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Question on Kaplan's question on Binomial Trees
An example of a standard tree used by FIData is given in Figure 2.Figure 2: Binomial Interest Rate Tree
|Year 0||Year 1|
FIData's website uses rates in Figure 2 to value a two-year, 5% annual-pay 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% annual-pay bond using the interest rate tree given in the three bonds in Figure 2 is closest to:
So I averaged node U2 (1005/1.071826) and node L2 (1005/1.05321) to come up with 943.6846. Then I discounted that by the year 0 rate of 4.5749% and came up with 907.1819. I answered A.
Kaplan says the answer is C. Their explanation is: The value of the 5%, two-year annual pay $1000 par bond is $992.88.
I find that explanation underwhelming. Can someone help me out here? Where did I screw up?