Deck 3: Principles of Option Pricing

Question 1

What is the lowest possible value of a European put?

A) Max(0, X - S₀)
B) X(1 + r)^-T
C) Max[0, S₀ - X(1 + r)^-T]
D) Max[0, X(1 + r)^-T - S₀)]
E) none of the above

Answer 1

D

Question 2

Suppose the stock is about to go ex-dividend in one day. The dividend will be $4.00. Which of the following calls will you consider for exercise?

A) November 115
B) November 110
C) December 115
D) all of the above
E) none of the above

Answer 2

B

Question 3

What is the time value of the November 115 put?

A) 1.75
B) 2.80
C) 1.10
D) 0.00
E) none of the above

Answer 3

C

Question 4

What is the intrinsic value of the November 105 put?

A) 0.30
B) 8.25
C) 8.50
D) 0.00
E) none of the above

Question 5

Suppose you use put-call parity to compute a European call price from the European put price, the stock price, and the risk-free rate. You find the market price of the call to be less than the price given by put-call parity. Ignoring transaction costs, what trades should you do?

A) buy the call and the risk-free bonds and sell the put and the stock
B) buy the stock and the risk-free bonds and sell the put and the call
C) buy the put and the stock and sell the risk-free bonds and the call
D) buy the put and the call and sell the risk-free bonds and the stock
E) none of the above

Question 6

What is the European lower bound of the December 105 call?

A) 9.86
B) 0.00
C) 8.25
D) 9.26
E) none of the above

Question 7

Consider a portfolio consisting of a long call with an exercise price of X, a short position in a non-dividend paying stock at an initial price of S₀, and the purchase of riskless bonds with a face value of X and maturing when the call expires. What should such a portfolio be worth?

A) C + P - X(1 + r)^-T
B) C - S₀
C) P - X
D) P + S₀ - X(1 + r)^-T
E) none of the above

Question 8

The following quotes were observed for options on a given stock on November 1 of a given year. These are American calls except where indicated. Use the information to answer questions 7 through 20.
The stock price was 113.25. The risk-free rates were 7.30 percent (November), 7.50 percent (December) and 7.62 percent (January). The times to expiration were 0.0384 (November), 0.1342 (December), and 0.211 (January). Assume no dividends unless indicated.
What is the intrinsic value of the December 115 put?

A) 1.75
B) 0.00
C) 3.90
D) 3.00
E) none of the above

Question 9

What is the time value of the November 110 call?

A) 0.00
B) 4.40
C) 1.15
D) 3.25
E) none of the above

Question 10

What is the time value of the December 105 put?

A) 1.30
B) 8.30
C) 0.00
D) 7.00
E) none of the above

Question 11

On March 2, a Treasury bill expiring on April 20 had a bid discount of 5.80, and an ask discount of 5.86. What is the best estimate of the risk-free rate as given in the text?

A) 5.86 %
B) 5.83 %
C) 6.11 %
D) 6.14 %
E) none of the above

Question 12

From American put-call parity, what are the minimum and maximum values that the sum of the stock price and December 110 put price can be?

A) 101.81 and 102.87
B) 2.50 and 113.25
C) 116.038 and 117.10
D) 7.125 and 110
E) none of the above

Question 13

Suppose you knew that the January 115 options were correctly priced but suspected that the stock was mispriced. Using put-call parity, what would you expect the stock price to be? For this problem, treat the options as if they were European.

A) 113.73
B) 123.23
C) 121.23
D) 112.77
E) none of the above

Question 14

What is the intrinsic value of the November 115 call?

A) 1.50
B) 0.00
C) 2.80
D) 1.75
E) none of the above

Question 15

If there are no dividends on a stock, which of the following statements is correct?

A) An American call will sell for more than a European call
B) A European call will sell for more than an American call
C) An American call will be immediately exercised
D) An American call and an American put will sell for the same price
E) none of the above

Question 16

What is the intrinsic value of the January 110 call?

A) 0.00
B) 8.30
C) 3.75
D) 5.00
E) none of the above

Question 17

The maximum difference between the January 105 and 110 calls is which of the following?

A) 11.50
B) 4.92
C) 5.00
D) 4.0
E) none of the above

Question 18

What is the time value of the January 115 call?

A) 5.30
B) 0.00
C) 3.50
D) 1.70
E) none of the above

Question 19

What is the European lower bound of the November 115 call?

A) 1.44
B) 0.00
C) 1.75
D) 2.06
E) none of the above

Question 20

Another expression for intrinsic value is

A) parity
B) parity value
C) exercise value
D) all of the above
E) none of the above

Question 21

Put-call parity is a relationship that can be used to provide the price of both a European put and call simultaneously.

Question 22

Which of the following statements about an American call is not true?

A) Its time value decreases as expiration approaches
B) Its maximum value is the stock price
C) It can be exercised prior to expiration
D) It pays dividends
E) none of the above

Question 23

The difference between a Treasury bill's face value and its price is called the

A) time value
B) discount
C) coupon rate
D) bid
E) none of the above

Question 24

The lower bound of a European call on a non-dividend paying stock is lower than the intrinsic value of an American call.

