Question

In: Finance

Current (annualised) US Treasury spot rates are as follows: 6 months 1 year 18 months 2...

  1. Current (annualised) US Treasury spot rates are as follows:

6 months

1 year

18 months

2 year

0.4%

0.5%

0.6%

0.67%

Assuming that Z-spread is equal to 45 basis points, calculate the bond’s arbitrage free price. Show calculations.

Coupon Rate = 4.2%

frequency; semi annual

Solutions

Expert Solution

P= C + C + C + C
{1+ (Rx+Z)/2)}^1 {1+ (Rx+Z)/2)}^2 {1+ (Rx+Z)/2)}^3 {1+ (Rx+Z)/2)}^4

C= Coupon payments, Rx= Treasury spot rates ; Z= Z spread

Assuming bond par value is $100, C= (4.2/100*100)/2= 2.1 (since the coupon rate is semi annual)

P= 2.1 + 2.1 + 2.1 + 102.1
{1+ (0.4+0.45)/2/100)}^1 {1+ (0.5+0.45)/2/100)}^2 {1+ (0.6+0.45)/2/100)}^3 {1+ (0.67+0.45)/2/100)}^4
P= 2.1 + 2.1 + 2.1 + 102.1
1.00425^1 1.00475^2 1.00525^3 1.0056^4

P= (2.1 * 0.9958) + (2.1* 0.9906)+ (2.1* 0.9844) + (102.1* 0.9779)

= $106

The bond price should be $106


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