Grok’s Definition of Theta Value

Thank you for clarifying that the option is a short put (i.e., you’ve sold a put option). Let’s rework the analysis with the updated information, focusing on the theta decay over one day, given the provided details:

• Current date and time: Wednesday, June 11, 2025, 6:02 AM CST.
• Option expiration: Friday, June 13, 2025 (3 days until expiration, assuming the market closes Friday afternoon).
• Option details:
  • Type: Short put (you sold the put, so you receive the premium and benefit from time decay).
  • Current option price: $1.15 per share (the market price of the put option).
  • Theta: 0.37 (indicating the put option loses $0.37 per share per day due to time decay).
  • Delta: 0.30 (for a put, delta is negative, so approximately -0.30, meaning the put’s price decreases by $0.30 for every $1 increase in the stock price, or increases by $0.30 for every $1 decrease).
  • Strike price: $200.
  • Underlying stock price: $202.50.
  • Expected stock price: Stays above $202.
• Objective: Calculate the value decay of the put option over one day due to theta, assuming the stock price remains at $202.50.

Step 1: Understanding a Short Put and Theta

• Short put position: As the seller of a put option, you collected the premium ($1.15 per share, or $115 per contract). Your profit increases as the put’s value decreases (due to time decay or a rising stock price), but you face the risk of the stock dropping below the strike price.
• Theta (0.37): For a put option, a theta of 0.37 means the option’s value decreases by $0.37 per share per day, assuming the stock price and other factors (e.g., volatility) remain constant. As the seller, this decay benefits you, as the put’s value drops, reducing your potential obligation to buy the stock (or allowing you to buy back the put at a lower price).
• Per contract: Since one contract covers 100 shares, the daily theta decay is $0.37 × 100 = $37 per contract.

Step 2: Calculating Value Decay Over One Day

• Time frame: From Wednesday morning to Wednesday evening (one trading day).
• Current put option value: $1.15 per share ($115 per contract).
• Theta decay: The put option loses $0.37 per share over one day.
• New option value (assuming stock price stays at $202.50):
  • $1.15 – $0.37 = $0.78 per share.
  • Per contract: $0.78 × 100 = $78 per contract.
• Impact on short position: As the seller, the put’s value dropping from $1.15 to $0.78 means your potential buyback cost decreases, or your unrealized profit increases by $0.37 per share ($37 per contract) over the day.

Step 3: Context of the Put Option

• Moneyness: The put has a strike price of $200, and the stock is at $202.50, so it’s out-of-the-money (OTM) (since the stock price is above the strike). OTM puts have no intrinsic value, only time value.
• Intrinsic and time value:
  • Intrinsic value: $0 (since the stock price $202.50 > strike $200, the put has no intrinsic value).
  • Time value: The entire option price ($1.15) is time value, which is subject to theta decay.
• Theta behavior: With only a few days until expiration, theta decay is significant for OTM puts, as they lose time value rapidly. The theta of 0.37 is reasonable for an OTM put close to expiration, especially if implied volatility is moderate.

Step 4: Impact of Stock Price Staying Above $202

• Expectation: The stock price is expected to stay above $202, keeping the put OTM.
• Delta (-0.30): For a put, delta is negative, meaning the put’s price decreases as the stock price increases. If the stock price stays exactly at $202.50, delta doesn’t affect the price change due to theta. However, if the stock moves slightly:
  • Stock rises to $203: Put price decreases by -(-0.30) × ($203 – $202.50) = -$0.15.
  • Stock drops to $202: Put price increases by -(-0.30) × ($202 – $202.50) = +$0.15.
• Since the stock is expected to stay above $202, it remains OTM, and the primary impact on the put’s value is theta decay, with minimal delta-driven changes if the price stays near $202.50.

Step 5: Profit for Short Put Seller

• As the seller, you initially collected $1.15 per share ($115 per contract).
• After one day, the put’s value drops to $0.78 per share ($78 per contract) due to theta decay.
• Unrealized profit: If you were to buy back the put to close the position, you’d pay $0.78 per share instead of the $1.15 you received, netting:
  • $1.15 – $0.78 = $0.37 per share or $37 per contract.
• If you hold until expiration and the stock stays above $200, the put expires worthless, and your profit is the full premium ($115 per contract).

Step 6: Considerations

• Accelerating theta: With only 2 days until expiration, theta may increase slightly on Thursday, causing faster decay as expiration approaches, especially if the stock remains OTM.
• Volatility risk: Theta assumes constant implied volatility. If volatility spikes (e.g., due to market events), the put’s price could increase, offsetting some theta decay. If volatility drops, decay could accelerate.
• Stock price risk: If the stock drops toward or below $200, the put could become in-the-money, increasing its value and creating a loss for your short position. However, the expectation of the stock staying above $202 reduces this risk.
• Trading hours: Since it’s Tuesday evening, the next trading day (Wednesday) is the focus. Theta decay occurs continuously, but market pricing updates during trading hours, so the $0.37 decay is an estimate for the full day.

Final Answer

For a short put with a theta of 0.37, if the stock price remains at $202.50 over one day (Tuesday evening to Wednesday evening), the put option will lose $0.37 per share in value due to time decay, reducing its value from $1.15 to $0.78 per share (or $78 per contract). As the seller, you benefit from this decay, gaining an unrealized profit of $37 per contract over the day. If you have additional details (e.g., implied volatility or exact stock price expectations), I can refine the analysis further!