Arbitrage (40 pts) 1. Suppose a zero-coupon bond that matures 1 year from today costs $98. A year from today, a zero-coupon bond that matures 2 years from today will also costs $98. (a) What must be the price of a 10% (yearly) coupon bond with a face value of $100 that matures 2 years from now? (b) Present a complete arbitrage strategy if the 2-year coupon bond were trading at $90? 2. Consider two securities A and B. There are two possible scenarios that can happen in a year: Economic Boom (EB) and recession (R). Bond A pays $100 in EB and 0 in R. Bond B pays $0 in EB and $100 in R. Suppose the price of A and B are $25 and $70 respectively. (a) Find the payoff in each contingency (EB or R) of a portfolio of one A security and one B security. (b) What would be the price of a 1-year zero (zero coupon bond) if the no-arbitrage condition is satisfied and there are no trading costs. What does the No-Arbitrage Condition imply about the price of a 1-year zero-coupon bond if there are no trading costs? (c) A 1-year zero is trading at $90. Find an arbitrage opportunity again assuming no trading costs. (d) Can you make an arbitrage trade if trading zero-coupon bonds is costless, but trading securities A and B cost $2 per $100 face value each?