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Options, Futures, and Other Derivatives

John C. Hull

Chapter 1

Introduction - all with Video Answers

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Chapter Questions

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Problem 1

What is the difference between a long forward position and a short forward position?

Nick Johnson
Nick Johnson
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Problem 2

Explain carefully the difference between hedging, speculation, and arbitrage.

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02:33

Problem 3

What is the difference between entering into a long forward contract when the forward price is $$\$ 50$$ and taking a long position in a call option with a strike price of $$\$ 50$$ ?

Narayan Hari
Narayan Hari
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Problem 4

Explain carefully the difference between selling a call option and buying a put option.

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01:47

Problem 5

An investor enters into a short forward contract to sell 100,000 British pounds for U.S. dollars at an exchange rate of 1.5000 USD per pound. How much does the investor gain or lose if the exchange rate at the end of the contract is (a) 1.4900 and (b) 1.5200 ?

Nick Johnson
Nick Johnson
Numerade Educator
01:47

Problem 6

A trader enters into a short cotton futures contract when the futures price is 50 cents per pound. The contract is for the delivery of 50,000 pounds. How much does the trader gain or lose if the cotton price at the end of the contract is (a) 48.20 cents per pound and (b) 51.30 cents per pound?

Nick Johnson
Nick Johnson
Numerade Educator

Problem 7

Suppose that you write a put contract with a strike price of $$\$ 40$$ and an expiration date in 3 months. The current stock price is $$\$ 41$$ and the contract is on 100 shares. What have you committed yourself to? How much could you gain or lose?

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Problem 8

What is the difference between the over-the-counter market and the exchange-traded market? What are the bid and offer quotes of a market maker in the over the counter or exchange traded market?

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05:08

Problem 9

You would like to speculate on a rise in the price of a certain stock. The current stock price is $$\$ 29$$ and a 3 month call with a strike price of $$\$ 30$$ costs $$\$ 2.90$$. You have $$\$ 5,800$$ to invest. Identify two alternative investment strategies, one in the stock and the other in an option on the stock. What are the potential gains and losses from each?

Narayan Hari
Narayan Hari
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Problem 10

Suppose that you own 5,000 shares worth $$\$ 25$$ each. How can put options be used to provide you with insurance against a decline in the value of your holding over the next 4 months?

Rashmi Sinha
Rashmi Sinha
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Problem 11

When first issued, a stock provides funds for a company. Is the same true of a stock option? Discuss.

James Kiss
James Kiss
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Problem 12

Explain why a futures contract can be used for either speculation or hedging.

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Problem 13

Suppose that a March call option to buy a share for $$\$ 50$$ operatorname{costs} $$\$ 2.50$$ and is held until March. Under what circumstances will the holder of the option make a profit? Under what circumstances will the option be exercised? Draw a diagram illustrating how the profit from a long position in the option depends on the stock price at maturity of the option.

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Problem 14

Suppose that a June put option to sell a share for $$\$ 60$$ costs $$\$ 4$$ and is held until June. Under what circumstances will the seller of the option (i.e., the party with the short position) make a profit? Under what circumstances will the option be exercised? Draw a diagram illustrating how the profit from a short position in the option depends on the stock price at maturity of the option.

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01:53

Problem 15

It is May and a trader writes a September call option with a strike price of $$\$20$$. The stock price is $$\$ 18$$ and the option price is $$\$ 2$$. Describe the trader's cash flows if the option is held until September and the stock price is $$\$ 25$$ at that time.

James Kiss
James Kiss
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Problem 16

A trader writes a December put option with a strike price of $$\$ 30$$. The price of the option is $$\$ 4$$. Under what circumstances does the trader make a gain?

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Problem 17

A company knows that it is due to receive a certain amount of a foreign currency in 4 months. What type of option contract is appropriate for hedging?

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Problem 18

A U.S. company expects to have to pay 1 million Canadian dollars in 6 months. Explain how the exchange rate risk can be hedged using (a) a forward contract and (b) an option.

