1. Consider a market with a risky asset 8, in which people can invest money in the bank at rate Ta per year and borrow money from the bank at rate 77, per year, with n, > rd (both interest rates are continuously compounded). You have to prove that in this market there exists an interval of oneyear forward prices on the stock such that there are no arbitrage opportunities, instead of a single price. Denote by So the initial price of the stock. (a) (b) If S pays no dividends, construct an arbitrage opportunity when F (0) > Soc\" and when F(O) Soc\" we have an arbitrage as follows. At t = 0 we enter into a short position in the forward contract and buy the stock at price So by borrowing money from the bank. At t = 1 we honor the forward contract, sell the stock at price F(0) and use the money to pay the current debt of So a"b to the bank, obtaining a risk-free prot. If F (0) E we have an arbitrage as follows. At t = 0 we enter into a short position in the forward contract and buy the stock at price So by borrowing money from the bank. As soon as we receive a dividend, we deposit it in the bank. At t = 1 we honor the forward contract, sell the stock at price F (0) and use the money and what we have in the bank to pay the current debt of Soc\". We obtain a risk-free prot. If F(0)