Commodity Future Pricing

[Anonymous]

Hoping someone can help clarify these for me.

Kesdee’s Futures and Forwards training module calculates commodity futures as:

Price = (spot x e^rt) + storage costs
OR
Price = (spot + PV(storage costs)) x e^rt

The module then provides examples that utilize both equations, but I still don’t quite understand when to use which. Any help here?

Also, the PRMIA handbook seems to focus on the non-continuously compounded formula for commodity futures prices:

Price = spot x (1 + r + storage costs)^t

The continuously compounded formula that, I think, Kesdee focuses on is relegated to a footnote in the handbook. So I’m concerned about preparing for Exam I with Kesdee’s continuously compounded formula, which will give slightly different answers from PRMIA’s formula noted above. Are the formulas actually correct and I’m just missing something in the math here?

Thanks in advance for any help or advice!

[Anonymous]

KESDEE formula that you are referring to:

Both formula are essentially the same.

The first one will be used when you are given the storage cost that is to be paid at the end of the contract period.

The second one uses PV(storage cost), So this will be used when what is given to you is the value of the cost in todays term – and we need to take it forward to the end of contract maturity.

The idea is – we need to have the price for some future time.

If the cost given is already the cost of the ending time – No need to have the Present Value and then take it forward — It can directly be added (Like in the first equation)

On the other hand, if what is given to you is the present value – you need to add it to today’s price — and then take all of that forward by e^rt (second equation)

PRMIA formula

First Note that the formula you have quoted would have storage cost in % terms which is why it is being added to the risk free rate – unlike the KESDEE formula you quoted where the cost was in $ terms.

The continuous way of writing the PRMIA formula would be:

Price = Spot x e^[(r + cost)*t]

Similarly you can also re-write your KESDEE formula on a non-continuous basis:

Price = [spot x (1+r)^t] + storage cost
Or
Price = (spot+PV(cost)) x (1+r)^t

Therefore what you need to understand:

1. Is the storage cost in percentage or in $ — If it is in percentage you need to use the PRMIA formula — If it is in $ terms you need to use the KESDEE ones

2. Is the cost given – already in future terms or is it the present value — This will only be the case if the cost is given in $ terms – and you can use the logic I explained above with KESDEE formula — If the cost is in % terms this wont be concern, you can just use the PRMIA formula

3. Is it supposed to continuous compounding method or discrete method? This the question should actually specify. If not try both, there will be only option close to one of the answers you get. It is doubtful that you will have an option matching the discrete method answer and an option matching the continuous method answer

[Anonymous]

Wow thank you so much aakashahuja! That’s a very comprehensive and clear explanation; very much appreciated!

[Author]

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