2c) Give an example to show that the American put can be worth more than the European put, that is, where immediate exercise of the American gives payout at times T strictly greater than the payout of the European. Hint: Exercising early means the strike price K will be received early.

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Asked Nov 11, 2019
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2c) Give an example to show that the American put can be worth more than the European put, that is, where immediate exercise of the American gives payout at times T strictly greater than the payout of the European. Hint: Exercising early means the strike price K will be received early.

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Expert Answer

Step 1

The put option for both American and European options are as follows:

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P,(0)2 (K-S(0)) P (0)2 (KB (0,T)-S(0)) Where The American put option is P (0) The exercise price is K The stock price is S(0) The European put option is P(0) The profit bounded by K at time zero is KB(0,T)

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Step 2

It is proved from the above two put options is that if 

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P,(0)< (K-S(0))

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Step 3

Then buy an American put option and exercise it immediately, yielding, then, the total cash f...

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P(0)+(K-S(0))>0

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