solution

Suppose that in the fixed-income securities market, the current one-year spot interest rate is 4.000%.[That is, R_0,1 = 4.00%] In addition, the current one-year forward rate one year from now [ F^0,Mrkt_1,1] is 6.000%. Then, as per the no-arbitrage principle, what is the theoretical value of the current two-year spot interest rate, per annum continuously compounded? In other words, what is the theoretical value of R_0,2 (R^Theo_0,2 )?

A. a.4.250% b.5.000% c.2.000% d.8.000% e.4.759%

B. Suppose that in the fixed-income securities market, the current one-year and two-year spot interest rates are 4.000% and 5.500%, respectively. (That is, R^Mrkt_0,1 = 4.000% and R^Mrkt_0,2 = 5.500%). In addition, in the market, the current one-year forward rate one-year from now (F^0,Mrkt_1,1) is 6.000%. What should be an arbitrager’s strategy at t = 0 (now)?

S1) They will [“Borrow”, “Lend”, “Do Nothing”] at one-year forward rate one-year from now.

S2) They will [“Borrow”, “Lend”, “Do Nothing”] at one-year spot rate.

S3) They will [“Borrow”, “Lend”, “Do Nothing”] at two-year spot rate.

C. Suppose that in the fixed-income securities market, the current one-year and two-year spot interest rates are 4.000% and 5.500%, respectively. (That is, R^Mrkt_0,1 = 4.000% and R^Mrkt_0,2 = 5.500%.) In addition, in the market, the current one-year forward rate one year from now [F^0,Mrkt_1,1] is 6.000%.

Assume that an arbitrager can borrow or lend exactly $1,000 in the forward interest rate market. They execute an arbitrage strategy such that their net cash flows at time t=0 (now) and at the end of Year 1 (t=1) are equal to zero. However, they have a positive net cash flow at the end of Year 2 (t=2). What is the amount of that positive net cash flow at the end of Year 2 (t = 2)? (4 decimal places required)