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Delta stock (DAL) is trading at 11.70 dollars today.

Consider an American put option on $1$ share of DAL with $K$ = 12 and expiration in $T$ = .25 years.

The put is selling today for $1.46.

Assume the risk-free rate is 1%.

You hold the option until expiration. At that time DAL is trading at $10.

What is the payoff of the put option? What is your profit?

I am confused about the profit and how future value money plays into this. The payoff would be: $$(K-s_T)$$

Which in this case is just $2.

How about the profit? Would it be just $$2-(premium paid)?$$

How does the $FV$ plays into this?

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    You have to decide when you are valuing the trade. Your formula isn't right because $2$ is the value at expiry and the premium was paid at inception. Presuming you are valuing the entire transaction at expiry, you need to compute the value of the premium as of that date. – 2017-02-16
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    the problem does not address this. So I am assuming it is at the expiration date. – 2017-02-16
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    Where did I say that? I said that you have to declare whether you are valuing the transaction at expiry or at inception. If the former (which is what I expect) then you have the profit right but the premium value wrong. If the latter, then it is the other way round. – 2017-02-16
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    Ok. I understand now. If I value at the end, then I use the FV. – 2017-02-16
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    Yes, that is correct. – 2017-02-16
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    My confusing was about when one pays the premium. I thought you paid at the start. So I didnt understand why the FV had to calculated. – 2017-02-16
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    Now I get it. thx – 2017-02-16
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    You do pay the premium at the start!! But it's value on the expiry date is the future value of that cash. Look at the risk free example: If I pay $100$ for a bond with a $1\%$ coupon which matures in one year (for a payout of $101$) then my profit is $0$, not $1$. – 2017-02-16
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    OK! I really understand it now. Thanks for the clarification – 2017-02-16

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