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Sagot :
To determine the circumstances under which the investor makes a profit and when the option will be exercised, follow the detailed step-by-step solution:
1. Initial Conditions:
- The cost of the put option (premium) = \[tex]$3 - Current stock price = \$[/tex]42
- Strike price of the put option = \[tex]$40 2. Profit Calculation: - For the investor to make a profit from buying the put option, the final stock price at maturity must be less than the strike price by more than the cost of the option. - Therefore, the investor makes a profit if the final stock price is less than \( \text{strike price} - \text{option cost} \). 3. Determining the Profit Threshold: - Strike price = \$[/tex]40
- Option cost = \[tex]$3 - Profit threshold = \$[/tex]40 - \[tex]$3 = \$[/tex]37
So, the investor makes a profit if the stock price at expiration is less than \[tex]$37. 4. Exercise Condition for the Option: - The put option will be exercised if the stock price at option expiry is below the strike price. - Therefore, the option will be exercised if the stock price is below \$[/tex]40.
5. Summary of Conditions:
- Profit Threshold: The investor makes a profit if the stock price at maturity is less than \[tex]$37. - Exercise Threshold: The option will be exercised if the stock price at maturity is less than \$[/tex]40.
6. Diagram of Profit Variation:
- Let's create a conceptual diagram to show how the investor's profit varies with the stock price at the maturity of the option.
```
Profit ([tex]$) | | / | / | / | / | / |___/____________________ 37 40 Stock Price ($[/tex])
- The y-axis represents the investor's profit.
- The x-axis represents the stock price at maturity.
- The profit threshold is at \[tex]$37, below which the investor makes a profit. - The exercise threshold is at \$[/tex]40, below which the option is exercised.
```
In conclusion, the investor will make a profit if the stock price at maturity is less than \[tex]$37, and the option will be exercised if the stock price at maturity is less than \$[/tex]40.
1. Initial Conditions:
- The cost of the put option (premium) = \[tex]$3 - Current stock price = \$[/tex]42
- Strike price of the put option = \[tex]$40 2. Profit Calculation: - For the investor to make a profit from buying the put option, the final stock price at maturity must be less than the strike price by more than the cost of the option. - Therefore, the investor makes a profit if the final stock price is less than \( \text{strike price} - \text{option cost} \). 3. Determining the Profit Threshold: - Strike price = \$[/tex]40
- Option cost = \[tex]$3 - Profit threshold = \$[/tex]40 - \[tex]$3 = \$[/tex]37
So, the investor makes a profit if the stock price at expiration is less than \[tex]$37. 4. Exercise Condition for the Option: - The put option will be exercised if the stock price at option expiry is below the strike price. - Therefore, the option will be exercised if the stock price is below \$[/tex]40.
5. Summary of Conditions:
- Profit Threshold: The investor makes a profit if the stock price at maturity is less than \[tex]$37. - Exercise Threshold: The option will be exercised if the stock price at maturity is less than \$[/tex]40.
6. Diagram of Profit Variation:
- Let's create a conceptual diagram to show how the investor's profit varies with the stock price at the maturity of the option.
```
Profit ([tex]$) | | / | / | / | / | / |___/____________________ 37 40 Stock Price ($[/tex])
- The y-axis represents the investor's profit.
- The x-axis represents the stock price at maturity.
- The profit threshold is at \[tex]$37, below which the investor makes a profit. - The exercise threshold is at \$[/tex]40, below which the option is exercised.
```
In conclusion, the investor will make a profit if the stock price at maturity is less than \[tex]$37, and the option will be exercised if the stock price at maturity is less than \$[/tex]40.
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