Rate Vol in Forward Binomial Model

CFA Level II
#1

In the Fixed Income text, it’s stated that standard deviation of rates at each time step scales with the level of the one year forward rate at that step. Following that, the examples don’t include a scaling factor (as far as I can tell?), but a constant level across all steps.

One method vs. the other likely wouldn’t make a difference if you’re calibrating the tree to price a par bond, but it seems as though this would matter a lot of pricing bonds with embedded options. Is it preferred to scale or not scale vol by the forward rate when building this tree in practice?

#2

The tree typically uses a constant volatility factor (e2σ), but as that’s multiplied by the forward rate, the standard deviation of rates at a particular time will be proportional to the forward rate at that time.

#3

Ah. So, the effect is as a coefficient and not in the exponent.

Thanks.

#4

My pleasure.