10. The N-period spot rate is represented by the interest rate on a pure discount bond whose life extends from today through N future periods. The N-period forward rate M periods hence is represented by the interest rate, determined today, on a pure discount bond that will come into existence M periods from today and mature N periods after M.
11. The forward rate between periods t-1 and t is given by:
(1 ft 1,t) (1 st)t/(1 st 1)t 1
14. a. The discount factors on the three bonds can be determined sequentially. In the case of the first bond, the one-year discount factor equates the price of the bond to the discount cash flow of the bond. That is：
In the case of the second bond, the one-year discount factor is applied to the first year cash flow and the two-year discount factor is that discount factor that, when applied to the second year cash flow, equates the price of the bond to the discounted cash flows of the bond. That is: 991.81=100*d1+1100*d2
The three year discount factor is found in a similar manner:
b. Given the discount factors from part(a), the forward rates/can be derived. In general: (1 ft 1,t) (1 st)t/(1 st 1)t 1 (1/d1)/(1/d2)
The forward rate from today to year one (which is simply the one-year spot rate) is given by: (1+f0,1)=(1/d1)/(1/d0)
The forward rate from year one to year two is given by:
The forward rate from year two to year three is given by:
c. The amount of the loan should be equal to the discounted value of the cash payments. The one ,two, and the three-year discount factors should be applied to these cash payments in order to calculate their present value.
12. The initial value of Corns’ portfolio is:
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