problem 1: prepare brief notes on:
a) Speculator.
b) Arbitrager.
c) Hedgers.
problem 2: Describe various types of orders and different types of margin.
problem 3: A call option with a strike price of $50 costs $2. A put option with a strike price of $45 costs $3. Describe how strangle can be made from such two options. What the pattern of profits is from strangled?
problem 4: Assume that put options on a stock with strike prices $30 and $35 cost $4 and $7, correspondingly. How can the options be used to create:
a) A bull spread and
b) A bear spread
Construct a table which shows the profit and payoff for both spreads.
problem 5: A call with a strike price of $60 costs $6. A put with the same strike price and expiration date costs $4. Construct a table which shows the profit from a straddle. For what range of stock prices would the straddle lead to a loss?
problem 6: An investor enters into two long futures contracts on frozen orange juice. Each contract is for the delivery of 15,000 pounds. The present futures price is 160 cents per pound, the initial margin is $6,000 per contract and the maintenance margin is $4,500 per contract. What price change would lead to a margin call? Under what conditions $2,000 could be withdrawn from the margin account?
problem 7: Assume that the current spot price of gold is S = $350 per oz, the risk-free three-month rate of interest is 3% and there are no costs of holding gold. Determine the three-month forward price of gold?
problem 8: The forward price of wheat for delivery in three months is $3.90 per bushel, while the spot price is $3.60. The three-month interest rate in continuously compounded terms is 8% per annum. Is there an arbitrage opportunity in this market if wheat might be stored costless?
problem 9: Assume that the current price of gold is $365 per oz and that gold might be stored costless. Also assume that the term structure is ?at with a continuously compounded rate of interest of 6% for all maturities.
a) Compute the forward price of gold for delivery in three months.
b) Now assume that it costs $1 per oz per month to store gold (payable monthly in advance). Determine the new forward price?
c) Suppose storage costs are as in part (b). If the forward price is given to be $385 per oz, describe whether there is an arbitrage opportunity and how to exploit it.
problem 10: What is the price of a European call option on a non-dividend-paying stock when the stock price is $52, the strike price is $50, the risk-free interest rate is 12% per annum, the volatility is 30% per annum and the time to maturity is three months?