The current market price of a two-year 25 percent coupon bond with a $1,000 face value is $1,219.71 (recall that such a bond pays coupons of $250 at the end of years 1 and 2, and the principal of $1,000 at the end of year 2). The current market price of a one-year pure discount bond with a $50 face value is $44.64.
(a) What must the price of a two-year pure discount bond with a $2,500 face value be in order to avoid arbitrage?
(b) Suppose the price of the two-year pure discount bond with a $2,500 face value is only $1,900. Is there an arbitrage opportunity? Is yes, how would you structure a trade that has zero cashflow in years 1 and 2 and a positive cash-flow only in year 0 (i.e. now). Show your work.