Exercise 4 A$1 zero-coupon bond of maturity T>O is priced Z(0,T) at time t = 0 for each Tin (1,3): Z(0.1) = 0.95, Z(0,2) = 0.85, Z(0,3) = 0.70. 1. Assuming continuous compounding, find the term structure of interest rates today, i.e., the rate RTO; T) as a function of T. Assume now that the market also quotes at time t0 the price of risk-free coupon bonds. The traded coupon is as follows: C1Y = 10 is the coupon is the coupon paid at year 3. The coupon bond also pays the nominal N3Y = 100 at year 3. 2. Find the theoretical price of this coupon bond 3. Assume that the market price of this coupon bond is 98. Is this the "fair price? If not, is there an arbitrage strategy to earn money without risk? What would you do to exploit this arbitrage? Same question if the market price of the coupon bond is equal to 90. 4. Exercise 4 A$1 zero-coupon bond of maturity T>O is priced Z(0,T) at time t = 0 for each Tin (1,3): Z(0.1) = 0.95, Z(0,2) = 0.85, Z(0,3) = 0.70. 1. Assuming continuous compounding, find the term structure of interest rates today, i.e., the rate RTO; T) as a function of T. Assume now that the market also quotes at time t0 the price of risk-free coupon bonds. The traded coupon is as follows: C1Y = 10 is the coupon is the coupon paid at year 3. The coupon bond also pays the nominal N3Y = 100 at year 3. 2. Find the theoretical price of this coupon bond 3. Assume that the market price of this coupon bond is 98. Is this the "fair price? If not, is there an arbitrage strategy to earn money without risk? What would you do to exploit this arbitrage? Same question if the market price of the coupon bond is equal to 90. 4