Question

all but skip probelm 3 please :)

1) Consider bank A that offers an interest rate of 8% for one year and bank B that offers a rate of 7% for three years. Assume all rates are continuous compounding, a) Based on this information, what should the two-year forward interest rate one-year from now be to avoid arbitrage? b) Suppose another Bank C offers you 7.5% on r(1,3), the two-year rate, one year forward. What strategy would you employ to create an arbitrage? How much would you earn on Simn? 2) Consider the table of spot rates below. Compute the forward rates for each intermediate period. 23 6% 5% r(0) 4% 3) Suppose spot rates are given by the quadratic: r(t) = -.000252 +.005t +.05. Use a spreadsheet to determine the zero-coupon bond price for maturities, t = 1,2,...,15 and compute the forward rates rt,t + 1). Graph the spot and forward rates on one graph and interpret. 4) Given the forward rates in the table below, compute the spot rates to time t2 014.0% 12 3.5% 2 3 6.25%

Answer 1

a) e 0.07x3 - 0.08 +2 ° i i 1.)338 28 = e9x2 in (1.138828) = 2 r = ln (1.138828) 2 rate forward a 6.5 % 2 year 12 b) hear Anbitrage exists as the 2 year forward rate one. from now is higher than 65 %. iy 2 2. Borron Inn at 7% spot for 3 years forom B & invest in A at 8% for a year followed by investment in C at 7.5% of for 2 years. Rething from investment in A&C= 100000o eoxe oto 0.075x2 - - 1258600 0.07x3 s payable to B in 3 years = 1000000 e. = 1233 678.06 Gain = 1258600 - 1233678.06 = 24,921.94