1. Consider a market with a risky asset S, in which people can invest money in the bank at rate Ta per year and borrow money from the bank at rate Tb per year, with > Ta (both interest rates are continuously compounded). You have to prove that in this market there exists an interval of one-year 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) (5 pts) If S pays no dividends, construct an arbitrage opportunity when F(O) > Soeb and when F(O)Soe Conclude there are no arbitrage opportunities if and only if F(0) E [Soeto, Soerb (b) (3 pts) If S pays a dividend of d dollars every three months, find E and F such that there are no arbitrage opportunities if and only if F(O) e E (c) (5 pts) Suppose now that S represents the price in dollars of one unit of a foreign currency, with foreign risk-free interest rate rf (continuously compounded). Find f and f such that there are no arbitrageo