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list1
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Re: American option exercise time

March 30th, 2017, 2:35 pm

I have a voucher that entitles the holder to one of the following tomorrow:

 
A car worth $50,000
A holiday worth $5,000
A cup of coffee worth $5
 
The holder can choose any one of those three. 

I think that the example does not relevan because the choice of incomparable options. In the same way it looks more simpler to ask what is better apples or bears. If one think that the choice of exercise time leads to incomparable issues why does one talk about optimality or even suggests to hold it up to maturity moment?
 
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outrun
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Re: American option exercise time

March 30th, 2017, 2:42 pm

Image
 
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list1
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Re: American option exercise time

March 30th, 2017, 4:56 pm

Image
As far as I failed to take a right choice one who asked or participated in discussion can easily demonstrate the right choice and explain why.
 
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Paul
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Re: American option exercise time

March 30th, 2017, 5:06 pm

You don't have to worry about relevance. Just see if you can answer this question. It's quite simple!
 
frolloos
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Re: American option exercise time

March 30th, 2017, 8:37 pm

A coffeeshop in amsterdam
I think he (list) already is, quite sure all his posts are from an Amsterdam coffeshop, with accompanying cake :-D
 
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list1
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Re: American option exercise time

March 31st, 2017, 1:34 am

There are two primary points one should understand in order to make valuation approach to AO
1. for any random moment [$]\tau ( \omega )[$] when option is exercised the value of American option call or put is equal to its European version

[$]V_A ( 0 , S ( 0 ) ; t , K ) \chi ( \tau ( \omega ) = t ) = V_E ( 0 , S ( 0 ) ; t , K ) \chi ( \tau ( \omega ) = t )[$] 

and nothing can be other. This construction leads to random price and randomness is specified by time of exercise.

2. Next one should define spot price, A reasonable model of the spot price is expected value of the random price. Now we should define optimal exercise time for Aos. The point is one moment is more optimal than other if its expected rate of return on [ 0 , T ] is larger. We should apply risk free rate to continue payoff from the moment [$]\tau [$] up to T. 

If one disagree with such approach arguments should be look more formal than a voucher Amsterdam coffeeshop.
 
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outrun
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Re: American option exercise time

March 31st, 2017, 6:01 am

You don't know how to answer Paul's question?!
 
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Paul
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Re: American option exercise time

March 31st, 2017, 6:19 am

I suspect that list is on the Autism Spectrum. That is why he struggles with analogies.

List, have you been diagnosed as having Autism Spectrum Disorder?
 
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list1
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Re: American option exercise time

March 31st, 2017, 8:08 am

I do not see a connection Paul's question to the problem to a definition of the exercise moment of American option. If this connection will be clear  I will try to answer.
 
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outrun
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Re: American option exercise time

March 31st, 2017, 8:15 am

Looks like we have a standoff!

Paul said that if you answer the question then he we gradually change the example to the American call, and then the connection will become clear to you.

Image
 
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list1
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Re: American option exercise time

March 31st, 2017, 8:32 am

Looks like we have a standoff!

Paul said that if you answer the question then he we gradually change the example to the American call, and then the connection will become clear to you.

Image
Sorry, the picture does not help me to find a connection voucher's question to AO exercise time definition. 
 
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Paul
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Re: American option exercise time

March 31st, 2017, 8:39 am

List, are you on the Autism Disorder Spectrum? This will help us to come up with better explanations.
 
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list1
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Re: American option exercise time

March 31st, 2017, 8:51 am

I do not see yet how does Autism Disorder Spectrum new question helps you to answer how does Voucher problem relates to early exercise AO.
 
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Paul
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Re: American option exercise time

March 31st, 2017, 8:55 am

Because if you have ASD (and it is very common among mathematicians) then we should use examples with numbers and symbols rather than analogies. Knowing this about you will help us to choose the best way of explanation for American options.
 
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outrun
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Re: American option exercise time

March 31st, 2017, 9:00 am

Looks like we have a standoff!

Paul said that if you answer the question then he we gradually change the example to the American call, and then the connection will become clear to you.

Image
Sorry, the picture does not help me to find a connection voucher's question to AO exercise time definition. 
The picture is one of the most iconic shootout movie scenes. Three people are waiting for the other to make a first move, they wait for ages. This is what you are doing: you refuse to answer a very simple question because you don't see the connection. However the purpose of asking the questions, and you answering it is precisely to help you understand the connection that you fail to see!