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Choosing a Structured Note’s Threshold Using Digital Option Value

Article Quant Q&A · Author: Riley
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Summary

This discussion examines a partially principal-protected note whose premium is paid only if a stock finishes above a threshold. The central design question is how to choose that threshold using market data when the digital payoff itself is not directly quoted as a traded option. The response suggests first defining a pricing objective, such as selecting the threshold that makes the note’s value equal to par. This makes the choice of threshold an explicit valuation target rather than an undefined judgment about whether the product is attractive.

For valuing the digital component, the response points to an analytical formula when volatility and interest-rate inputs are available, or an approximation using a call spread. It does not provide a worked calculation, specify a calibration procedure, or establish investor attractiveness. The answer is therefore a framework for structuring the exercise, with results dependent on the chosen target, market inputs, and approximation quality.

Key ideas

  • A note’s payoff threshold can be chosen to meet a defined valuation target, such as par value.
  • A digital payoff can be valued analytically when suitable volatility and interest-rate inputs are available.
  • A call spread can approximate the value of a digital option.
  • The discussion gives valuation approaches but no worked threshold calculation or investor suitability test.

Tags

OptionsDerivatives pricingEquities
Full text
# PPPN: premium with real market data


# 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:

\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?

## Answer by Gordon (score 3)

https://quant.stackexchange.com/a/22344

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.