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So I have a problem from Marcel Finan's "A Basic Course in the Theory of Interest and Derivative Markets." We are going over floors and caps, covered puts and covered calls.

Consider the following combined position:

  • Buy an index for 500
  • Buy a 500-strike put with expiration date 3 months with a 3-month risk free rate of 1% and premium of 41.95.
  • Borrow 495.05 with 3-month interest rate of 1%.

Graph the payoff diagram and the profit diagram of this position.

So, since we are simultaneously buying an asset and a purchased put, this makes this a floor. According to Broverman, the formula for a floor's payoff is $$\text{payoff}=\begin{cases} K, & \text{if $S_T\le{K}$} \\ S_T, & \text{if $S_T\gt{K}$} \\ \end{cases} $$ So in this case we know that the cost to purchase both the asset and the put is 541.95 and we are borrowing 495.05 from the start. So is the expiry price $S_T=500(1.01)=505$? This would make the payoff $505$, since $505\gt{500}$.
What about the profit? Again Broverman has the profit function as $$\text{profit}=\begin{cases} K-(S_0+P_0)e^{rT}, & \text{if $S_T\le{K}$} \\ S_T-(S_0+P_0)e^{rT}, & \text{if $S_T\gt{K}$} \\ \end{cases} $$ So since $S_T\gt{K}$ is the profit just $505-(500+41.95)(1.01)=-42.37$?

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and the question is ? – TheBridge Jun 5 '13 at 16:56
I guess this is it – Bob Jansen Jun 5 '13 at 16:57
Is th is right? Is the fact that we borrowed $495.05 extraneous information to this question? We have to pay that back at some point correct? But this information is no where in the formula so where do we employ that? – Eleven-Eleven Jun 5 '13 at 17:04
Where did you get $S_T$? – Bob Jansen Jun 5 '13 at 17:30
wouldn't $S_T$ just be the future value of $S_0$? – Eleven-Eleven Jun 5 '13 at 17:35
up vote 1 down vote accepted

As the asker already found out:

No this is not simply the answer. $S_T$ is not known at the moment of investment so the future profit is a function of the stochast $S_T$.

A graph is a useful tool to gain insight into the amount of profit for each realized value of $S_T$.

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