3. Forward Rates and No-arbitrage Pricing - 30 Points Suppose t=0 and continuously compounded forward rate for the period [1,2] is given by f1,2=7.5%. Consider the following two securities: - a 2 year zero coupon bond (2YZ) which pays $1000 at time 2 and has a current price P2YZ= $869.36. - a 3 year annuity (3YA) which pays $1000 at times 1,2 , and 3 and has a current price P3YA= $2,604.94. (a) Consider a (long) forward (FOR) contract initiated at time 0 for the delivery at time 2 at a price F of a claim which pays $2,000 at time 3 . What is the delivery price F set at time 0 ? (b) What is the continuously compounded forward rate for the period [2,3] denoted by f2,3 ? (c) Consider a growing bond (GB) that pays $1000 at time 1,$2000 at time 2, and $3000 at time 3 with the current price PGB=$5100. Using the 2 year zero coupon bond (2YZ), the 3 year annuity (3YA), the forward (FOR), and the growing bond (GB), find a portfolio which generates $1 million profit initially with zero payout at all future dates