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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.

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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.

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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

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thanks a lot

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