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24 April, 17:32

The current price of a stock is $50, the annual risk-free rate is 6%, and a 1-year call option with a strike price of $55 sells for $7.20. What is the value of a put option, assuming the same strike price and expiration date as for the call option? Select one: a. $7.33 b. $7.71 c. $8.12 d. $8.55 e. $9.00

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  1. 24 April, 21:26
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    The value of the put option is;

    e. $9.00

    Explanation:

    To determine the value of the put option can be expressed as;

    C (t) - P (t) = S (t) - K. e^ (-rt)

    where;

    C (t) = value of the call at time t

    P (t) = value of the put at time t

    S (t) = current price of the stock

    K=strike price

    r=annual risk free rate

    t=duration of call option

    In our case;

    C (t) = $7.2

    P (t) = unknown

    S (t) = $50

    K=$55

    r=6%=6/100=0.06

    t=1 year

    replacing;

    7.2-P=50-55*e^ (-0.06*1)

    7.2-P=50 - (55*0.942)

    7.2-P=50-51.797

    P=51.797+7.2-50

    P=$8.997 rounded off to 2 decimal places=$9.00
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