A few days ago, I posted a question about PPPN's (partially principal protected notes), which can be found here:PPPN: participation rate, stocks and premium.
A PPPN in short is a structured product where you get for example 80% of your investment plus a premium.
I'm still trying to understand how this all works, so I'm trying to make some of the example questions, like this one:
\begin{equation}
\text{premium} = \begin{cases}
30 &\mbox{if } S_T > K \\
0 &\mbox{otherwise.}
\end{cases}
\end{equation}
The question is now to determine $K$ using real market data such that the product is attrictive for investors.
So in order for this exercise to get more real, I've chosen a random stock, say facebook, credits to Yahoo Finance:
But now, since this is a digital option which is not traded in the market, we don't have any prices. I thought maybe I could construct a digital option myself, from call/put options, where the digital option pays 1 if $S_T \geq K$ or 0 if $S_T < K$, but I can't seem to finish that line of thought.
So... Any ideas/hints/solutions?
