$1)(50$ pts$.$ total$)$ Suppose you are a market$-$maker in an index forward contracts market. The index spot price is $$1,100,$ the risk$-$free rate is $5\%,$ and the dividend yield on the index is $0.$

a$)(10$ pts$.)$ What is the no$-$arbitrage forward price for delivery in $9$ months?

b$)(20$ pts$.)$ Suppose a customer wishes to enter a short index futures position. If you take the opposite position, demonstrate how you would hedge your resulting long

c$)(20$ pts$.)$ Suppose a customer wishes to enter a long index futures position. If you take the opposite position, demonstrate how you would hedge your resulting short position using the index and borrowing or lending in the money market.