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Topic Title: Another weird but real life exotic
Created On Thu Nov 14, 02 04:29 PM

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Trendfollower
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Thu Nov 14, 02 04:29 PM

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This is an option on the spread between the commodity price on any of the first 15 business days of the month and the average of the full month (21 business days).

The option holder can chose the expiry day as any day between the 1st and 15th day of the month and the payout is the price on the chosen expiry day against the average of the month.

If the option is not exercised by the 15th day then it is automatically settled using the price on the 15th and the average of the month (positive or negative so it is not really an just an option but also some kind of forward).

Assume there is cash setlement always at the end of the month after the average is known.

For example, if the market is in contango then one would probably exercise on the first day of the month while if the market is in backwardation one would wait longer.

Any ideas?

Ziggy
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Fri Nov 15, 02 01:39 AM

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I've seen similar structures in oil business (corporate). I don't see the optionality in the structure, since you are commited to fix the price within the 15 day timeframe, you cannot excape fixing it at some point. You can fully hedge the structure with forwards, provided you select the day of strike-setting in beforehand (either first day or last depending on backwardation/contango).

If I understand you correctly, you pay the average and receive the strike. If we have a contango and fully hedge it would probably be best to excercise on the 15th
Initially you would do the follwing: Buy 21 forwards each 1/21 of the principal, expiring every day of the month and sell full principal forward with maturity on the 15th.
Every day you close all maturing forward contracts on the spot price.

Payout of individual components is the following:
The option structure is: Short the average ( S-A) & Long the strike (X-S)

21 long forwards: (A-Fa) since the combined spot values for all dates 1/21 is just the average
1 Short forward: (Fx-X)

Combined payout is:
(S-A)+(X-S)+(A-fA)+(Fx-X) = Fx-Fa. This result is determined at trade date

S = initial spot
A= average for whole month
X = Strike price
Fx = forward price at initial date maturing on strike date
Fa = average forward price of the 21 forwardss

But then again, here I'm assuming that this "option contract" is the only commodity exposure you are having. If you have other underlying exposures you might hedge differently, but the standalone value of the contract would still be the same.

Z

Trendfollower
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Fri Nov 15, 02 08:47 AM

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Thank you Ziggy. You are right we should not be calling this structure an option but perhaps "flexible forward" or something like that. However, I do see optionality in it. Suppose the tenor is one year out, say December 2003 and the market is in contango at first but can change several times during that one year period.

The hedge is to buy the Average (21 forwards) and sell 21 times larger amount on the last day (i.e. 15th). If the market is in backwardation then I still have to buy the Average but I will be selling the first day instead of the last.

So if the market keeps changing from contango to backwardation I will have to keep changing my hedge between the 1st and the 15th. This is where the hedging cost becames important and we need to know what is the delta. I do not think assuming delta equal to 1 is optimal.

Suppose the market is flat then I would probably put one half the short position into 1st day and another half into the 15th day (the long position will be unchanged and spread through the 21 days).

There is a premium for this structure even in a flat market and there should be a way to calculate both the premium the delta perhaps by assuming some correlation between the 1st and 15th day.

Trendfollower
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Fri Nov 15, 02 09:45 AM

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Thinking a bit more about this: perhaps I can just buy the Average, sell the 1st, and buy the option on the spread between 1st and 15th? Would not this be a perfect hedge?

Ziggy
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Fri Nov 15, 02 08:38 PM

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I missed out the optionality which is in in the changing cost of carry. So if you start of with backwardation and then few days later the market is contago you can increase profits by moving the excercise day closer in time and closing out the single-forward agreement. In many scenarios this option is almost worthless, e (like backwardation with very negative cost of carry), and the value of the option depends on the volatility of the CC slope. The net-profile for the first 15 days is that every day you have the option of selling forward to the 15th at SPOT PRICE not the forward price

I think that you overhedge by buying the spread between 1st and 15th, since the residual option-exposure is on carry, not spot rates.

Z

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