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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: enter image description here

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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In general, PPN is the short form for principal protected notes. Here, the principal, or notional, $N$ is generally return in full. I am a little confused why only 80 % is returned. It may be a contractual specification, and it is also called a PPN.

Regarding the variable interest, or premium in your term, is the return that the investor will achieve. In your specification, the variable interest is defined by \begin{align*} p N/S_0 (S_T-S_0)^+ &= pN \left(\frac{S_T}{S_0} -1 \right)^+. \end{align*} Note that $\left(\frac{S_T}{S_0} -1 \right)^+$ is the positive part of the return. Here, $p$ is usually called the participation rate, and $N$ is the notional.

In summary, this PPN will return 80 % of the notional $N$ to the investor, and will pay the investor a ratio of $p$ of the final equity return if it is positive. The value of this PPN is the sum of the value of a zero-coupon bond plus a ratio of a European option. The participation rate $p$ can be determined so that the PPN value is higher than the value for a direct deposit into a banking account.

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  • $\begingroup$ Ok, so far so good, thanks. But how does one determine the value $p$ and moreover, since $S_T$ is unknown, how do you even begin to tackle this problem? $\endgroup$
    – Riley
    Dec 13, 2015 at 18:09
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    $\begingroup$ Using the market volatility quote, you can value the option with payoff $(S_T-S_0)^+$ using Black-Scholes's formula. For $p$, it is based on business judgment, depending on what you want to do with your client, but that is out of my knowledge. $\endgroup$
    – Gordon
    Dec 13, 2015 at 18:25
  • $\begingroup$ In my product, I want to make us of the Put-Call Parity formula. So I need the interest rate. I was wondering, because the maturity date is in more then over a year, which interest rate $r$ do I have to choose? $\endgroup$
    – Riley
    Dec 16, 2015 at 17:40
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    $\begingroup$ You need the interest rate not only for put-call parity, but also the option valuation. For the specific interest rate to use, there are too many choices, for example, OIS curve for products with collateral and the Libor curve for products without collateral. In general, this will be based on business or management judgement. $\endgroup$
    – Gordon
    Dec 16, 2015 at 17:44
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    $\begingroup$ Usually, a zero rate, or discount, curve is used. Such curve is usually called swap curve. For European option, you use the zero rate corresponding to the option maturity. You may also google methodology for swap curve construction. $\endgroup$
    – Gordon
    Dec 16, 2015 at 17:48

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