Options Greeks
What Are the Greeks
The Greeks are metrics that measure how sensitive an option's price is to changes in various factors. They are named after Greek letters.
Option prices change based on multiple factors including the underlying asset's price, time, and volatility. Understanding the Greeks allows you to predict these changes, manage risk, and execute more sophisticated strategies.
Delta (Δ)
Definition
How much the option price changes when the underlying asset's price changes by $1.
Delta = Option price change / Underlying asset price change
Range
| Option Type | Delta Range |
|---|---|
| Call Option | 0 to +1 |
| Put Option | -1 to 0 |
Delta and Option Status
| Status | Call Delta | Put Delta | Meaning |
|---|---|---|---|
| Deep In-the-money (Deep ITM) | ~0.9-1.0 | ~-0.9 to -1.0 | Moves nearly 1:1 with spot |
| At-the-money (ATM) | ~0.5 | ~-0.5 | Moves about half as much as spot |
| Deep Out-of-the-money (Deep OTM) | ~0-0.1 | ~-0.1 to 0 | Barely responds to spot movement |
Practical Interpretation
BTC at $100,000, call option delta of 0.5:
- BTC rises $1,000 → option price rises approximately $500
- BTC falls $1,000 → option price falls approximately $500
Delta is also sometimes interpreted as a rough estimate of "probability of profit." A call option with delta 0.3 has approximately a 30% probability of expiring in-the-money. This isn't precise but serves as a useful intuitive reference.
Delta Neutral
A strategy of making the portfolio's total delta zero. Used to pursue profits from volatility regardless of price direction, or to hedge positions.
Gamma (Γ)
Definition
How much delta changes when the underlying asset's price changes by $1. It is the rate of change of delta.
Gamma = Delta change / Underlying asset price change
Characteristics
- Gamma is highest at ATM: Small price changes cause large delta shifts
- Gamma increases as expiration approaches: ATM options near expiry have extremely high gamma
- Gamma is lower for ITM/OTM: Delta is already at extreme values, so changes are minimal
Practical Interpretation
Options with high gamma have delta that changes rapidly with price movement. This is a double-edged sword:
Option buyer perspective: High gamma means when price moves favorably, delta increases rapidly, accelerating profits. This is a "long gamma" position.
Option seller perspective: High gamma means when price moves unfavorably, losses accelerate. This is a "short gamma" position. ATM short positions near expiry have maximum gamma risk.
Theta (Θ)
Definition
How much the option price decreases as one day passes. It is the rate of time value decay.
Theta = Option price change / Time change (1 day)
Characteristics
- Theta is always negative (from buyer's perspective): Options lose value as time passes
- Theta is highest at ATM: The most time value exists here, so decay is fastest
- Theta increases rapidly as expiration approaches: Non-linear decay
Time Value Decay Pattern
Option time value decays acceleratingly as expiration approaches.
- 90 days before expiry: About 0.5% of total time value decays daily
- 30 days before expiry: About 1.5% decays daily
- 7 days before expiry: About 5% decays daily
- 1 day before expiry: About 30% decays daily
These figures are approximate references based on ATM options.
Practical Interpretation
Option buyers: Theta is the enemy. Position value erodes as time passes. If price doesn't move favorably quickly after buying, time decay causes losses.
Option sellers: Theta is an ally. The value of sold options erodes over time, becoming profit. However, gamma risk coexists.
Vega (ν)
Definition
How much the option price changes when implied volatility (IV) changes by 1 percentage point.
Vega = Option price change / Implied volatility change
Implied Volatility (IV)
IV is the magnitude of future price movement expected by the options market. Higher IV means the market expects larger moves, and option prices become more expensive.
| IV Level | BTC Reference | Meaning |
|---|---|---|
| Below 30% | Low | Market expects stability. Options cheap |
| 30-60% | Normal | Typical volatility expectation |
| 60-100% | High | Large moves expected. Pre-event |
| Above 100% | Extreme | Panic or extreme uncertainty |
IV Crush (Volatility Collapse)
A phenomenon where IV spikes before important events (FOMC, ETF decisions, etc.) then plunges afterward. If you buy expensive options before an event, you can lose money even if price direction is correct due to post-event IV collapse.
Practical Interpretation
Long vega (option buying): Profit when IV rises. Buy options when expecting volatility to increase.
Short vega (option selling): Profit when IV falls. Sell options when expecting volatility to decrease. Selling strategy when IV is excessively high just before events.
Relationships Between Greeks
Delta-Gamma Relationship
High gamma means delta changes rapidly. Since gamma is highest near ATM, delta changes are also greatest there.
Theta-Gamma Tradeoff
Positions with high gamma also have high theta. This is the fundamental "gamma vs theta" tradeoff.
- Option buying: Long gamma (advantage) + theta burden (disadvantage)
- Option selling: Short gamma (disadvantage) + theta income (advantage)
Vega and Time
Options with longer expiration have higher vega. Long-dated options are sensitive to IV changes, while short-dated options are more sensitive to gamma/theta.
Greeks Summary Table
| Greek | Measures | For Buyers | For Sellers | Maximum At |
|---|---|---|---|---|
| Delta | Price sensitivity | Directional exposure | Inverse directional exposure | Deep ITM |
| Gamma | Rate of delta change | Advantage (accelerates profit) | Disadvantage (accelerates loss) | ATM, short-dated |
| Theta | Time value decay | Disadvantage (daily loss) | Advantage (daily income) | ATM, short-dated |
| Vega | Volatility sensitivity | Advantage when IV rises | Advantage when IV falls | ATM, long-dated |
Practical Application
Position Selection
- Confident in direction + expect quick move: High delta (buy ITM). Theta burden exists so quick movement needed
- Expect big move, direction uncertain: ATM straddle. High gamma. Heavy theta burden
- Expect volatility rise: Buy long-dated ATM. High vega. Lower theta burden
- Expect consolidation: Option selling strategies. Theta income. Manage gamma risk
Risk Management
- Calculate total portfolio Greeks to understand overall exposure
- Use delta neutral to eliminate directional risk
- Be cautious of positions with extremely high gamma near expiry
- Check vega exposure before IV Crush events
Summary
The Greeks are essential tools for understanding and predicting option price changes. Delta measures directional sensitivity, gamma measures delta acceleration, theta measures time decay, and vega measures volatility sensitivity. Option buyers benefit from gamma but pay theta, while sellers harvest theta but bear gamma risk. Understanding this tradeoff is the core of options trading.
Next article: Max Pain and Options Expiry - The Price Magnet on Expiration Day