
Consider the following data for a European option: Expiration = 6 months; Stock price = $80; Dividend = $0; Exercise price = $75; Call option price = $12; Risk-free rate = 3 percent per year. Using put-call parity, calculate the price of a put option having the same exercise price and expiration date.





The **put-call parity** equation establishes a relationship between the prices of European call and put options that have the same strike price and expiration date. The formula is:

\[
C + PV(X) = P + S
\]

Where:
- $ C $ = Call option price
- $ PV(X) $ = Present value of the strike price (exercise price), discounted at the risk-free rate
- $ P $ = Put option price
- $ S $ = Stock price

We are given:
- Call option price $ C = 12 $
- Stock price $ S = 80 $
- Exercise price $ X = 75 $
- Risk-free rate $ r = 3\% $ per year
- Time to expiration $ T = 6 $ months = $ 0.5 $ years

First, we calculate the **present value of the strike price** $ PV(X) $:

\[
PV(X) = X \times e^{-rT} = 75 \times e^{-0.03 \times 0.5}
\]

Using the approximation $ e^{-0.015} \approx 0.9851 $:

\[
PV(X) \approx 75 \times 0.9851 = 73.88
\]

Now, substitute the known values into the put-call parity formula:

\[
12 + 73.88 = P + 80
\]

Solve for $ P $ (put option price):

\[
P = 12 + 73.88 - 80 = 5.88
\]

Thus, the **put option price** is approximately **$5.88**.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How does the put-call parity change if the stock pays dividends?
2. How would a change in the risk-free rate affect the put option price?
3. What is the impact of a longer expiration date on put-call parity?
4. Can put-call parity be used for American options?
5. What happens to the parity relationship if the stock price drops significantly?

**Tip:** Put-call parity is crucial for spotting arbitrage opportunities in options markets!

Consider the following data for a European option: Expiration = 6 months; Stock price = $80; Dividend = $0; Exercise price = $75; Call option price = $12; Risk-free rate = 3 percent per year. Using put-call parity, calculate the price of a put option having the same exercise price and expiration date.

Learn how to calculate the price of a put option using the put-call parity theorem for a European option. This example features a stock price of $80, call option price of $12, and risk-free rate of 3% per year, with expiration in 6 months. Suitable for finance students.

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