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Determine the cash price of a 6% Treasury bond that matures in 14 months using the zero rates below. The Treasury bond has semiannual coupon payments.

First, I calculated the coupon payments. There are two full coupon payments at months 6 and 12. At month 14 I tired to add the accrued interest. This part is what I'm struggling with the most. How do I account for the cash flow for the last 2 months.
For months 6 and 12 = .06/2 *100 = 3
For month 14 = 2/6 * 3 = 1

Since the zero rates are semiannual compounding I need to convert them to continuous compounding.
2*ln(1+.06/2) = 0.0591
2*ln(1+.12/2) = 0.1165
2*ln(1+.14/2) = 0.1353

The cash price is the present value of the clash flows. And since it is continous compounding is use the following equation to determine the price of the bond.
3e(-.0591*.5)+3e(-.1165*1)+101e(-.1353*1.1667)=91.8341

mark
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1 Answers1

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Hint: If the bond matures in 14 months, I'd think the coupons are due in 2, 8 and 14 months, not in 6 and 12 (and partially 14) months. This is because I'm fairly sure that Treasury bonds are issued with maturities of whole years (20-30 years actually; although whole half years would give the same). This (also) implies that the Treasury bond in the question was issued earlier, not "now".

Also see: https://en.wikipedia.org/wiki/United_States_Treasury_security#Treasury_bond

Řídící
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  • Isn't this the same? The first coupon payment at 2 months will only be a partial payment. There won't be three full coupon payments. I think the question is just asking what is the price of the bond today, not when it was first issued. – mark Jul 09 '16 at 21:36
  • No. It is not the same. Also, there will be three full coupon payments. And the cash price includes the accrual for the current coupon. – Řídící Jul 10 '16 at 08:40
  • Maybe I'm not getting it. Why are there three full coupon payments? Isn't the 2 month payment only partial. This is why I did (2/6) * 100 = the partial payment. – mark Jul 10 '16 at 15:11
  • The US Treasury doesn't care that you only owned the bond for two months. It pays the full semi-annual coupon to the person who holds the bonds at coupon time. However, if you'd have to buy such a bond today, your seller will insist on being compensated for missing four months' worth of coupon. This accrual needs to be included in the bond price. (You cannot short-cut this as the accrual method, by convention, is slightly different than the pricing of the other components.) – Řídící Jul 10 '16 at 15:19
  • Ok I understand what you mean now. That's what I was trying to get at. You receive two coupon payments plus accrued interest for 2 months. But how is the accrual calculated? Why not use (2/6) * 3 = accrued interest. Coupon payments are $3 but only 2 months have past so you only receive 2/6. – mark Jul 10 '16 at 15:48
  • No. As I said: there will be three full coupon payments. Just price the full coupons and the principal and you're done. – Řídící Jul 10 '16 at 15:58