List1, can you -just like me- also see other people besides me on this forum? Can you see Paul's post?
I read a few times Paul's questions and did not quite understand them and its connection to primary line of discussion.
The primary line of discussion is "what is the difference between selling and exercising an option".
Why don't you understand Paul's questions? Is it because you don't know wat "exercise" means? I've also asked this many times: "what happens when you excersise a call?".
If you don't know the answer you can Google "exercise an option", read it, and then answer the question.
My concern was to the rule to specify the moment when option should be sell or exercise if the moment coincides with maturity. My point speaking broadly is the moment when 'adjusted' rate of return on option is maximum. That is why in particular that the problem is related to buyer only and seller of the option does not involved. To calculate rate of return we need option premium at initiation C ( 0 , S ( 0 ) ) as well the value of the contract at the final moment. It does not matter whether final moment is prior to maturity or maturity itself as value of the contract is uniquely defined. The call price at t , [$] C ( t , S ( t , ]\omega )) , t \le T [$] is what should be used to calculate random rate of return. We should specify random time which actually not Markov stopping time that presents maximum
[$] \frac { C ( t , S ( t ) ) - C ( 0 , S ( 0 ))} { C ( 0 , S ( 0 ))} [$] (1)
Discussion turned to the what is the difference between the option price prior to maturity and exercise price. For representation of the rate of return (1) it is not a problem. It is [$] C ( t , S ( t ,\omega )) , \, t \le T \, or \,[ S ( T ) - K ] \chi ( S ( T ) > K ) [$].