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thtang
May 2nd 2008, 06:10 AM
I would like to ask why for a non-dividend stock option, an american call will not be exercised early while an american put may be exercised early?

How to prove that?

Thanks.

JDav
May 2nd 2008, 09:55 AM
Essentially, it's because the drift (expected change) of the underlying asset is positive, which helps a call holder but works against a put holder. So, any call holder in any state of the world (aside from on expiry day) does better on a risk-neutral expected-value basis to hold, while _some_ put holders may see all future risk-neutral expected-value rewards to be lower than the immediate reward available from exercise.

Suppose strike is 10, and the current asset price is 3. Immediate exercise gains 7, while waiting any amount of time means an expected rise in the asset price (working against you) plus whatever reward you get needs to be discounted to compare to the 7 you can get today.

Hope that helps.

zmkramer
May 2nd 2008, 10:58 AM
Essentially, it's because the drift (expected change) of the underlying asset is positive, which helps a call holder but works against a put holder. So, any call holder in any state of the world (aside from on expiry day) does better on a risk-neutral expected-value basis to hold, while _some_ put holders may see all future risk-neutral expected-value rewards to be lower than the immediate reward available from exercise.

Suppose strike is 10, and the current asset price is 3. Immediate exercise gains 7, while waiting any amount of time means an expected rise in the asset price (working against you) plus whatever reward you get needs to be discounted to compare to the 7 you can get today.

Hope that helps.

To add to that: From a purely theoretical standpoint

The reason why you would exercise an american call early is to take advantage of the dividends you would receive as opposed to present value of interest on the strike price

Since a non-dividend paying stock pays no dividends, any benefit of early exercise is nullified.