Reference no: EM133016575

Problem 1 - Suppose that you enter into a long futures contract to buy July silver for $67.40 per ounce. The size of the contract is 2500 ounces. The initial margin is $6000, and the maintenance margin is $4300. What change in the futures price will lead to a margin call? What happens if you do not meet the call?

Problem 2 - The formula of optimal hedge ratio is

You want to hedge your rice crop of 8,000 bushels in September by corn futures. Each corn futures contract is on 4000 bushels of corn.

1. How much is your optimal hedge ratio? (Facts: Standard deviation of corn futures price is $0.0397. Standard deviation of rice price is $0.0293. The correlation between the two is 0.871. )

2. How many contracts do you need?

Problem 3 - A two-year long forward contract on a non-dividend-paying stock is entered into when the stock price is $73 and the risk-free rate of interest is 5% per annum with continuous compounding.

1. What are the forward price and the initial value of the forward contract?

2. Six months later, the price of the stock is $77.5 and the risk-free interest rate is still 5%. What are the forward price and the value of the contract?

3. If the stock pays a dividend of $3.5 twice a year (ie. Pay $3.5 every six months), what is the forward price?

Problem 4 - The current price of the gold is $600 per ounce. The storage cost is a continuous cost of 5% every year. If the interest rate is 3% per annum for all maturities, what is the futures price for futures price of gold delivering in nine months?

Problem 5 - Instruction: Please specify and describe the detailed actions for setup and close out of arbitrage strategy, including actions in all markets, their timing, and their consequence -- gain or loss.

Arbitrage trading forces market price to converge to the intrinsic value of a security. Therefore arbitrage argument is one of the major approaches to justify theoretical derivatives prices. Can you provide a complete arbitrage strategy for the following situation? Make sure to show that the arbitrager: 1) enters market without asset or cash; and 2) leaves the market with no obligation and positive cash.

Situation: The spot price for corn today is 100/bushel. Interest rate is 3.5%. The market ONE-YEAR futures price now is 102/bushel. Detect the arbitrage opportunity and describe the arbitrage step by step.