Today’s zero-rate curve is summarised in the table below. Calculate the price (p

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.

Time period (years) Zero rate%p.a 0.5 5.755 1.0 6.250 1.5 6.455 2.0 6.555 2.5 6.600 3.0 6.610

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)

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