Interest rate Vol on tree

Understand that it is calculated as Vol x 2. Then take the E sigma of that and multiply by node to get rate above.

In CFA EOC FIxed income (p305 questin 3) The answer suggests it cannot be B because E Sigma is 0.8.

The vol in the tree is 10%, so is this not 0.10 x 2 = 0.20 2 (then on calc. 2nd Ln) = 1.22 (Which we would multiply against 4.2009% for Node 4-1 (=5.13%)

Where is the 0.8 coming from?


it’s from the formula e^(2 x sigma)

In the table is states that volatility = 10%

If you’re calculating _ based on node 4-5 _, going all the way up to node 4-1, the formula is e^(8 x 0.1) = e^0.8, not e^0.4.

So does that mean we start from the bottom node and deduce its 0.2 (10% x 2) Then we essentially mutiply that by which node we want. So Node 4 means 0.2 x 4 = 0.8?

I was under the impression that you can just calculate the lowest node, like i did in the OP and multiply it against whichever rate we need to get the one above

You can start from which ever node you wants as long as you use the appropriate formula, but the question specifically asks that if you were to calculate it based on node 4-5. Your answer for node 4-1 is right, but it doesn’t answer the question.