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3.The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $26. Assume the risk-free rate is zero. An investor sells call options with a strike price of $32. What is the value of each call option?

A.$1.6

B.$2.0

C.$2.4

D.$3.0

A.$1.6

B.$2.0

C.$2.4

D.$3.0

Answer: A

The formula for the risk-neutral probability of an up movement is

In this case u=36/30 or 1.2 and d=26/30 =0.8667. Also r=0 and T=0.5. The formula gives

p=(1-0.8667/(1.2-0.8667) =0.4.

The payoff from the call option is $4 if there is an up movement and $0 if there is a down movement. The value of the option is therefore 0.4×4 +0.6×0 = $1.6. (We do not do any discounting because the interest rate is zero.)

The formula for the risk-neutral probability of an up movement is

In this case u=36/30 or 1.2 and d=26/30 =0.8667. Also r=0 and T=0.5. The formula gives

p=(1-0.8667/(1.2-0.8667) =0.4.

The payoff from the call option is $4 if there is an up movement and $0 if there is a down movement. The value of the option is therefore 0.4×4 +0.6×0 = $1.6. (We do not do any discounting because the interest rate is zero.)

Flashcard info:

Author: CoboCards-User

Main topic: Finance & Investment

Topic: Derivatives

Published: 27.10.2015