Evaluate financial derivatives

1. Option Details

• Type of Option: Call Option
• Underlying Asset: Tesla Inc. (TSLA) Stock
• Strike Price: $700
• Expiration Date: 3 months from the current date
• Premium Paid: $30 per share
• Current Stock Price: $650

2. Potential Outcomes

A. Profitable Outcome (Stock Price Above Strike Price at Expiration)

If Tesla’s stock price rises above the strike price of $700 before the option’s expiration date, the call option holder stands to benefit.

• Break-even Point: The break-even price is calculated as the strike price plus the premium paid.

  $$\text{Break-even}=700+30=730$$Therefore, Tesla’s stock price would need to rise above $730 for the option to be profitable. At any stock price above $730, the holder would start making a profit.

• Profit Calculation:
  For instance, if Tesla’s stock rises to $750:
  • The intrinsic value of the option is $750 – $700 = $50.
  • The total profit would be $50 (intrinsic value) – $30 (premium paid) = $20 per share.
• Risk/Reward:
  • The maximum profit potential is theoretically unlimited, as Tesla’s stock could continue to rise.
  • The maximum loss is limited to the premium paid ($30 per share), which is the cost of the option.

B. Unprofitable Outcome (Stock Price Below Strike Price at Expiration)

If Tesla’s stock price does not rise above the strike price, the call option will expire worthless.

• Expiration Worthless:
  If Tesla’s stock price remains at or below $700, the option holder will not exercise the option, as buying at the market price would be more advantageous.
  • In this case, the holder loses the premium paid ($30 per share).
  • For example, if the stock price remains at $650 or drops, the option becomes worthless, and the entire premium is lost.

C. Break-even Outcome

• If Tesla’s stock price rises to exactly $730 at expiration, the holder would neither gain nor lose money.
  • The value of the option would be $30 (intrinsic value) but equal to the premium paid, resulting in no profit or loss.

3. Sensitivity Analysis and Key Risks

• Implied Volatility:
  Implied volatility has a significant impact on the option’s premium. If the market anticipates greater volatility in Tesla’s stock (due to earnings announcements, market events, etc.), the premium may increase. A higher implied volatility increases the cost of options but also increases the potential for significant price movement, which could be beneficial for the option holder.
• Time Decay (Theta):
  As the expiration date approaches, the time value of the option declines. This phenomenon, known as time decay, erodes the premium paid for the option. If the stock price does not rise significantly before expiration, the holder could lose value due to time decay, even if the stock price remains steady.
• Market Conditions:
  Broader market conditions, such as interest rates, economic indicators, and market sentiment, can also impact the stock price of Tesla. A bearish market could lead to a decrease in Tesla’s stock price, making the call option unprofitable.

4. Conclusion and Key Insights

• Upside Potential: The call option offers significant upside potential, with the possibility of unlimited profit if Tesla’s stock price rises well above $700.
• Downside Risk: The risk is limited to the premium paid ($30 per share), which is the maximum loss if the stock price remains below the strike price at expiration.
• Volatility Considerations: Implied volatility plays a crucial role in determining the option’s cost and potential profitability. Higher volatility could lead to higher premiums, but it also increases the chance of substantial price movements in Tesla’s stock.
• Time Sensitivity: The option’s value erodes as time passes, and the holder needs to consider whether there is enough time for the stock price to reach a profitable level.