Question #13 - 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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- How many of Inka's opening statements are correct? A) Two. B) Three. C) One. Explanation Statement 1 is true. The value of a callable bond = value of an identical straight bond – value of embedded call. The value of embedded options, (both call and put) will increase in times of higher expected interest rate volatility. Therefore, the value of a callable bond will fall when rate volatility rises. Statement 2 is false. The Z-spread on a callable bond will be affected by credit risk and liquidity risk, relative to benchmark bonds used to calculate the spot rates. Z-spreads are also affected by embedded options. Embedded call (put) option increases (decreases) the Z-spread. The option adjusted spread (AOS) removes the uncertainty of the embedded option feature by modelling the impact on the bonds cash flows. Instead of the Z-spread, a constant OAS should be added to each spot and expected future 1-period rates in a binomial tree such that the backwardly induced price converges with market price. The OAS reflects credit and liquidity risk relative to the benchmark securities only. Statement 3 is true. Callable bonds exhibit negative convexity when yields fall to low levels. This is due to the price compression the bond experiences relative to a straight bond as the option moves towards the money. (Module 27.6, LOS 27.l)

Question

Which value for the backwardly induced price of the corporate callable bond using the binomial tree in Exhibit 1 is most accurate?

Answer Choices:

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)

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