Question 25

Which of the following is the lowest possible value of an American call on a stock with no dividends?

A) Max(0, S₀ - X(1 + r)^-T)
B) S₀
C) Max(0, S₀ - X)
D) Max(0, S₀ (1 + r)^-T - X)
E) none of the above

Question 26

An option can be priced at less than zero because it can potentially generate a large profit for its owner.

Question 27

The effect of volatility on a call/put's price is

A) decreased price due to decreased possible losses
B) nominal volatility will not noticeably effect a call/put's price
C) increased price due to increased possible gains
D) decreased price due to increased possible losses
E) none of the above

Question 28

The difference between an American call's price and its intrinsic value is called the time value because the call can be exercised at any time.

Question 29

A situation in which early exercise of an American put can be justified is

A) bankruptcy
B) merger
C) if X exceeds S₀ by greater than any transaction costs.
D) both a and b
E) both a and b and c

Question 30

The maximum value of a call is the stock price.

Question 31

The concept of the intrinsic value does not apply to European calls prior to expiration because they cannot be exercised immediately.

Question 32

If one portfolio always provides a return at least as high as another portfolio, then that portfolio will have a price no less than that of the other portfolio.

Question 33

Holding everything else constant, call options are more expensive in periods of high interest rates.

Question 34

Given a longer-lived American call and a shorter-lived American call with the same terms, the longer-lived call must always be worth

A) at most the value of the shorter-lived call
B) at least as much as the shorter-lived call
C) exactly the same as the shorter-lived call
D) the shorter-lived call discounted to the length of the longer-lived call
E) none of the above

Question 35

The time value of an option is also referred to as the

A) synthetic value
B) strike value
C) speculative value
D) parity value
E) none of the above

Question 36

Which of the following inequalities correctly states the relationship between the difference in the prices of two European calls that differ only by exercise price

A) (X_2? - X₁)(1 + r)^-T ≥ C_e(S₀,T,X₁) - C_e(S₀,T,X₂)
B) (X_2? - X₁) ≥ C_e(S₀,T,X₂) - C_e(S₀,T,X₁)
C) (X₂ - X₁)(1 + r)^-T ≥ C_e(S₀,T,X₁) + C_e(S₀,T,X₂)
D) (X_2? - X₁) ≥ C_e(S₀,T,X₁) - C_e(S₀,T,X₂)
E) none of the above

Question 37

Which of the following is the lowest possible value of an American put on a stock with no dividends?

A) X(1 + r)^-T
B) X
C) Max(0, X(1 + r)^-T - S₀)
D) Max(0, X - S₀)
E) none of the above

Question 38

Suppose that you observe a European option on a currency with an exchange rate of S₀ and a foreign risk-free rate of $\rho$ . Which of the following inequalities correctly expresses the lower bound of the call?

A) C_e(S₀,T,X) ≥ Max[0,S₀(1 + $\rho$ )^-T + X(1 + r)^-T]
B) C_e(S₀,T,X) ≥ Max[0,S₀ - X(1 + $\rho$ )^-T]
C) C_e(S₀,T,X) ≥ Max[0,S₀(1 + $\rho$ )^-T - X]
D) C_e(S₀,T,X) ≥ Max[0,S₀(1 + $\rho$ )^-T - X(1 + r)^-T]
E) none of the above

Question 39

An American call should be exercised early when the stock price is extremely high and is expected to fall.

Question 40

An American put might be exercised early even when there are no dividends on the underlying stock.

Question 41

The price of a call option is directly related to interest rates.

Question 42

High volatility is bad for option holders because it increases the probability that the option will expire out-of-the-money.

Question 43

A stock is equivalent to a long call, short put and long risk-free bond.

Question 44

The time value of a call is greatest when the stock price is very high.

Question 45

An American call on a non-dividend paying stock will be worth more than a European call on that same stock.

Question 46

The lower bound of a European put on a non-dividend paying stock is lower than the intrinsic value of an American put.

Question 47

The lower the exercise price, the more valuable the call option.

Question 48

The gain from the early exercise of an American put is X(1 + r)^-T - S₀.

Question 49

The put-call parity rule for American options is stated as equalities.

Question 50

Even if there are no dividends on the stock, American put-call parity will not be the same as European put-call parity.

Question 51

At expiration the call price must converge to the stock price.

Question 52

Selling short a risk-free bond is equivalent to borrowing.

Question 53

The value of a European call is higher for lower strike prices.

Question 54

Holding everything else constant, a longer-term European put is always worth more than a shorter-term European put.

Question 55

Holding everything else constant, put options are more expensive in periods of high interest rates.

Question 56

The difference between two American put options with different strike prices is less than or equal to the dollar difference between the strike prices, the higher strike price minus the lower strike price.

Question 57

If an option portfolio generates a zero cash flow at expiration and a positive cash flow today, an arbitrage opportunity is available.

Question 58

The spread between the prices of two European puts, alike in all respects except exercise price, cannot exceed the difference in their exercise prices.

Question 59

Transactions to exploit pricing errors in the put-call parity relationship are called conversions and reversals.

Question 60

At expiration, the value of a European call is S_T - X.