Deck 9: Parity and Other Option Relationships

Question 1

The spot exchange rate in dollars per euro is $1.31. Dollar denominated interest rates are 4.0% and euro denominated interest rates are 3.0%. What is the difference in call and put option prices given a 2-year option and a $1.34 strike price?

A) -$0.1041
B) -$0.0652
C) $0.1233
D) $0.1546

Answer 1

A

Question 2

Rankin Corp. common stock is priced at $74.20 per share. The company just paid its $1.10 quarterly dividend. Interest rates are 6.0%. A $70.00 strike European call, maturing in 6 months, sells for $6.50. How much arbitrage profit/loss is made by shorting the European call, which is priced at $2.50?

A) $0.12 loss
B) $0.12 gain
C) $0.36 loss
D) $0.36 gain

Answer 2

B

Question 3

Put options with strikes of $70, $75, and $85 have option premiums of $6.00, $8.50, and $11.00, respectively. Using strike price convexity, which option premium, if any, is not possible?

A) P (70)
B) P (75)
C) P (85)
D) All are possible.

Answer 3

B

Question 4

A company is forecasted to pay dividends of $0.90, $1.20, and $1.45 in 3, 6, and 9 months, respectively. Given interest rates of 5.5%, how much dollar impact will dividends have on option prices? (Assume a 9-month option.)

A) $3.45
B) $3.90
C) $4.22
D) $4.50

Question 5

Which of the following options will NOT be exercised early?

A) Put on a dividend paying stock
B) Call on a dividend paying stock
C) Put on a non-dividend paying stock
D) Call on a non-dividend paying stock

Question 6

Call options with strikes of $30, $35, and $40 have option premiums of $1.50, $1.70, and $2.00, respectively. Using strike price convexity, which option premium, if any, is not possible?

A) C (30)
B) C (35)
C) C (40)
D) All are possible.

Question 7

How is the price of a European call option impacted by a $2.00 dividend being paid immediately before expiration of a 6 month option if interest rates are 5.0%?

A) Decreased by $1.95
B) Decreased by $2.00
C) Increased by $1.95
D) Increased by $2.00

Question 8

The price of a non-dividend paying stock is $55 per share. A 6-month, at the money call option is trading for $1.89. If the interest rate is 6.5%, what is the likely price of a European put at the same strike and expiration?

A) $0.05
B) $0.13
C) $0.56
D) $0.88

Question 9

The price of a stock is $52.00. Lacking additional information, what is your forecasted difference between a put option and a call option on this stock? Assume 38 days to expiration and 6.0% interest.

A) $0.16
B) $0.32
C) $0.48
D) $0.64

Question 10

Consider the case of an exchange option in which the underlying stock is Eli Lilly and Company with a current price of $56.00 per share. The strike asset is Merck, with a per share price of $52.00. Interest rates are 5% and the 3-month call option is trading for $7.00. What is the price of the put?

A) $3.00
B) $4.00
C) $7.00
D) $11.00

Question 11

Jafee Corp. common stock is priced at $36.50 per share. The company just paid its $0.50 quarterly dividend. Interest rates are 6.0%. A $35.00 strike European call, maturing in 6 months, sells for $3.20. What is the price of a 6-month, $35.00 strike put option?

A) $1.20
B) $1.64
C) $2.04
D) $2.38

Question 12

If today is March 10th, and four options are eligible for early exercise, which ex-dividend date is most likely to produce the highest potential profit?

A) March 16
B) March 23
C) March 30
D) April 6

Question 13

The 6-month call and put premiums are $0.114 and $0.098, respectively, with a $0.94 strike. Dollar and euro interest rates are 7.0% and 6.0%, respectively. What spot exchange rate is implied by this data?

A) $0.98 dollars per euro
B) $1.02 dollars per euro
C) $1.05 dollars per euro
D) $1.09 dollars per euro

Question 14

What term is used to describe the creation of a synthetic T-bill by buying the stock, buying a put and selling a call?

A) Put-Call parity
B) Leveraged position
C) Draw strategy
D) Conversion

Question 15

An arbitrage investor shorts a stock at $76, longs a $75 strike call at $1.50, and shorts a $75 strike put at $0.80. What is the arbitrage profit on the strategy, per share?

A) $ 0.30
B) $ 0.80
C) $ 1.00
D) $ 1.50

Question 16

The spot exchange rate of dollars per euro is 0.95. Dollar and euro interest rates are 7.0% and 6.0%, respectively. The price of a $0.93 strike 6-month call option is $0.08. What is the price of the put?

A) $0.016
B) $0.032
C) $0.056
D) $0.078

Question 17

Which option has the highest probability of being exercised early?

A) Non-dividend paying European option
B) Dividend paying European option
C) Non-dividend paying American option
D) Dividend paying American option

Question 18

Jillo, Inc. stock is selling for $54.70 per share. Calls and puts with a $55 strike and 40 days until expiration are selling for $1.65 and $1.23, respectively. What potential arbitrage profit exists?

A) $0.12
B) $0.24
C) $0.36
D) $0.48

Question 19

A European call option with a strike price of $30.00 expires in 3 months. In put-call parity, what impact does the interest on the strike price have given 6.0% interest rates?

A) Causes the call price to be $0.45 lower than the put price
B) Causes the call price to be $0.90 lower than the put price
C) Causes the call price to be $0.45 higher than the put price
D) Causes the call price to be $0.90 higher than the put price

Question 20

An investor longs a $65 strike call at $1.20, and shorts a $65 strike put at $0.90. If at expiration of the options, the investor wishes to own the security, what is the net cost of the position?

A) $65.00
B) $65.30
C) $65.90
D) $66.20

Question 21

Jillo, Inc. stock is selling for $54.70 per share. Calls and puts with a $55.00 strike and 40 days until expiration are selling for $1.65 and $1.23, respectively. Draw a profit and loss graph illustrating the arbitrage.

Question 22

Explain in simple terms why a call option on a non-dividend paying stock should never be exercised early.

Question 23

The necessary condition for early exercise is that we prefer to receive something sooner rather than later. With a dividend paying call and a non-dividend paying put, what do we receive?

Question 24

Using the synthetic long stock strategy, explain the difference in call and put prices.

Question 25

All else being equal, explain why American options are at least as valuable as European options.