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]$37.
- Exercise Threshold: The option will be exercised if the stock price at maturity is less than \$[/tex]40.
6. Diagram of Profit Variation:
- Let's create a conceptual diagram to show how the investor's profit varies with the stock price at the maturity of the option.
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Profit ([tex]$)
|
| /
| /
| /
| /
| /
|___/____________________
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.
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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.
