Chapter 5: Q1CP (page 591)
The open interest on a futures contract at any given time is the total number ofoutstanding:
a. Contracts.
b. Un-hedged positions.
c. Clearinghouse positions.
d. Long and short positions.
a. contracts
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One Chicago has just introduced a new single stock futures contract on the stock of Brandex, a company that currently pays no dividends. Each contract calls for delivery of 1,000 shares of stock in one year. The T-bill rate is 6% per year.
a. If Brandex stock now sells at \(120 per share, what should the futures price be?
b. If the Brandex stock price drops by 3%, what will be the change in the futures price and the change in the investor’s margin account?
c. If the margin on the contract is \)12,000, what is the percentage return on the investor’s position?
We will derive a two-state put option value in this problem. Data: S0 = 100; X = 110; 1 + r = 1.10. The two possibilities for ST are 130 and 80.
a. Show that the range of S is 50 while that of P is 30 across the two states. What is the hedge ratio of the put?
b. Form a portfolio of three shares of stock and five puts. What is the (nonrandom) payoff to this portfolio? What is the present value of the portfolio?
c. Given that the stock currently is selling at 100, show that the value of the put must be 10.91.
A put option with strike price \(60 trading on the Acme options exchange sells for \)2. To your amazement, a put on the firm with the same expiration selling on the Apex options exchange but with strike price \(62 also sells for \)2. If you plan to hold the options position until expiration, devise a zero-net-investment arbitrage strategy to exploit the pricing anomaly. Draw the profit diagram at expiration for your position.
A collar is established by buying a share of stock for \(50, buying a six-month put option with exercise price \)45, and writing a six-month call option with exercise price \(55. Based on the volatility of the stock, you calculate that for an exercise price of \)45 and maturity of six months, N (d1) = .60, whereas for the exercise price of \(55, N (d1) = .35.
a. What will be the gain or loss on the collar if the stock price increases by \)1?
b. What happens to the delta of the portfolio if the stock price becomes very large? Very small?
You establish a straddle on Walmart using September call and put options with a strike price of \(50. The call premium is \)4.25 and the put premium is \(5.
a. What is the most you can lose on this position?
b. What will be your profit or loss if Walmart is selling for \)58 in September?
c. At what stock prices will you break even on the straddle?
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