Binomial interest rate tree

CFA Level II Fixed Income
#1

BB example 4: Calibrating a binomial tree

While working on nodes in Time 1, volatility has not been multiplied by 2, viz .15 has been taken. Whereas in time 2 nodes, volatility is multiplied by 2 and a value of .30 has been used. It has been categorically mentioned that volatility is 15% for all years.

What am I missing?

#2

I think you are missing the lognormal distribution part. High rate/Low rate = e(2*volatility)

So at each time period, you multiply this by a factor of 2.

#3

I presume that you’re referring to the calculations:

  • F1,1d = (4.040%)e−0.15
  • F1,1u = (4.040%)e0.15

If so, then what you’re missing is that the 0.30 value for 2_σ_ is used to get from one node to the next higher node, not to get from the midpoint to the upper node or the lower node. Here, F1,1u ÷ F1,1d = (4.040%)e0.15 ÷ (4.040%)e−0.15 = e0.30, as you expected.

#4

Thanks a lot! You’re a saviour

#5

My pleasure.