Options and Derivatives Chapter 1 Solutions

Topics: Futures contract, Derivative, Option Pages: 11 (2863 words) Published: September 28, 2013

CHAPTER 1
Introduction

Practice Questions

Problem 1.1
What is the difference between a long forward position and a short forward position?

When a trader enters into a long forward contract, she is agreeing to buy the underlying asset for a certain price at a certain time in the future. When a trader enters into a short forward contract, she is agreeing to sell the underlying asset for a certain price at a certain time in the future.

Problem 1.2.
Explain carefully the difference between hedging, speculation, and arbitrage.

A trader is hedging when she has an exposure to the price of an asset and takes a position in a derivative to offset the exposure. In a speculation the trader has no exposure to offset. She is betting on the future movements in the price of the asset. Arbitrage involves taking a position in two or more different markets to lock in a profit.

Problem 1.3.
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?

In the first case the trader is obligated to buy the asset for $50. (The trader does not have a choice.) In the second case the trader has an option to buy the asset for $50. (The trader does not have to exercise the option.)

Problem 1.4.
Explain carefully the difference between selling a call option and buying a put option.

Selling a call option involves giving someone else the right to buy an asset from you. It gives you a payoff of

Buying a put option involves buying an option from someone else. It gives a payoff of

In both cases the potential payoff is. When you write a call option, the payoff is negative or zero. (This is because the counterparty chooses whether to exercise.) When you buy a put option, the payoff is zero or positive. (This is because you choose whether to exercise.)

Problem 1.5.
An investor enters into a short forward contract to sell 100,000 British pounds for US dollars at an exchange rate of 1.4000 US dollars per pound. How much does the investor gain or lose if the exchange rate at the end of the contract is (a) 1.3900 and (b) 1.4200?

(a) The investor is obligated to sell pounds for 1.4000 when they are worth 1.3900. The gain is (1.4000-1.3900) ×100,000 = $1,000.

(b) The investor is obligated to sell pounds for 1.4000 when they are worth 1.4200. The loss is (1.4200-1.4000)×100,000 = $2,000

Problem 1.6.
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; (b) 51.30 cents per pound?

(a) The trader sells for 50 cents per pound something that is worth 48.20 cents per pound. Gain .

(b) The trader sells for 50 cents per pound something that is worth 51.30 cents per pound. Loss .

Problem 1.7.
Suppose that you write a put contract with a strike price of $40 and an expiration date in three 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?

You have sold a put option. You have agreed to buy 100 shares for $40 per share if the party on the other side of the contract chooses to exercise the right to sell for this price. The option will be exercised only when the price of stock is below $40. Suppose, for example, that the option is exercised when the price is $30. You have to buy at $40 shares that are worth $30; you lose $10 per share, or $1,000 in total. If the option is exercised when the price is $20, you lose $20 per share, or $2,000 in total. The worst that can happen is that the price of the stock declines to almost zero during the three-month period. This highly unlikely event would cost you $4,000. In return for the possible future losses, you receive the price of the option...
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