The building blocks of this BRC are (assuming the most common specification, there is always variations but it's impossible to tell the details without any termsheet provided):
- long a zero-coupon bond
- short a down-and-in rainbow put on the min (worst-of), with barrier below strike usually, and either European or American exercise style
The discount of the ZCB plus the option premium you collect by selling the option, make up your "coupon" of the structured note.
Now, the two key concepts (linking you to their Wiki articles) are (a) the barrier, and (b) the multi-asset optionality. Let's take a short numerical example that helps illustrate the key idea - I take your three assets A (say current price is 120 EUR), B (price 40 EUR), C (price 90 EUR). Let's say the rainbow put is struck at-the-money, meaning your strike is either 120, 40, or 90 EUR - depending on which of the three assets is the worst performing. (Note that often in practice this is rewritten in some sort of conversion ratio, meaning if you invest 1000 EUR, you'd get 1000/120 = 8.33 shares, or 8 shares, and the rest in cash for the case A is the min of the rainbow... 1000/40 = 25 shares of B, etc.)
However, you need to consider that this rainbow put is not alive since inception - the condition for it to become alive is that at least one of the 3 assets needs to breach its so-called barrier level. This is the level where the put becomes active (down & in). Assume it is defined as "60% of the current asset level", so this gives you barrier levels of 72, 24, and 54 EUR. Hence, when either one of the three assets crosses this level, you're effectively short the put option - and that means someone is entitled to sell you either A, B, or C for the agreed strike of either 120, 40, or 90 EUR. Do note that barrier breaching asset does not need to be the worst performing (you sometimes observe A dropping from 120 to 72, breaching the barrier and being the activator for the put - but then A recovers, while B drops... then you'd get delivered B as it is still the worst-of).
In your case, an additional complication comes in: A is not a single asset, but a portfolio/index itself. Think of it as a basket of 1 stock of A at 100 EUR and 0.5 stock of A' at 40 EUR, giving you a 120 EUR portfolio. As indicated in my comments:
I did come across something like that here and there; however, I recall that the "basket within the basket" was basically only due to the result of a spin-off in stock A (that created newly listed stock A') and that was the way it was depicted in the structured note / BRC. For barrier breach / delivery of worst-of, I think (not 100% sure, and can't find the termsheets anymore) the method was to observe the barriers of the initial basket (A only, no A' yet), and if there was a breach + A was the worst-of, then you'd get delivered not only 1 A but additionally 0.5 A'.
If, however, the note was already emitted using the 1A+0.5A' basket, the situation is a bit different w.r.t. to determining the barrier (I assume the barrier would in most cases also be the weighted average of the two initial fixing levels times the barrier level)... but other than that you'd simply get delivered the basket in case it was the worst of the rainbow.
Returning to the above example, it's impossible to tell what's the case for you without any termsheet. It might be that the BRC is issued with the first barrier still being 72 EUR, and either A or A' can be the driver of a potential breach. It could also be structured in a way that the A barrier is 60% * 100 = 60 EUR and the A' barrier 60% * 40 = 24 EUR and if either one of the two breaches it's "individual" barrier the put becomes active, regardless of the A+A' basket being still above 72 EUR. Similar considerations can be made w.r.t. to delivery, in case A, A', or A+A' is the worst-of.
Finally, wrapping up a long and hopefully helpful introductory answer for you, the last layer of the product is the quanto feature, which is another option component and allows you to obtain a USD notional payoff in the BRC whereas your assets are priced in EUR.