 # Reading 57: Valuing Bonds - Calculating rates in bionomial tree

Maturity Yield to Maturity Market Price 1Y 3.5% 100 2Y 4.2% 100 3Y 4.7% 100 4Y 5.2% 100 Volatility is 10%. Forward rates are as follows, and I totally understand this calculation: 0f1=3.500% 1f1=4.935% 2f1=5.784% 3f1=6.893% Once again, the volatility is 10%. How are the rates calculated below, and what does 10% have to do with the calculations of these rates? Nhh /4.7 3.500% ----------------Nh / 7.0053 | 97.823 / | 4.7% / | 5.4289% | |--------------Nl --------------Nhl 99.777 4.7 4.7% 99.021 4.4448% 5.7354% \ \ \ \ \ Nll 4.7% 100.004 4.6958% I truly can’t understand how to get the interest rates Nh, Nl, or Nhh, Nhl, and Nll. Another thing, why isn’t the Nhl = 2f1 = 5.784%?

How do I calculate the rates here? Maturity Yield to Maturity Market Price 1Y 3.5% 100 2Y 4.2% 100 3Y 4.7% 100 4Y 5.2% 100 Volatility is 10%. Forward rates are as follows, and I totally understand this calculation: 0f1=3.500% 1f1=4.935% 2f1=5.784% 3f1=6.893% Once again, the volatility is 10%. How are the rates calculated below, and what does 10% have to do with the calculations of these rates? Nhh /4.7 3.500% ----------------Nh / 7.0053 | 97.823 / | 4.7% / | 5.4289% | |--------------Nl --------------Nhl 99.777 4.7 4.7% 99.021 4.4448% 5.7354% \ \ \ \ \ Nll 4.7% 100.004 4.6958% I truly can’t understand how to get the interest rates Nh, Nl, or Nhh, Nhl, and Nll. Another thing, why isn’t the Nhl = 2f1 = 5.784%?

i skimmed this area so far… it seemed like it was an area that wasn’t explained very well (but like i said), i went fast… on page 115, i was thinking the callable bond gets called at year 1 in up and down case, so basically the rest of the tree is irrelevent. but like i said again, i went really quickly and plan on coming back and doing detailed work once i’ve got thru all 6 books on a first detailed skim/quick read.

Westbruin, Thanks for your efforts. I totally understand how to calculate the prices at each node. However, I’m not sure how the nodes were populated with interest rates and the pertinence of 10%.