Problem

A stock currently sells for $50. In six months, it will either rise to $55 or decline to $45. The risk-free interest rate is 6% per year.

1. Find the value of a European call option with an exercise price of $50.

2. Find the value of a European put option with an exercise price of $50, using the binomial approach.

3. Verify the put-call parity using the results of Questions 1 and 2.

Problem

An investor sold seven contracts of June/2012 corn. The price per bushel was $1.64, and each contract was for 5000 bushels.  The initial margin deposit is $2000 per contract with the maintenance margin at $1250.

1. How much did the investor have to deposit on the investment?

2. The prices of the futures on the four days following the short sales were 1.60, 1.66, 1.70, and 1.75. Calculate the current balance on each of the next four days.

3. If the investor closed out her position on the fifth day, what was her final gain or loss over the five days in dollars and as a percentage of investment?

4. If the investor kept her position, and the futures price on the sixth day was 1.80, would the investor face a margin call? If yes, how much would she need to put up?