Chapter 1

Question 1

Consider a forward contract on a stock market index. Identify the false statement. Everything else being constant,

a. The forward price depends directly on the level of the stock market index.
b. The forward price will fall if underlying stocks increase the level of dividend payments over the life of the contract.
c. The forward price will rise if time to maturity is increased.
d. The forward price will fall if the interest rate is raised.

Answer 1

d. The forward price will fall if the interest rate is raised.

Question 2

Consider an eight-month forward contract on a stock with a price of $98/share. The delivery date is eight months hence. The firm is expected to pay a $1.80 per share dividend in four months. Riskless zero-coupon interest rates (continuously compounded) are 4% for four months, and 4.5% for eight months. The theoretical forward price (to the nearest cent) is

a. 99.16
b. 99.26
c. 100.98
d. 96.20

Answer 2

a. 99.16

Question 3

Calculate the price of a 1-year forward contract on gold. Assume the storage cost for gold is $5.00 per ounce, with payment made at the end of the year. Spot gold is $290 per ounce and the risk-free rate is 5%.

a. $304.86
b. $309.87
c. $310.12
d. $313.17

Answer 3

b. $309.87

Question 4

Use the following information to answer the next two questions. The two-year risk-free rate in the United Kingdom and France is 8% and 5% per annum, continuously compounded, respectively. The current French franc (FF) to the GBP currency exchange rate is that one unit of GBP currency costs 0.75 units of French franc. What is the two-year forward price of one unit of the GBP in terms of the French franc so that no arbitrage opportunity exists?

a. 0.578
b. 0.706
c. 0.796
d. 0.973

Answer 4

b. 0.706

Question 5

If the observed two-year forward price of one unit of the GBP is 0.850 units of the French franc, what is your strategy to make an arbitrage profit?

a. Borrow GBP, buy FF and enter a short forward contract on French francs.
b. Borrow GBP, buy FF, and enter a short forward contract on GBP.
c. Borrow FF, buy GBP, and enter a short forward contract on French francs.
d. Borrow FF, buy GBP, and enter a short forward contract on GBP.

Answer 5

d. Borrow FF, buy GBP, and enter a short forward contract on GBP.

Question 6

An investor enters into a short position in a gold futures contract at USD 294.20. Each futures contract controls 100 troy ounces. The initial margin is USD 3,200 and the maintenance margin is USD 2,900. At the end of the first day, the futures price drops to USD 286.6. Which of the following is the amount of the variation margin at the end of the first day?

a. 0
b. USD 34
c. USD 334
d. USD 760

Answer 6

a. 0

Question 7

Which one of the following statements is incorrect regarding the margining of exchange traded futures contracts?

a. Day trades and spread transactions require lower margin levels.
b. If an investor fails to deposit variation margin in a timely manner, the positions may be liquidated by the carrying broker.
c. Initial margin is the amount of money that must be deposited when a futures contract is opened.
d. A margin call will be issued only if the investor’s margin account balance becomes negative.

Answer 7

d. A margin call will be issued only if the investor’s margin account balance becomes negative.

Question 8

For assets that are strongly positively correlated with interest rates, which one of the following is true?
a. Long-dated forward contracts will have higher prices than long-dated futures contracts.
b. Long-dated futures contracts will have higher prices than long-dated forward contracts.
c. Long-dated forward and long-dated futures prices are always the same.
d. The “convexity effect” can be ignored for long-dated futures contracts on the asset.

Answer 8

b. Long-dated futures contracts will have higher prices than long-dated forward contracts.

Question 9

According to put-call parity, writing a put is like
a. Buying a call, buying stock, and lending
b. Writing a call, buying stock, and borrowing
c. Writing a call, buying stock, and lending
d. Writing a call, selling stock, and borrowing

Answer 9

b. Writing a call, buying stock, and borrowing

Question 10

Which of the following is the riskiest form of speculation using option contracts?
a. Setting up a spread using call options
b. Buying put options
c. Writing naked call options
d. Writing naked put options

Answer 10

c. Writing naked call options

Question 10

A two-year European call option has a market price of $50 with a strike price of $140. The underlying stock price is $100 with a two-year annualized interest rate of 5%and a dividend yield of 2% (annualized). What is the number closest to the market price of a two-year European put struck at $140?
a. $77
b. $10
c. $90
d. $81

