Deck 10: Early-Exercise Put-Call Parity

Question 1

Given that call prices are convex in strike prices, the implication is that
(a) Put prices are concave in strike prices.
(b) Put prices are linear in strike prices.
(c) Put prices are convex in strike prices.
(d) Put prices may be convex or concave in strike prices.

Answer 1

C.

Question 2

Consider an American call option and an American put option, on the same dividend-paying stock, both for the same strike and maturity. Which of the following statements is most accurate?
(a) Either both options are exercised or neither one is exercised early.
(b) If the call is exercised early then the put will not be exercised early.
(c) If the put is exercised early then the call will not be exercised early.
(d) Both options may be exercised early.

Answer 2

D.

Question 3

A stock that pays no dividends has a price of $50. The rate of interest is 10%. The one-month maturity, 60-strike American put is optimally exercised. What can you infer about the insurance value of the option at the time of exercise?
(a) The minimum insurance value is $0.62
(b) The minimum insurance value is $0.50
(c) The maximum insurance value is $0.41
(d) The maximum insurance value is $10

Answer 3

C.

Question 4

If the interest rate is positive, then which of the following statements is valid for at-the-money call and put options written on the same underlying stock for the same strike and maturity?
(a) The call is worth more than the put.
(b) The call price is equal to the put price.
(c) The call price is less than the put price.
(d) More information is needed to determine the relative values of the call and put.

Question 5

An American call option on a stock that pays no dividends:
(a) May be exercised early if the stock rises sharply just before maturity.
(b) Is always exercised early when the the call is deep in-the-money, and the volatility of the stock drops from its initial level.
(c) Is not exercised early unless the growth in the stock exceeds the rate of interest.
(d) Is never exercised early.

Question 6

Consider two identical European call options on two identical stocks A and B, except that the former stock pays dividends and the latter stock does not. Which of the following statements is most valid?
(a) Call A is greater in value than call B.
(b) The time value of call A is greater than that of call B.
(c) The time value of call B is greater than that of call A.
(d) The insurance value of call B is greater than that of call A.

Question 7

When an American call has been exercised early, which of the following inferences about the stock and option is valid?
(a) The stock must pay dividends after the date of exercise.
(b) The intrinsic value of the option is positive.
(c) The time value of the option is negative.
(d) All of the above.

Question 8

The stock price is $34. The strike price of a three-month European call option is $32. If the call option is priced at $5, and the risk-free rate of interest is 2%, and the stock pays a dividend of $1 in one month, then the time value of the option is
(a) 1.16
(b) 2.16
(c) 3.16
(d) 4.16

Question 9

Consider a portfolio comprised of a short call and a short put, both options written on the same stock, same strike, and for the same maturity. Which of the following is valid?
(a) The intrinsic value of the portfolio is zero.
(b) The time value of the portfolio is zero.
(c) The insurance value of the portfolio is negative.
(d) All of the above.

Question 10

The six-month at-the-money European call option on a stock worth $25 is priced at $5. The rate of interest is 2%. The put is priced at $7. The dividend paid at the end of three months must be
(a) 1.23
(b) 2.26
(c) 3.83
(d) 4.77

Question 11

For a stock that pays no dividends, which of the following statements is most accurate?
(a) Identical American call and put options have the same price.
(b) An American call has a higher price than an identical American put if the strike price is the forward price of the stock for the maturity of the options.
(c) An American call has a lower price than an identical American put if the strike price is the forward price of the stock for the maturity of the options.
(d) Identical American call and put options have the same price if the options are struck at-the-money.

Question 12

If you are short a call and long an otherwise identical put on the same stock, where the strike price is the forward price of the stock for the same maturity as the options, you essentially have the following position:
(a) A short forward on the stock for the maturity of the option.
(b) A synthetic collar.
(c) An options position for which you pay a positive net premium up front.
(d) An options position for which you receive a net premium up front.

Question 13

A stock that pays no dividends has a price of $50. The one-month maturity, at-the-money European call and put are trading at $10 and $9.90, respectively. The one-month forward price of the stock is:
(a) 49.90
(b) 50.00
(c) 50.10
(d) 50.20

Question 14

Consider two six-month American calls at strikes 90 and 100 on a non-dividend paying stock. The risk free rate is 2%. The difference between the two call prices at any time before maturity will always be
(a) Less than $10.
(b) Equal to $10.
(c) Greater than $10.
(d) One cannot be sure of which of the preceding three choices is valid and more information may be required.

Question 15

Put-call parity is valid for
(a) Stock returns that are normally distributed, that is, stock movements are symmetric, but not otherwise.
(b) American calls and puts when the stock pays no dividends.
(c) European calls and puts when the stock pays dividends.
(d) Stocks but not for currencies.

Question 16

The stock price is $30. The strike price of a three-month European put option is $32. If the put option is priced at $5, and the risk-free rate of interest is 2%, and the stock pays no dividends, then the insurance value of the option is
(a) 1.84
(b) 2.00
(c) 3.16
(d) 4.96

Question 17

The stock price is $50. The strike price of a three-month European put option is $52. If the put option is equal in price to the call option and the stock pays no dividends, then the rate of interest for three month's maturity is
(a) 4.61%
(b) 9.23%
(c) 12.66%
(d) 15.69%

Question 18

An American put option on a stock that pays no dividends:
(a) May be exercised early if the stock drops sharply before maturity.
(b) Is always exercised early when the the put is deep in-the-money, and the volatility of the stock rises sharply from its initial level.
(c) Is not exercised early unless the growth in the stock is lower than the rate of interest.
(d) Is never exercised early.

Question 19

A stock that pays no dividends has a price of $40. If the interest rate is zero, then which if the following statements is valid?
(a) The three-month call is worth less than the two-month call.
(b) The time value of the three-month call is the same as that of the two-month call.
(c) The insurance value of the three-month call is the same as that of the two-month call.
(d) The intrinsic value of the three-month call is less than that of the two-month call.

Question 20

An American put option is sometimes exercised early because:
(a) The holder of an in-the-money option believes that the stock has bottomed out and expects the stock to rise in the future.
(b) The absolute time value of the option is larger than the insurance value.
(c) The volatility of the stock has just increased.
(d) The skewness of the stock has just increased from its initial level.