Q2: Forward with transaction cost (4 marks)

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. In addition to the difference in borrowing and lending rate, 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. What is the non-arbitrage upper bound of the above forward?