Question $7$

a$)$ The current stock index level is $350.$ The continuously compounded risk$-$free interest rate is $4\%$ per annum, and the continuous dividend yield on the index is $3\%$ per annum. What is the $4-$month futures price of the stock index?

b$)$ The continuously compounded risk$-$free interest rate is $6\%$ per annum, and the continuous dividend yield on the index is $4\%$ per annum. If the current stock index level is $400,$ what will the $4-$month futures price be$?$ Is there an arbitrage opportunity?