Derivatives- BFW 2751

Please give a full explanation worth 20% each question with diagrams and tables. Thanks

Question 1

A company wishes to hedge its exposure to a new fuel whose price changes have a 0.6 correlation with gasoline futures price changes. The company will lose $1 million for each 1 cent increase in the price per gallon of the new fuel over the next three months. The new fuel's price change has a standard deviation that is 50% greater than price changes in gasoline futures prices. If gasoline futures are used to hedge the exposure what should the hedge ratio be? What is the company's exposure measured in gallons of the new fuel?What position measured in gallons should the company take in gasoline futures? How many gasoline futures contracts should be traded? Each contract is on 42,000 gallons.

Question 2

A security is currently trading at $96. It will pay a coupon of $4 in three months. No other payouts are expected in the next six months.

(a) If the term structure is at 10%, what should the forward price be on the security for delivery in six months?

(b) If the actual forward price is $98, explain how an arbitrage may be created.

Question 3

Suppose that Getting Berhad shares are currently priced as $45, call options on this shares with strike prices of $50 and $70 costs $5 and $3, respectively and you are bullish about the price movement of this stock. How can the options on this stock be used to create a bull spread? Construct a diagram and a table that shows the payoff and profit.

Question 4

Suppose that Sima Day Berhad shares are currently selling at $60 and put options on these shares with strike prices $45 and $55 cost $5 and $9, respectively and you are bearish about the stock price movements in the short term. How can the options be used to create a bear spread? Construct a table and a diagram that shows the profit and payoff.

Question 5

Three put options on a stock have the same expiration date and strike prices of $70, $80, and $90 are available at prices of $5, $8, and $10, respectively. Explain how a butterfly spread can be created. Construct a table showing the profit from the strategy. For what range of stock prices would the butterfly spread lead to a loss?