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# Arbitrage (gold future contracts), Binomial tree

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3. The current interest rate is 5 percent per year. You can treat it as 2.5% per six months. You can borrow or lend at this interest rate. The futures contract for gold six months in the future is selling for \$346.30, whereas the futures contract 12 months in the future is selling for \$360.00. Is there an arbitrage opportunity here? If so, how would you exploit it?

4. A stock is currently selling for \$100 per share. It does not pay a dividend. Each month it either goes up by 5% or it goes down by 2%. There is no necessary relationship between what happens one month and what happens the next. There are call options available that expire exactly three months from now. They have an exercise price of \$104. Assume that the interest rate is 6 percent per year or one-half percent per month. Using the two-state approach, determine the value of these call options. That is, determine what they should sell for today. {Hint: you probably want to use a spreadsheet and calculate what the options will be worth three months from now (under various outcomes), then two months from now, then one month from now, and then now}.

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#### Solution Summary

Answers to 2 questions: 1) Arbitrage among gold future contracts, 2) Value of call option using Binomial tree

\$2.19

## Options, Warrants , Futures and Bonds

Q1- Consider a European call option on stock (A) that that expires on December 21 and has a strike price of \$50.
a. If stock A is trading at \$55 on December 21, what is the payoff to the owner of the option?
b. If stock A is trading at \$55 on Dec. 21, what is the payoff to the seller of the option?
c. If stock A is trading at \$45 on Dec. 21, what is the payoff to the owner of the option?
d. If stock A is trading at \$45 on Dec. 21, what is the payoff to the seller of the option?
e. Draw the payoff diagram to the owner of this option with respect to the stock price at expiration.
f. Draw the payoff diagram to the seller of this option with respect to the stock price at expiration.
g. If the seller of a call option never receives cash at expiration, why should anyone ever sell a call option?

Q2- MMInc. Must purchase gold in three months to use in its operations. The management has estimated that if the price of gold were to rise above \$375 per ounce, the firm would go bankrupt. The current price of gold os \$350 per ounce;. The firm's CFO believes that the price f gold will either rise to \$400 per ounce or fall to \$325 per ounce over the next three months. Management wishes to eliminate any risk of going bankrupt . MMInc. Can borrow and lend at the risk free interest rate of 16.99% per annum(effective annual yield) .
a. Would MMInc. be interested in buying a call option or a put option on the price of gold? In order to avoid bankruptcy, what strike price and time to expiration would the firm like this option to have?
b. How much should such an option sell for in the open market?
c. If no option currently trade on gold, is there a way for the company to creat a synthetic option which identifies payoffs to the option described above? If there is, how would the firm do it?
d. How much does the synthetic option cost? Is this greater than , less than, or equal to what the actual option costs? Does this make sense?

Q3
a. What is the primary difference between warrants and call options?
b. Why is this difference important? What is dilution?

Q4 Explain three ways in which futures contracts differ from forward contracts

Q5 Consider three zero-coupon, \$1000 face value bonds . bond A matures one year from today, bond B matures five years from today, and bond C matures ten years from today. The current market interest rate is 11% per annum (effective annual yield).
a. What is the current price of each bond?
b. If the market interest rate suddenly rises to 14% per annum , what wil be the price of each of these bonds?
c. Which bond experienced the greatest percentage change in price?

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