A put option on a stock with a current price of $33 has an exercise price of $35. The price of the corresponding call option is $2.25. According to put-call parity, if the effective annual risk-free rate of interest is 4% and there are three months until expiration.



To determine the price of the put option using put-call parity, we can use the following formula:

\[ P + S = C + K e^{-rt} \]

where:
- $ P $ is the price of the put option
- $ S $ is the current stock price
- $ C $ is the price of the call option
- $ K $ is the exercise price
- $ r $ is the risk-free interest rate
- $ t $ is the time to expiration in years

Given the dataTo determine the price of the put option using put-call parity, we can use the following formula:

\[ P + S = C + K e^{-rt} \]

where:
- $ P $ is the price of the put option
- $ S $ is the current stock price
- $ C $ is the price of the call option
- $ K $ is the exercise price
- $ r $ is the risk-free interest rate
- $ t $ is the time to expiration in years

Given the 
- $ S = \$33 $
- $ K = \$35 $
- $ C = \$2.25 $
- $ r = 4\% $ or $ 0.04 $
- $ t = \frac{3}{12} $ or $ 0.25 $ years

First, we calculate $ K e^{-rt} $:

\[ K e^{-rt} = 35 e^{-0.04 \times 0.25} \]

\[ K e^{-rt} = 35 e^{-0.01} \]

\[ K e^{-rt} \approx 35 \times 0.99005 \]

\[ K e^{-rt} \approx 34.65175 \]

Now, we apply the put-call parity formula:

\[ P + 33 = 2.25 + 34.65175 \]

\[ P + 33 = 36.90175 \]

\[ P = 36.90175 - 33 \]

\[ P = 3.90175 \]

So, the price of the put option is approximately $ \$3.90 $.

Would you like more details or have any questions about this solution? 

Here are 5 related questions to expand on this information:

1. How does the time to expiration affect the price of a put option according to put-call parity?
2. What would happen to the price of the put option if the risk-free rate increased?
3. How does volatility impact the prices of call and put options?
4. Can put-call parity be used for options on other assets besides stocks? If so, how?
5. What are the limitations of using put-call parity in real-world trading?

**Tip:** Understanding the impact of different variables on option pricing can help you make more informed trading decisions. Always consider factors like interest rates, time to expiration, and volatility.

A put option on a stock with a current price of $33 has an exercise price of $35. The price of the corresponding call option is $2.25. According to put-call parity, if the effective annual risk-free rate of interest is 4% and there are three months until expiration, what is the price of the put option?

Learn how to calculate the price of a put option using the put-call parity formula. In this example, the stock price is $33, the call option price is $2.25, the exercise price is $35, and the risk-free rate is 4% with three months to expiration. Detailed steps included.

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