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01:47

Problem 19

A trader enters into a short forward contract on 100 million yen. The forward exchange rate is $$\$ 0.0090$$ per yen. How much does the trader gain or lose if the exchange rate at the end of the contract is (a) $$\$ 0.0084$$ per yen and (b) $$\$ 0.0101$$ per yen?

Nick Johnson
Nick Johnson
Numerade Educator

Problem 20

The CME Group offers a futures contract on long-term Treasury bonds. Characterize the traders likely to use this contract.

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Problem 21

"Options and futures are zero-sum games." What do you think is meant by this?

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04:10

Problem 22

Describe the profit from the following portfolio: a long forward contract on an asset and a long European put option on the asset with the same maturity as the forward contract and a strike price that is equal to the forward price of the asset at the time the portfolio is set up.

Narayan Hari
Narayan Hari
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03:03

Problem 23

In the $1980 \mathrm{~s}$, Bankers Trust developed index currency option notes (ICONs). These were bonds in which the amount received by the holder at maturity varied with a foreign exchange rate. One example was its trade with the Long Term Credit Bank of Japan. The ICON specified that if the yen-USD exchange rate, $S_T$, is greater than 169 yen per dollar at maturity (in 1995), the holder of the bond receives $$\$ 1,000$$. If it is less than 169 yen per dollar, the amount received by the holder of the bond is
$$
1,000-\max \left[0,1,000\left(\frac{169}{S_T}-1\right)\right]
$$
When the exchange rate is below 84.5 , nothing is received by the holder at maturity. Show that this $I C O N$ is a combination of a regular bond and two options.

Natalie Britton
Natalie Britton
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Problem 24

On July 1, 2017, a company enters into a forward contract to buy 10 million Japanese yen on January 1, 2018. On September 1, 2017, it enters into a forward contract to sell 10 million Japanese yen on January 1, 2018. Describe the payoff from this strategy.

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Problem 25

Suppose that USD/sterling spot and forward exchange rates are as follows:
$$
\begin{array}{ll}
\hline \text { Spot } & 1.5580 \\
\text { 90-day forward } & 1.5556 \\
\text { 180-day forward } & 1.5518 \\
\hline
\end{array}
$$
What opportunities are open to an arbitrageur in the following situations?
(a) A 180-day European call option to buy $£ 1$ for $$\$ 1.52$$ costs 2 cents.
(b) A 90-day European put option to sell $£ 1$ for $$\$ 1.59$$ costs 2 cents.

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Problem 26

A trader buys a call option with a strike price of $$\$ 30$$ for $$\$ 3$$. Does the trader ever exercise the option and lose money on the trade? Explain your answer.

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Problem 27

A trader sells a put option with a strike price of $$\$ 40$$ for $$\$ 5$$. What is the trader's maximum gain and maximum loss? How does your answer change if it is a call option?

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Problem 28

"Buying a put option on a stock when the stock is owned is a form of insurance." Explain this statement.

James Kiss
James Kiss
Numerade Educator
01:53

Problem 29

On May 3, 2016, as indicated in Table 1.2, the spot offer price of Google stock is $$\$ 696.25$$ and the offer price of a call option with a strike price of $$\$ 700$$ and a maturity date of September is $$\$ 39.20$$. A trader is considering two alternatives: buy 100 shares of the stock and buy 100 September call options. For each alternative, what is (a) the upfront cost, (b) the total gain if the stock price in September is $$\$ 800$$, and (c) the total loss if the stock price in September is $$\$ 600$$. Assume that the option is not exercised before September and if the stock is purchased it is sold in September.

James Kiss
James Kiss
Numerade Educator

Problem 30

What is arbitrage? Explain the arbitrage opportunity when the price of a dually listed mining company stock is $$\$ 50$$ (USD) on the New York Stock Exchange and $$\$ 60$$ (CAD) on the Toronto Stock Exchange. Assume that the exchange rate is such that 1 U.S. dollar equals 1.21 Canadian dollars. Explain what is likely to happen to prices as traders take advantage of this opportunity.

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Problem 31

Trader $\mathrm{A}$ enters into a forward contract to buy an asset for $$\$ 1,000$$ in one year. Trader $\mathrm{B}$ buys a call option to buy the asset for $$\$ 1,000$$ in one year. The cost of the option is $$\$ 100$$. What is the difference between the positions of the traders? Show the profit as a function of the price of the asset in one year for the two traders.

