It is used for multiplication; it’s being multiplied by e^{-0.20}.
Why did they multiply with .2 and not .1? Isn’t the volatility level 10% for the tree that contains A?
The difference between any node and the one above it is 2σ.
At time t = 1, for example, you can think of one rate as being one standard deviation below the middle, and the other as being one standard deviation above the middle; hence, 2σ between them.
Understood. Isn’t the question asking us to calculate Forward rate A and that same tree has a volatility of .1, not .2. So where does the negative .2 come from for sigma?
Negative 0.2 isn’t sigma; it’s −2σ.
Going from one rate at a given time to the next higher rate at that same time involves multiplying by e^{2\sigma}; going from one rate at a given time to the next lower rate at that time involves dividing by e^{2\sigma}, which is the same as multiplying by e^{-2\sigma}.
That is precisely the explanation I was looking for; I’m framing that one!
I hope that it matches your decor.
!!
One more aljibeer question from 9th grade and only because I have a captive tutor. I understand the rules regarding why 2 becomes -2 when moved from denominator to numerator. Why doesn’t Sigma become negative too?
I believe I can answer my own question after 3 minutes of thinking. Believing that Sigma can turn negative is akin to having pi become negative; i.e. that is impossible.
You’re growing, grasshopper.