "Parameters"  (top)

This sheet is the final input sheet and holds three pieces of data: the short-term mean-reversion speed, the long-term mean-reversion speed, and capacity constraint on the net-delta. This last parameter is a percentage of tolerance, relative to the lease's maximum capacity, of how far off the calculated optimal delta hedges are allowed to be from fully hedged. For example, both a value of 10.0 (meaning 10%) for this parameter and a value of 1 million MMBtus for the maximum capacity mean that the current inventory plus calculated injection delta hedges must be within 100,000 MMBtus of the calculated withdrawal delta hedges (but the total capacity hedged may be under the maximum capacity by more than 100,000 units, i.e., the parameter does not constrain this from happening). Thus, the optimal delta hedges calculated are calculated under the constraint implied by this parameter.

The two mean-reversion speeds are referenced in the white-paper as a and b, respectively. Note that the white-paper can be downloaded and printed from the web site. These two inputs are needed to run the model, but their values will probably change only very infrequently.² Estimated values for a are typically in the 9.0 or over range, while estimated values for b are typically around 0.1. In the SOS model, a can be thought of as representing short-term weather effects on cash prices, while b can be thought of as representing longer-term supply/demand effects. For example, a spike in weather affects the cash price for several days, but that effect usually diminishes quickly; however, a new set of commercial customers coming on-line would cause movements in whole strips of forward prices due to these firms securing long-term supplies of natural gas.

The typical estimated values for both a and b are greatly different from the mean reversion speeds estimated from a one-factor model: The one-factor speeds are typically estimated to be 1.5 to 2.0 and can be thought of as an average of the short-term and long-term mean-reversion speeds.

The SOS model allows for input of estimated mean-reversion speeds since different speeds may apply for different storage locations. The user must estimate these values outside the model, but within the model, they are considered constants during valuations.

When one clicks the button "Erase and Rebuild This Sheet," the sheet is cleared, cells are reformatted and reloaded with proper labeling for data entry, and default mean-reversion speeds are filled in. The default values are a = 9.0 and b = 0.1. These default values were estimated using data on different storage years, cycle-rates, and gas hubs around North America, so one may use these values if one cannot estimate them for the time being. A screen shot of this sheet is below.



Note that both a and b have upper and lower bounds within the model. If either input value violated its bounds during a model run, then the bound value is used within the model, and the input value will be overwritten with the bound value after the model finishes. Bounds facilitate stable calibration, but one should not find the bounds very constraining. The following bounds are in effect:

	Upper Bound	Lower Bound
a	150.00	5.00
b	1.5	0.05

Very, very rarely will credible estimates of a or b be outside these bounds.

Worksheet "4 - Output"  (top)

WE RECOMMEND THAT YOU SAVE THE WORKBOOK PRIOR TO EACH VALUTATION; doing so will cause all of your input to be saved if Excel should end abnormally during a valuation, which is extremely rare but does happen.

Running the Model  (top)

On this worksheet 2 click buttons are present. The button labeled "Erase and Rebuild This Sheet" is used to clear the sheet and reload various cells with proper labeling and formatting.

Clicking the button labeled "Get Results" immediately causes all the data entered on all before-mentioned worksheets to be checked for correctness. If a problem exists with the data, then an error message appears that tells the user about the problem. If not, then the model runs for a few minutes and produces the output that was shown above in the "Overview" section. On most of today's PCs, the model takes about 8 minutes per year of storage trading in the lease to run.

Interpreting Odd-Looking Output  (top)

At certain times, especially when the storage lease end-date is near, the model's recommended physical trades will look odd. Specifically, the results table on the sheet "4-Output" will show several pockets of inventory levels for which the recommended trade is zero. Below is an example of such output.



Notice the output says that we should trade to one of three inventory regions, depending upon our current inventory: the region of 5,000 to 25,000, 60,000, and 75,000. First, note that a ratchet exists at 60,000 in which the maximum daily withdrawal quantity dramatically increases (mathematically, ratchets are the cause of several such pockets occurring) Also note that 20 days are left in the storage lease in this example.

