 # Binomial bond

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

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 V1L, the value of the bond at node 1L.

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

V1L = (½)[(V2LU + C) / (1 + r1L)] + [(V2,LL + C) / (1 + r1L)]

V1L = (½)[(99.455 + 8) / (1 + 0.05331)] + [(102.755 + 8) / (1 + 0.05331)] = \$103.583

(Study Session 14, LOS 50.i)

Compute V1U, the value of the bond at node 1U.

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

V1U = (½)[(V2,UU + C) / (1 + r1U)] + [(V2,UL + C)/(1 + r1U)]

V1U = (½)[(98.565 + 8) / (1 + 0.079529)] + [(99.455 + 8) / (1 + 0.079529)] = \$99.127

(Study Session 14, LOS 50.i)

Compute V0, the value of the bond at node 0.

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

V0 = (½)[(V1U + C) / (1 + r0)] + [(V1L + C) / (1 + r0)]

From the previous question the value for V1U was determined to be \$99.127

V0 = (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.

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:

V0 = (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.

Vputable = Vnonputable + Vput

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

Vput = Vputable − Vnonputable

Vputable was computed to be \$105.173 in the previous question, and Vnonputable 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.