Today’s zero-rate curve is summarised in the table below. Calculate the price (p
ID: 2612201 • Letter: T
Question
Today’s zero-rate curve is summarised in the table below.
Calculate the price (per $100 par value), to three decimal places, of a three-year fixed-coupon bond paying a coupon rate of 9% pa if the bond pays coupons every half year. Assume that the bond is default-free and that a coupon has just been paid -- that is, price the bond on an ex-interest basis.
Hint: find the bond price as the present value of its future cash flows, using the discount factors retrieved from the zero-rate curve.
Explanation / Answer
Answer,
The half yearly coupon payment for the bond = $100*(9%/2) = $4.5
Remaining coupon payments = 3*2-1 = 5 (a coupon payment just made)
Price of the bond = Present value of all the coupon and principal payments discounted using zero/spot rate.
= $4.5/(1+0.05755/2)1+$4.5/(1+0.06250/2)2 + $4.5/(1+0.06455/2)3+$4.5/(1+0.06555/2)4 + $104.5/(1+0.06600/2)5
= $4.5/1.02878+$4.5/1.06348 + $4.5/1.09998+$4.5/1.13769+ $104.5/1.17626 = $105.493 (Ans)