Question

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3. A term structure is defined by the following accumulation function: p0.03t at) = 60.06+0.0025(1++)2, for 0) < t < 5, for t > 5. If a 10-year bond makes level coupon payments at year 2, 4, 6, 8 and 10. Find the par yield of this bond.

Answer 1

The par yield is the coupon rate that causes the Bond price = par value. So let the par value of the bond be 100.

Now, the bond makes level coupon payments at year 2, 4, 6, 8 and 10. This means that equal amount of coupon is paid by the bond at year 2, 4, 6, 8 and 10. Hence, let that equal amount of coupon be x. Hence, we will be receiving x amount at year 2, 4, 6 and 8 and (100+x) at year 10.

Now, when we pull all these figures to year 0, by using the term given term structure, and hence we will get the par value, which is 100.

So, equation will be as follows:

Par Value = Present Value of all future Cash Inflows

100+ 0 100 = 20.03.2 20.03.4 +20.06+0.0025 (1+0)2 + 20.06+0.0025 (1 +8) 2 0.06+0.0025 (1 +10)2

100+ 0 100 = 1.061837 + 1.127497 + 1.200214 + 1.300176 + 1.436917

) 100 = 2.5281811 + 2.380951.1 +2.2366960 +2.064731.2 +1.868246(100+ (1.061837)*(1.127497)*(1.200214)*(1.300176)*(1.436917)

100 = - 11.07881.+ 186.8246 2.684515

100 x 2.684515 = 11.07881.+ 186.8246

258.4515 – 186.8246 = 11.07881.

81.62688 11.07881 =

7.367842 =

Hence, if the coupon amount of 7.367842 is paid at the year 2, 4, 6, 8 and 10 on the bond having par value of 100, then in the given term structure, the value of bond will be equal to the par value.

Hence, Par yield =
Coupon Amount Par Value
=
7.367842 100
= 7.3678% (approx)