At first glance, the output looks wrong, especially for inventories of 60,000 and greater. The output is correct; here is the intuition. Recall that storage value occurs from trading on profitable trends in cash prices, and that having some gas in storage allows one the added optionality of profiting from both up and down trends. Since the lease end-date is only 20 days away, a high-optionality inventory region from 5,000 to 25,000 makes sense: One can take advantage of both up and down trends in cash prices without the threat of leaving gas in storage by the lease end-date. Further, attempting to inject to 60,000 so as to take advantage of the higher withdrawal rate does not make sense if it will take several consecutive days of injection to do so.

However, if your current inventory is 55,000, then injecting one more day allows one to profit from higher withdrawal rates on subsequent days. And if one is at 65,000, then withdrawing only 5,000 allows one to still profit from higher withdrawal rates on subsequent days. This reasoning explains why an inventory of 60,000 has added value.

Lastly, the inventory of 75,000 becomes significant since the higher withdrawal rate just happens to be 15,000/day: At 75,000, one may withdrawal at 15,000/day for two days, as opposed to just one day for inventories below 75,000 but greater than or equal to 60,000. Thus, being at 75,000 has added value over being at, say, 60,000.

This reasoning explains a lot of the "saw-tooth" pattern seen in recommended trades across inventories. But at higher inventories in this example, the saw-tooth pattern is not present since one must keep withdrawing, rather than choosing particular days to withdrawal, so as to not leave gas in storage by the lease end-date.

Worksheet "VaRCalculator"  (top)

This worksheet is utilized after the storage model runs and results display on sheet "4-Output." This sheet's main purpose is to aid the user in assessing how hedges not proposed by the model protect total storage value, both intrinsic and extrinsic value, for the current inventory. Storage traders typically lay hedges on to lock-in intrinsic value; however, those hedges may not do an adequate job of protecting extrinsic value (which is protected more by hedges that reduce daily VaR), especially if physical and financial storage positions are adjusted frequently! This sheet allows traders a way of assessing extrinsic protection among different sets of proposed hedges.

On this sheet, the user inputs a proposed set of hedges, clicks a button, and the VaR of the whole position (storage values hedged with the proposed hedges) is displayed in a yellow-highlighted cell. Next to that in another yellow-highlighted cell is the VaR using optimal hedging. This result is displayed as reference for the user to know how VaR may be minimized. Thus, if the two VaRs are close in value, then the trader may be confident that the proposed hedges protect extrinsic storage value.

Also on this sheet, 2 click buttons are present. The button labeled "Erase and Rebuild This Sheet" is used to clear the sheet and reload various cells with proper labeling and formatting for data entry. All input is entered in the light-blue highlighted cells. This button should be clicked anytime the user is unsure of where inputs should go.

Clicking the button labeled "Get VaR" immediately causes all data entered on this worksheet to be validated. If a problem exists, then an error message appears that tells the user about the problem. If not, then the two before-mentioned VaRs appear in yellow-highlighted cells.

The input labeled "Held-Over Inventory" allows the user to input the amount of stored gas (in MMBtus) to be held over from the current day to the next (how well the hedges protect extrinsic is dependent upon held-over inventory). Thus, the model does not assume that the user will follow the recommended physical trade that day. The "Held-Over Inventory" must be greater than or equal to zero and less than or equal to the maximum capacity.

Just below the "Held-Over Inventory" is a range of cells to input the proposed set of hedges (in MMBtus; longs are positive numbers, shorts are negative). The tenors of the forward contracts used in hedging are displayed just to the left of the input cells (Click "Erase and Rebuild This Sheet" to update the contract tenors). The tenors' range starts from the current date and goes to the storage end-date. If less than 2 tenors remain in the storage lease, the model will display 2 tenors (so the user can always use at least 2 contracts to hedge). A screen shot of this worksheet is shown below.



Note that one can see the VaR of the un-hedged storage lease (at the held-over inventory) by entering zeros for all the contract hedges. Doing this gives the user an idea of how much total risk needs to be hedged.