I'm a student of financial engineering and am very new to all of this stuff. Now, I'm trying to make an "example of a beginners exercise", but alas, I don't have any clue on how to solve or even on how to begin this one. The exercise goes like this:
Suppose you have a PPPN where the invester recieves at maturity date $80 \%$ of his investment plus a premium, defined by: \begin{equation} p \cdot N/S_0 \cdot (S_T - S_0)^{+}, \end{equation} where $(S_T - S_0)^{+} = \max(S_T - S_0,0)$ is the positive stock return over the period $[0,T]$ ($t=T$ is the time to the Maturity date), an investment $N$ and where $p$ is the participation rate. Now, set $p$ such that the product is attractive for investors and you have a certain margin.
In order for this exercise to get more real, I've chosen a stock at random, say Facebook, and assumed a maturity date of 13/12/2016. Here is the information of the stock found today, credits to yahoo finance: 
I thought it would be wise to choose $N= S_0= 102.12$, so that the equation of the premium simplifies to:
\begin{equation} p \cdot (S_T-102.12)^{+}. \end{equation}
Unfortunately, that's where my insights end. I don't have any clue on how to make further progress on this problem. Personally, I would just set $p =100 \%$, so you get the maximum possible return, but that can't be right. Any ideas/pointers/solutions?
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