Binomial Interest Tree

[frCiscobr]

Hey guys, a really stupid question for you:
In reading 43, 3.1, after Exhibit 5, its said that ‘i2H,L’ will be close to the implied one-year forward rate one year from now (f(1,1)). This relation is always valid? Is it based on the fact that i1,h > i2hl > i1l ? I understood the relation between these rates inside the time step (based in a logn model), but from one time step to the next still is not so clear for me.
I would really appreciate any help!

 

[Harrogath]

Advanced question.
Well, as far as I see, the binomial tree is created under the non-arbitrage assumption behind the forward interest rates. First, you got the spot curve (risk-free rates), then you calculate the forward curve (for risk-free assets), then you add volatility to each year creating possible scenarios. Then, calibrate the tree to match current prices (of risk-free assets). If not, then arbitrage is possible.
The farther the time you looking at, the wider the tree. The “spinal column” of the tree is the forward curve, simple as that.
This complicated set of projected / calibrated rates can only be calculated using software, so let’s the secret of the math behind the tree rest some more time

 

[frCiscobr]

The farther the time you looking at, the wider the tree. The “spinal column” of the tree is the forward curve, simple as that.
This is exactly what I understand, but when its said that the interest rate located at the middle point of the time step 2 will be close to the implied f(1,1) i get lost again. For me, using your words, the spinal column of this time step is f(2,1), not f(1,1).
Thank you very much!