# PPPN: premium with real market data

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:

$$\text{premium} = \begin{cases} 30 &\mbox{if } S_T > K \\ 0 &\mbox{otherwise.} \end{cases}$$ 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?

• Did you make any progression on this topic?
– user18684
Dec 16 '15 at 14:59
• Not yet! I keep trying. Why? Any additional info? :) Dec 16 '15 at 22:00

To determine the value of $K$, you should have some target in mind, for example, to find the $K$ so that the value of the structured note is at par. Regarding the value of the digital option, there is an analytical formula if you have the volatility and interest rate data, or approximate it by a call spread. See discussions in this question.