Question

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

Answer 1

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