HOLLOW POINT TRADING
What is Delta?
Delta is the cornerstone of options trading—arguably the most important Greek you'll ever learn. It represents the expected change in an option's price for a $1 move in the underlying stock.
A delta of 0.50 means the option will gain approximately $0.50 for every $1 the stock rises (for calls) or falls (for puts). Think of delta as your option's sensitivity to price movement.
The sign tells you the direction of your exposure: positive delta profits when the underlying rises, while negative delta profits when it falls.
Delta Values by Moneyness
Understanding how delta changes based on where your strike price sits relative to the stock price is crucial for strike selection.
| Option Type | Deep ITM | ATM | Deep OTM |
|---|---|---|---|
| Calls | 0.80 to 1.00 | ~0.50 | 0.05 to 0.20 |
| Puts | -0.80 to -1.00 | ~-0.50 | -0.05 to -0.20 |
🎯 Delta Relationships
- ATM options have approximately 0.50 delta (calls) or -0.50 (puts)
- As options go deeper ITM, delta approaches 1.00 (or -1.00)
- As options go deeper OTM, delta approaches 0
- Call delta + |put delta| ≈ 1.00 at the same strike
- Delta changes faster near ATM and near expiration
Delta as Probability Proxy
The 30 Delta Rule
Delta approximates the probability that an option will expire in the money. A call with 0.30 delta has roughly a 30% chance of expiring ITM. A put with -0.70 delta has roughly a 70% chance of expiring ITM.
⚠️ Important Caveat
This is an approximation, not an exact probability. It's derived from risk-neutral pricing assumptions, not real-world probabilities. But it's an incredibly useful mental model for thinking about option positioning and strike selection.
Delta as Share Equivalency
Directional Exposure
Delta tells you how many shares of stock your option position is equivalent to:
Example: You own 10 call options with 0.60 delta.
Your delta exposure = 10 × 100 × 0.60 = 600 shares equivalent
If the stock rises $1, your position gains approximately $600 (10 contracts × 100 shares × $0.60).
Portfolio Delta
Professional traders sum the deltas across all positions to understand their total directional exposure:
| Position | Delta Calculation | Net Delta |
|---|---|---|
| Long 5 calls (0.40 delta) | 5 × 100 × 0.40 | +200 |
| Short 3 puts (-0.30 delta) | -3 × 100 × (-0.30) | +90 |
| Total Portfolio Delta | +290 |
This portfolio is equivalent to being long 290 shares of stock.
How Delta Changes
Changes with Price (Gamma)
As the underlying moves, delta changes. This rate of change is measured by Gamma (another Greek). When a stock rallies, call deltas increase and put deltas decrease.
This acceleration is why options can produce explosive returns on big moves—your position gets more sensitive as it moves in your favor.
Changes with Time
As expiration approaches, delta becomes more binary. ITM options move toward 1.00 delta, OTM options move toward 0.
ATM options experience the most dramatic changes near expiration—their delta can swing wildly based on small price movements.
Changes with Volatility
Higher implied volatility expands the range of possible outcomes, which changes delta distribution:
- • OTM options get higher deltas — more probability of expiring ITM
- • Deep ITM options get lower deltas — more uncertainty
Trading Applications
💼 Using Delta in Practice
- Strike selection: Choose delta based on your directional conviction
- Position sizing: Use delta to normalize position sizes across different strategies
- Hedging: Offset delta exposure with stock or other options
- Probability: Estimate likelihood of profit at expiration
- Risk assessment: Calculate portfolio's total directional exposure
Common Delta Strategies
| Delta Range | Strategy Type | Best For |
|---|---|---|
| 0.70+ (High) | Stock replacement, conviction plays | Strong directional view, lower cost than stock |
| 0.40-0.60 (Medium) | Balanced risk/reward, ATM options | Moderate directional view, good leverage |
| 0.10-0.30 (Low) | Lottery tickets, hedges, premium selling | Cheap exposure, defined risk strategies |
Delta-Neutral Trading
Some strategies aim for zero net delta—called "delta neutral." This removes directional exposure and profits from other factors like volatility or time decay.
📊 Delta Neutral Examples
• Iron condors
• Straddles (if hedged)
• Market making
• Volatility trading
⚡ Maintaining Neutral
As the underlying moves, delta changes. Traders must continuously rebalance (hedge) to stay neutral—this is called "delta hedging."
Delta is Your Directional Compass
Understanding delta is fundamental to options trading. It tells you how much you'll make or lose per dollar move, estimates probability of profit, and helps you compare positions across different strategies.
Master delta first—the other Greeks build on this foundation.