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Question 20.A.2: Valuing a Put Option PROBLEM: In Learning by Doing Applicati...

Valuing a Put Option
PROBLEM: In Learning by Doing Application 20.1, we found that a call option on a share of Grote Agricultural Company stock is worth $8.77 when the stock price is $35, the exercise price is $30, the risk-free rate is 4 percent, and the time to maturity is 1 year. What is the value of a put option on a share of this stock if the exercise price and all other variables have the same values?
APPROACH: Use the put-call parity relation, Equation 20.1, to calculate the value of a put option.

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The value of the put option is as follows:

\begin{matrix} P &=& C+Xe^{-rt}-V &&&&& 20.1 \\ &=& \$8.77+\$30e^{-(0.04)(1)}-\$35 \\ &=& \$8.77+\$28.82-\$35 \\ &=& \$2.59 \end{matrix}

Note that the value of the put option is less than the value of the call option in this example. This is because the current price of the stock is above the exercise price.

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