Suppose the S&R index is 1000 and the dividend yield is zero. The continuously compounded borrowing rate is 5% while the continuously compounded lending rate is 4.5%. The maturity of the forward contract is 6 months.

(a) Suppose when you buy or sell the index, there is a transaction cost of $1 at t=0. There is also a transaction cost of $2 if you take a long or short forward position at t=0. There are no transaction costs on the maturity date. The futures price is 1026. Which of the statement is true?

A. You can do cash-and-carry arbitrage

B. You can do reverse cash-and-carry arbitrage

C. You can do both cash-and-carry and reverse cash-and-carry arbitrage

D. You cannot arbitrage

(b) Following part (a), what is the non-arbitrage upper bound of the forward price?