Answer 10

d. $81

Question 11

The price of a non-dividend paying stock is $20. A six-month European call option with a strike price of $18 sells for $4. A European put option on the same stock, with the same strike price and maturity, sells for $1.47. The continuously compounded risk-free interest rate is 6% per annum. Are these three securities (the stock and the two options) consistently priced?
a. No, there is an arbitrage opportunity worth $2.00.
b. No, there is an arbitrage opportunity worth $2.53.
c. No, there is an arbitrage opportunity worth $14.00.
d. Yes.

Answer 11

d. Yes.

Question 12

Which of the following will create a bull spread?
a. Buy a put with a strike price of X = 50, and sell a put with K = 55.
b. Buy a put with a strike price of X = 55, and sell a put with K = 50.
c. Buy a call with a premium of 5, and sell a call with a premium of 7.
d. Buy a call with a strike price of X = 50, and sell a put with K = 55.

Answer 12

a. Buy a put with a strike price of X = 50, and sell a put with K = 55.

Question 13

Consider a bullish spread option strategy of buying one call option with a $30 exercise price at a premium of $3 and writing a call option with a $40 exercise price at a premium of $1.50. If the price of the stock increases to $42 at expiration and the option is exercised on the expiration date, the net profit per share at expiration (ignoring transaction costs) will be:
a. $8.50
b. $9.00
c. $9.50
d. $12.50

Answer 13

a. $8.50

Question 14

15. Consider a bearish option strategy of buying one $50 strike put for $7, selling two $42 strike puts for $4 each, and buying one $37 put for $2. All options have the same maturity. Calculating the final profit (P/L) per share of the strategy if the underlying is trading at $33 at expiration.

a.) $1 per share
b.) $2 per share
c.) $3 per share
d.) $4 per share

Answer 14

b.) $2 per share

Question 15

16. Which of the following regarding option strategies is/are/ not correct?

I. A long strangle involves buying a call and a put with equal strike prices.
II. A short bull spread involves selling a call at lower strike price and buying another call at higher strike price.
III. Vertical spreads are formed by options with different maturities.
IV. A long butterfly spread is formed by buying two options at two different strike prices and selling another two options at the same strike price.

a. I only
b. I and III only
c. I and II only
d. III and IV only

Answer 15

b. I and III only

Question 16

Given strictly positive interest rates, the best way to close out a long American call option position early (option written on a stock that pays no dividends) would be able to

a.) Exercise the call
b.) Sell the call
c.) Deliver the call
d.) Do none of the above

Answer 16

b.) Sell the call

Question 17

Which of the following statements about options on futures is true?

a.) An American call is equal in value to a European call.
b.) An American put is equal in value to a European put.
Put-call parity holds for both
c.) American and European options.
d.) None of the above statements is true.

Answer 17

d.) None of the above statements is true.

Question 18

What is the lower pricing bound for a European call option with a strike price of 80 and one year until expiration? The price of the underlying asset is 90 and the one-year interest rate is 5% per annum. Assume continuous compounding of interest.

a.) 14.61
b.) 13.90
c.) 10.00
d.) 5.90

Answer 18

b.) 13.90

Question 19

Using the Black-Scholes model, calculate the value of a European call option given the following information: Spot rate = 100; Strike price = 110; Risk free rate = 10%; Time to expiry = 0.5 years; N(d1) = 0.457185; N(d2) = 0.374163.

a.) $10.90
b.) $9.51
c.) $6.57
d.) $4.92

Answer 19

c.) $6.57

Question 20

Which of the following is (are) true regarding the Black-Scholes (BS) model?

I. The BS model assumes that stock returns are lognormally distributed.
II. The BS model assumes that stocks are continuously traded.
III. The BS model assumes that the risk-free interest rate is constant and the same for all maturities.

I only
b. III only
c. II and III
d. I, II, and III

Answer 20

c. II and III

Question 21

In the Black-Scholes expression for a European call option, the term used to compute option probability of exercise is

a.) d1
b.) d2
c.) N(d1)
d.) N(d2)

Answer 21

d.) N(d2)