# American options -  early exercise



## Rainmaker (2 May 2009)

Someone was explaining this to me, was hoping sombody could clarify:

Say you have a 1year call on usd/jpy (i.e. call on usd, put on jpy). Strike is say 100.

In 9 months time, spot is say at 120. If you wanted to sell the option, you have 2000 jpy points of intrinsic value and let's assume 20 points of time value. So you can receive 2020 jpy points if you sell the option.

If you want to exercise, you can buy spot at 100, immediately sell at the prevailing rate of 120, earning 2000 jpy points. You then roll your position by buing dollars forward for 3months (why are we doing this rolling??). Let's say forward points are -16, so you can buy dollars 3 months forward at 99.84. So you have actually "earnt" 16 jpy points by rollowing it forward (??). Hence in this case the "forward value" being greater than the time value of the option means you would exercise.

He said because you want to hold the underlying is the reason you "roll" the position forward. I thought simply the value of that early exercise was whatever the intrinsic value turned out to be (2000 jpy points in this case) ?

He went on to say that "there comes a point in the life of an American option, where exercising the option and holding the underlying to the expiry date is actually more advantageous than holding the option to the expiry date. So it's important to compare (and that's why you roll the spot forward) the return on the two available options if you held them over the same time horizon".

If anyone could help elaborate on this i would be grateful!


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## Timmy (2 May 2009)

I am not quite with you here, just clarify a couple of things for me pls:



Rainmaker said:


> If you want to exercise, you can buy spot at 100, immediately sell at the prevailing rate of 120, earning 2000 jpy points. You then roll your position



If you exercise at 100 and then immediately sell at 120 you don't have a position, you are square.  There is nothing to roll.






Rainmaker said:


> by buing dollars forward for 3months (why are we doing this rolling??). Let's say forward points are -16, so you can buy dollars 3 months forward at 99.84.



If spot is 120 and forward points are -16 then you are buying at 119.84, not 99.84?


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## Timmy (2 May 2009)

More generally, if you buy USD forward (in the case above 3 months forward) then you will take delivery of the USD in 3 months time (not in two days if you buy spot), thus forgoing 3 months of interest on the USD (that's why forward points exist).  That's why the USD looks cheaper 3 months out, but forward points compensate for this.


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## Rainmaker (3 May 2009)

Timmy said:


> I am not quite with you here, just clarify a couple of things for me pls:
> 
> 
> If you exercise at 100 and then immediately sell at 120 you don't have a position, you are square.  There is nothing to roll.
> ...





On your first point, i agree and I was told that the idea is that the investor "really wants to hold the underlying" so he can again buy forward USD at the prevailing forward rate (this is apparently needed to make a valid comparison). And you are correct on your forward points comment I believe.

I was further told "there comes a point in the life of an American option, where exercising the option and holding the underlying to the expiry date is actually more advantageous than holding the option to the expiry date. So it's important to compare (and that's why you roll the spot forward) the return on the two available options if you held them over the same time horizon. All this is encapsulated in the concept of 'cost of carry'."

Do you make any more sense out of that? I'm still confused about how rolling the spot forward is neccessary to make a valid comparison? 

Thanks!


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## sails (3 May 2009)

Rainmaker,

If it was a broker telling you that, I'd just a bit suspicious they are looking for multiple transactions which means more fees for them...   Doesn't make a lot of sense to me, but then I'm not into currencies.  I expect there are nuances with currency options, so wouldn't like to speculate on how they work either.  Have put a few links below that may be of help re currency options:

http://www.investopedia.com/articles/optioninvestor/09/early-exercise-oex.asp

http://www.cmegroup.com/trading/fx/files/FX-199_OptionsTraderHandbook.pdf

http://www.ise.com/assets/files/FX Options/FX_Options_-_Investor_FAQs_010609.pdf


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