Consider a government bond market with three zero coupon

Consider a government bond market with three zero coupon bonds. Bonds 1 and 3 have a face value of $100 each and bond 2 has a face value of 105. Bond i matures in i years , i=1,..,3. The price of bond 1 – $98, bond 2 – $96 and bond 3 – $95.

a. Determine whether that the no-arbitrage condition is satisfied in this market by solving for the discount factors and utilizing their properties.

b. If your conclusion in a) was that the no arbitrage is satisfied, skip this part, otherwise determine the arbitrage profit that can be obtained if you are allowed to borrow (taking a short position) not more than $100 and stipulate the arbitrage portfolio.