Interest rates are expressed as annualized rates for the term specified. Report your interest rate answers as fractional numbers like 0.11 for 11% per year.
Problem .
Take 3 semi-annual coupon paying bonds with face values of $100. They carry D1 percent, D2 percent and D3 percent coupons, mature in ½ year, 1 year, and 1 ½ year, with current market prices of D4, D5, and D6, respectively.
Find the "crude" (which does not use regression) term structure of discount factor, spot interest rate and forward interest rate. Assume semi-annual compounding and write your answers for:
1. Half-year discount factor.
2. One-year discount factor.
3. One and half-year discount factor.
4. Half-year spot rate.
5. One-year spot rate.
6. One and half-year spot rate.
7. Forward rate for period (0.5 - 1.0) year.
8. Forward rate for period (1.0 - 1.5) year.
9. What is the current fair price of a 1.5 year bond with face value 100, carrying an annual coupon of 10 percent, paid two times per year?
10. What is the current fair price of a 1 year zero coupon bond with face value 100?
11. What is the current fair price of a 6-month strip with face value 100?
D1=17
D2=20
D3=15
D4=104
D5=110
D6=111