Question $6$

a$)$ Explain how a manufacturing company can hedge the risk of rising raw material prices with futures contracts. Additionally, explain how a company can hedge against the risk of falling raw material prices with futures contracts. Discuss why the Central Counterparty Clearing $($CCP$)$ requires both parties in a futures contract to deposit an initial margin and how this helps prevent financial instability.

b$)$ The current stock price is $$350.$ The continuously compounded risk$-$free interest rate is $4\%$ per annum, and the continuous dividend yield is $3\%$ per annum. What will the $4-$month futures price be if the stock price remains unchanged?

c$)$ The continuously compounded risk$-$free interest rate is $6\%$ per annum, and the continuous dividend yield is $4\%$ per annum. If the stock price remains unchanged, what will the $4-$month futures price be when the stock price is $$405?$ Explain if an arbitrage opportunity exists.