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# Early exercise of american options

Discussion in 'Options' started by erasmus, Apr 29, 2009.

1. ### erasmus

My university tutor was explaining this to me, was hoping someone 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) ?

Thanks.

2. ### Martinghoul

You need to compare apples with apples...

The idea your professor is trying to convey is 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. All this is encapsulated in the concept of 'cost of carry'.

3. ### xflat2186

Since the cost of carry is priced into the option your options values in your example can not be right. Any advantage you would get in exercising those options early should be priced into the option since they're options on cash currency pairs

4. ### erasmus

thanks for your reply, i am still not really clear on this rolling forward idea.

I am thinking of two cases:

Case 1: Sell the option now. Invest proceeds at risk free rate for remaining 3 months.

Case 2: Exercise option now and lock in intrinsic value of 2000 jpy points. Invest this profit at risk free rate.

This actually doesnt make sense to me as you would always have more value in case 1 because of the options time value. I am probably missing something obvious here so if you could spell out your post I would be very grateful.

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