It looks like you're new here. If you want to get involved, click one of these buttons!



An example of a standard tree used by FIData is given in Figure 2.
Figure 2: Binomial Interest Rate TreeYear 0  Year 1 

4.5749%  7.1826% 
5.3210% 
FIData's website uses rates in Figure 2 to value a twoyear, 5% annualpay coupon bond with a par value of $1,000 using the backward induction method.
The question is: Using the backward induction method, the value of the 5% annualpay bond using the interest rate tree given in the three bonds in Figure 2 is closest to:
Comments
I've ignored the $ value of the bond for now, and work on a % basis (of par) to simplify things:
Using your definition of nodes:
U2 = 105/1.071826 = 97.9637
L2 = 105/105321 = 99.6952
Then fair value of bond today, V0 = 0.5 * [(97.9637+5)/1.045749] + 0.5 * [(99.6952+5)/1.045749]
= 0.5 * [98.4593+100.1150]
= 99.2872
So 99.2872% of a par value of $1,000 should be $993, i.e. answer C.
Hope this helps!