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# Reading 71: Option Markets and Contracts-LOS k 习题精选

Session 17: Derivatives
Reading 71: Option Markets and Contracts

LOS k: Calculate and interpret the lowest prices of European and American calls and puts based on the rules for minimum values and lower bounds.

Consider a call option expiring in 60 days on a non-dividend-paying stock trading at 53 when the risk-free rate is 5%. The lower bound for a call option with an exercise price of 50 is:

 A) \$0.
 B) \$3.40.
 C) \$3.00.

53 ? 50/(1.05)60/365 = 3.40.

Consider a put option expiring in 120 days on a non-dividend-paying stock trading at 47 when the risk-free rate is 5%. What are the lower bounds for an American put and a European put with exercise prices of 50?

 American Put European Put

A)
 \$2.20 \$2.20
B)
 \$3.00 \$3.00
C)
 \$3.00 \$2.20

An American put can be exercised immediately for a \$3 gain, the European put cannot be exercised until expiration so its minimum value is 50 / (1.05)120/365 ? 47 = \$2.20.

Consider a call option expiring in 110 days on a non-dividend-paying stock trading at 27 when the risk-free rate is 6%. The lower bound for a call option with an exercise price of 25 is:

 A) \$2.44.
 B) \$2.00.
 C) \$1.97.

27 - 25/(1.06)110/365 = 2.435.

A non-dividend-paying stock is trading at 62 when the risk-free rate is 5%. The minimum values for 6-month American and European calls on the stock with a strike price of 50 are closest to:

 American call European call

A)
 \$13.20 \$13.20
B)
 \$13.20 \$11.75
C)
 \$11.75 \$11.75

For both the American and European call, the minimum value is the greater of zero or [S ? X / (1 + RFR)T-t] , where S = the price of the underlying stock, X = the exercise price of the option, RFR = the risk-free rate, and (T-t) = time to expiration in years.
62 ? (50 / 1.050.5) = \$13.21

 thanks a lot
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