Question #14 - Reading 27 Valuation and Analysis of Bonds With Embedded Options

Reading: Reading 27 Valuation and Analysis of Bonds With Embedded Options - Anwers

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- Which value for the backwardly induced price of the corporate callable bond using the binomial tree in Exhibit 1 is most accurate? A) $105.69. B) $104.89. C) $105.20. Explanation First compute the missing rate using the relationship: upper rate = lower rate e2 × volatility = 2.85%e2×0.2 = 4.25% Then use backward induction: Value at T2 Upper: 106 / 1.0634 = 99.68. Value at T2 Middle: 106 / 1.0425 = 101.67. Replace with the call price of $101. Value at T2 Lower: 106 / 1.0285 = 103.06. Replace with the call price of $101. Value at T1 Upper: ((99.68 + 101) / 2 + 6) / 1.0545 = 100.84. Bond is not callable at T1. Value at T1 Lower: ((101 + 101) / 2 + 6) / 1.0365 = 103.23. Bond is not callable at T1. Value at T0 ((100.84 + 103.23) / 2 + 6) / 1.03 = $104.89. (Module 27.2, LOS 27.f)

Question

How many of Inka's comments about her binomial tree exercise are correct?

Answer Choices:

A. One

B. Two

C. Three. Explanation Comment 1 is true. A correctly calibrated (to treasury securities) binomial tree will reflect the credit and liquidity risk of treasury securities. Corporate bonds typically will have greater credit and liquidity risk than government securities and as a result, the rates in the tree are too low. Backward induction using the tree would value the corporate bond too high relative to its market price. Comment 2 is true. The option adjusted spread (OAS) is the constant spread when added to the treasury spot and expected future 1-period rates in the tree, will value the callable corporate bonds equal to its market price. Comment 3 is true. If the analyst increases the volatility assumption used to build the tree the spread between lower and upper forward rates will widen. Backwardly inducing the corporate callable bond will now result in a lower value. It is important to note that this is the analyst changing their assumption used to build the tree which will not impact the bond's actual market price. As the backwardly induced value is now lower but the market price remains unchanged, a smaller OAS needs to be added to force the backwardly induced value to be equal to the market price. (Module 27.4, LOS 27.h)

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