The value of a straight bond does not change with interest rate volatility. Why???
Look at the formula for determining the value of a straight bond.
Is there a volatility term in that formula?
There’s not.
So it has nothing to do with what we’ve been doing in reading 36, say spot rate yr 1=1%, yr 2=2%, f(1,1)=3%, if the volatility change from 10% to 40% on the downside, it would also change on the upside by the same amount, regardless of the dispersion gets wider or narrower as it is always centred around the forward rate, that’s why the effect offset each other? but when I tried to discount back the same coupon by volatility 40% and 10% volatility, I didn’t get the same value of bond tho…
You have to calibrate the tree. It isn’t exactly centered about the forward rate; it’s merely close.
Furthermore, if the 1- and 2-year spot rates are 1% and 2% respectively, 1f1 isn’t exactly 3%; it’s 3.0099% (to 4 decimal places).