how come the Vo already known in the table ? and why interest rate volatility 20% is not used ?

Please add some comments

Dawn Adams, CFA, along with her recently hired staff, have responsibilities that require them to be familiar with backward induction methodology as it is used with a binomial valuation model. Adams, however, is concerned that some of her staff, particularly those not enrolled in the CFA program, are a little weak in this area. To assess their understanding of the binomial model and its uses, Adams presented her staff with the first two years of the binomial interest rate tree for an 8% annually compounded bond (shown below). The forward rates and the corresponding values shown in this tree are based on an assumed interest rate volatility of 20%.

A member of Adams’ staff has been asked to respond to the following:

Compute V_{1L}, the value of the bond at node 1L.

**A)** $101.05. **B)** $95.99. **C)** $103.58.

**Your answer: C was correct!**

V_{1L} = (½)[(V_{2LU} + C) / (1 + r_{1L})] + [(V_{2,LL} + C) / (1 + r_{1L})]

V_{1L} = (½)[(99.455 + 8) / (1 + 0.05331)] + [(102.755 + 8) / (1 + 0.05331)] = $103.583

(Study Session 14, LOS 50.i)

Compute V_{1U}, the value of the bond at node 1U.

**A)** $99.13. **B)** $91.72. **C)** $99.01.

**Your answer: A was correct!**

V_{1U} = (½)[(V_{2,UU} + C) / (1 + r_{1U})] + [(V_{2,UL }+ C)/(1 + r_{1U})]

V_{1U} = (½)[(98.565 + 8) / (1 + 0.079529)] + [(99.455 + 8) / (1 + 0.079529)] = $99.127

(Study Session 14, LOS 50.i)

Compute V_{0}, the value of the bond at node 0.

**A)** $99.07. **B)** $104.76. **C)** $101.35.

**Your answer: B was correct!**

V_{0} = (½)[(V_{1U} + C) / (1 + r_{0})] + [(V_{1L} + C) / (1 + r_{0})]

From the previous question the value for V_{1U} was determined to be $99.127

V_{0} = (½)[(99.127 + 8) / (1 + 0.043912)] + [(103.583 + 8)/(1 + 0.043912)] = $104.755

(Study Session 14, LOS 50.i)

Assume that the bond is putable in one year at par ($100) and that the put will be exercised if the computed value is less than par. What is the value of the putable bond?

**A)** $103.04. **B)** $95.38. **C)** $105.17.

**Your answer: C was correct!**

The relevant value to be discounted using a binomial model and backward induction methodology for a putable bond is the value that will be received if the put option is exercised or the computed value, whichever is greater.

In this case, the relevant value at node 1U is the exercise price ($100.000) since it is greater than the computed value of $99.127. At node 1L, the computed value of $103.583 must be used.

Therefore, the value of the putable bond is:

V_{0} = (½)[(100.00 + 8) / (1 + 0.043912)] + [(103.583 + 8) / (1 + 0.043912)] = $105.17314

(Study Session 14, LOS 50.i)

Assume that the bond is putable in one year at par ($100) and that the put will be exercised if the computed value is less than par. What is the value of the put option?

**A)** $1.86. **B)** $0.42. **C)** $3.70.

**Your answer: B was correct!**

V_{putable} = V_{nonputable} + V_{put}

Rearranging, the value of the put can be stated as:

V_{put} = V_{putable} − V_{nonputable}

V_{putable} was computed to be $105.173 in the previous question, and V_{nonputable} was determined to be $104.755 in the question prior to that. So the value of the embedded put option for the bond under analysis is:

$105.173 − 104.755 = $0.418

(Study Session 14, LOS 50.e, i)

Which of the following statements regarding the option adjusted spread (OAS) is *least* accurate?

**A)** The OAS is equal to the Z-spread plus the option cost. **B)** The OAS for a corporate bond must be calculated using a binomial interest rate model. **C)** The OAS is the spread on a bond with an embedded option after the embedded option cost has been removed.

**Your answer: A was correct!**

The OAS is equal to the Z-spread *minus* the option cost. Both of the other choices are true statements. (Study Session 14, LOS 50.g)