Valuation of an option-free bond using binomial tree

CFA Level II Fixed Income
#1

In Schweser there is an example regarding Valuation of an option-free bond using binomial tree.

I will write the example down here but my question is that why did the author use the forward rates to solve for the bond value, should not it be the spot rate?

Question:

Samuel Favre is interested in valuing the same three-year, 3% annual-pay Treasury bond. The spot rate curve is as before, but this time Favre wants to use a binomial interest rate tree with the following rates:

One-Period Forward Rate in Year 0 1 2 3% 5.7883% 10.7383% 3.8800% 7.1981% 4.8250% Compute the value of the $100 par option-free bond.

#2

The typical methodology used with a binomial interest rate tree is to start with the cash flows on the right side of the tree, discount them one period at a time moving to the left, and at each node add the current cash flow before continuing the discounting to the left.

Because you’re discounting one period at a time, the discount rate must be a 1-period rate starting at the previous time and going to the current time; i.e., it must be a forward rate. Spot rate, you’ll recall, discount cash flows back to time zero, which may be more than one period.

I wrote a series of articles on binomial interest rate trees, starting here: http://www.financialexamhelp123.com/binomial-trees-for-fixed-income/. They cover how the tree is created, how you use it to value fixed-rate bonds with and without embedded options, how you use it to value floating-rate bonds, and how you use it to compute OAS.

(Full disclosure: as of 4/25/16 there is a charge to read the articles on my website. You can get an idea of the quality of the articles by looking at the free samples here: http://www.financialexamhelp123.com/sample-articles/.)

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#3

To make sure that I got it right, we always discount by the forward rate in case we are discounting one year (other than T=0), we use the spot rate in only two situations:

  1. the last discount from T=1 to T=0

  2. When I discount from T=X to T=0

#4

Correct.