Probability of Touch: What 21-Day Management Changes

Probability of Touch Across Different Deltas: A Detailed Analysis

Key Concepts:

• Probability of Touch (POT): The likelihood an option’s strike price will be reached by the underlying asset before expiration.
• Delta: A measure of an option’s price sensitivity to a $1 change in the underlying asset’s price.
• 21-Day Management: A trading strategy involving actively managing options positions by rolling or closing them around the 21-day mark before expiration.
• Volatility Contraction: The decrease in implied volatility as an option approaches expiration.
• Put Skew: The tendency for put options to be more expensive (higher implied volatility) than call options with the same strike price and expiration date, particularly in index options like SPY.
• Call Skew: The opposite of put skew, where call options are more expensive than put options.

---

I. Introduction & Theoretical vs. Realized Probability of Touch

The discussion centers around the probability of touch (POT) for short option strategies, specifically focusing on how it differs from theoretical calculations and how active management impacts it. Traditionally, traders estimate POT by doubling the delta of the option. However, prior research indicates that realized POT – the actual frequency of strike price touches – is significantly lower than this theoretical 2x delta estimate. The core argument is that actively managing positions, particularly by addressing them around the 21-day mark before expiration, substantially reduces the realized POT.

II. The Impact of 21-Day Management on Probability of Touch

A key point emphasized is that managing trades at the 21-day mark compresses profit and loss (P&L) volatility, directly leading to a lower probability of touch. This isn’t necessarily negative; it increases win rate and reduces overall risk. Rolling or closing winning trades at this point demonstrably reduces the frequency with which trades are “tested” (i.e., the underlying asset approaches the strike price).

The time value inherent in options with 21 days until expiration provides “wiggle room,” meaning a touch doesn’t immediately translate to a full loss. The POT doesn’t dictate whether a trade is good or bad. An example is given of short puts in Microsoft that are “in the money” (scratch) despite the stock being significantly lower than the initial trade price (400), illustrating how volatility contraction and time decay can offset unfavorable price movement.

III. Delta Change & Expected Delta Ranges

The analysis delves into the expected delta change when managing at 21 days. The discussion highlights that selling a 20 delta call can realistically lead to a 35 delta position as the stock price rises, and similarly, a 20 delta put can move to a 25 delta position. This underscores the need for traders to anticipate delta adjustments and maintain sufficient “wiggle room” in their positions. This concept ties into the “confirm and send” methodology, acknowledging that deltas won’t shift dramatically overnight but will fluctuate within a predictable range.

A statistical observation is made: a 30 delta put has approximately a 60% chance of being touched. While seemingly high, this doesn’t guarantee a loss, merely a possibility. As time progresses, this probability decreases.

IV. Empirical Analysis of SPY Options (10-45 Delta)

A study was conducted on SPY (S&P 500 ETF) out-of-the-money puts and calls with deltas ranging from 10 to 45. All options were initiated with 45 days to expiration and exited at 21 days. The results confirmed that the realized POT at expiration is lower than the theoretical 2x delta. However, managing positions at 21 days significantly improved these results across all deltas.

Specifically, the average realized POT when managed at 21 days was approximately 0.8x the delta. This means the theoretical POT is often overstated, aligning with the understanding that volatility is frequently overstated. For example, a 20 delta option might have a realized POT of only 10% when managed at 21 days, a substantial reduction from the theoretical 40%.

V. Delta and Probability of Touch: The Impact of At-the-Money vs. Out-of-the-Money Options

The analysis emphasizes that focusing solely on delta can provide an incomplete picture. The gap between theoretical and realized POT narrows as the delta increases (i.e., as options get closer to being at-the-money). This makes intuitive sense, as at-the-money options are more likely to be tested. Selling straddles or tight strangles (at-the-money options) should naturally result in more frequent testing.

VI. Call vs. Put Probability of Touch in SPY

The study found that realized probabilities of touch are higher for calls than for puts in SPY. This is attributed to the consistent upward drift observed in the market and the presence of put skew in SPY options. Put skew means put options are relatively more expensive than call options, reflecting a market expectation of potential downside risk.

However, the 21-day management strategy effectively aligned the probability ratios for puts and calls, bringing them closer to parity.

VII. Considerations for Single Stocks vs. SPY

The discussion acknowledges that these findings are specific to SPY and may differ for individual stocks like Apple, Microsoft, or Tesla. These stocks often exhibit unique dynamics, including binary events (e.g., earnings announcements) and different volatility characteristics. Tesla, for example, may exhibit greater volatility overstatement than SPY, potentially altering the relationship between implied and realized POT. Furthermore, Tesla may exhibit call skew, unlike SPY’s put skew.

VIII. Key Takeaways & Conclusion

The primary takeaways are:

• Puts in SPY exhibit a lower realized POT than calls across all deltas.
• Actively managing positions at 21 days significantly reduces the likelihood of strike price touches.
• The realized POT for puts is generally slightly below their corresponding delta, while calls align more closely with their delta.
• 21-day management minimizes the disparity between put and call POT.

The overall conclusion is that incorporating a 21-day management strategy into short option trades can substantially reduce P&L volatility and improve risk management, even though the initial probability of touch may appear high. The emphasis is on proactive management rather than relying solely on theoretical calculations.