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Problem 32

In March, a U.S. investor instructs a broker to sell one July put option contract on a stock. The stock price is $$\$ 42$$ and the strike price is $$\$ 40$$. The option price is $$\$ 3$$. Explain what the investor has agreed to. Under what circumstances will the trade prove to be profitable? What are the risks?

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Problem 33

A U.S. company knows it will have to pay 3 million euros in three months. The current exchange rate is 1.1500 dollars per euro. Discuss how forward and options contracts can be used by the company to hedge its exposure.

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Problem 34

A stock price is $$\$ 29$$. A trader buys one call option contract on the stock with a strike price of $$\$ 30$$ and sells a call option contract on the stock with a strike price of $$\$ 32.50$$. The market prices of the options are $$\$ 2.75$$ and $$\$ 1.50$$, respectively. The options have the same maturity date. Describe the trader's position.

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Problem 35

The price of gold is currently $$\$ 1,200$$ per ounce. The forward price for delivery in 1 year is $$\$ 1,300$$ per ounce. An arbitrageur can borrow money at $3 \%$ per annum. What should the arbitrageur do? Assume that the cost of storing gold is zero and that gold provides no income.

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Problem 36

The current price of a stock is $$\$ 94$$, and 3-month European call options with a strike price of $$\$ 95$$ currently sell for $$\$ 4.70$$. An investor who feels that the price of the stock will increase is trying to decide between buying 100 shares and buying 2,000 call options (=20 contracts). Both strategies involve an investment of $$\$ 9,400$$. What advice would you give? How high does the stock price have to rise for the option strategy to be more profitable?

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Problem 37

On May 3, 2016, an investor owns 100 Google shares. As indicated in Table 1.3, the share price is about $$\$ 696$$ and a December put option with a strike price of $$\$ 660$$ costs $$\$ 38.10$$. The investor is comparing two alternatives to limit downside risk. The first involves buying one December put option contract with a strike price of $$\$ 660$$. The second involves instructing a broker to sell the 100 shares as soon as Google's price reaches $$\$ 660$$. Discuss the advantages and disadvantages of the two strategies.

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03:38

Problem 38

A bond issued by Standard Oil some time ago worked as follows. The holder received no interest. At the bond's maturity the company promised to pay $$\$ 1,000$$ plus an additional amount based on the price of oil at that time. The additional amount was equal to the product of 170 and the excess (if any) of the price of a barrel of oil at maturity over $$\$ 25$$. The maximum additional amount paid was $$\$ 2,550$$ (which corresponds to a price of $$\$ 40$$ per barrel). Show that the bond is a combination of a regular bond, a long position in call options on oil with a strike price of $$\$ 25$$, and a short position in call options on oil with a strike price of $$\$ 40$$.

Nick Johnson
Nick Johnson
Numerade Educator

Problem 39

Suppose that in the situation of Table 1.1 a corporate treasurer said: "I will have $£ 1$ million to sell in 6 months. If the exchange rate is less than 1.42 , I want you to give me 1.42. If it is greater than 1.48 , I will accept 1.48 . If the exchange rate between 1.42 and 1.48 , I will sell the sterling for the exchange rate." How could you use options to satisfy the treasurer?

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Problem 40

Describe how foreign currency options can be used for hedging in the situation considered in Section 1.7 so that (a) ImportCo is guaranteed that its exchange rate will be less than 1.4700 , and (b) ExportCo is guaranteed that its exchange rate will be at least 1.4300 . Use DerivaGem to calculate the cost of setting up the hedge in each case assuming that the exchange rate volatility is $12 \%$, interest rates in the United States are $2 \%$, and interest rates in Britain are $1 \%$. Assume that the current exchange rate is the average of the bid and offer in Table 1.1.

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04:10

Problem 41

A trader buys a European call option and sells a European put option. The options have the same underlying asset, strike price, and maturity. Describe the trader's position. Under what circumstances does the price of the call equal the price of the put?

Narayan Hari
Narayan Hari
Numerade Educator