Lesson 6: Greeks 101 (Risk in Four Knobs)
Promise: Translate "options are complicated" into 4 intuitive sensitivities.
What Are Greeks?
Greeks measure how an option's price changes when different factors move. They're called "Greeks" because they use Greek letters.
Greeks are not magic. They are local slopes.
Each Greek answers a simple question:
Delta (Δ): Direction Exposure
Delta measures the option's sensitivity to spot price movement.
Interpretation: A delta of 0.5 means the option price moves ~$0.50 for every $1 move in the underlying.
See Delta In Action
Click or drag to move spot price. Toggle between position types and adjust time/volatility.
Delta by Moneyness
| Moneyness | Call Delta | Put Delta |
|---|---|---|
| Deep ITM | ~1.0 | ~-1.0 |
| ATM | ~0.5 | ~-0.5 |
| Deep OTM | ~0 | ~0 |
At High Vol, All Deltas Compress Toward 0.5
This is one of the most important things to understand in crypto: when volatility explodes, the sharp delta curve flattens out. OTM options that had tiny deltas suddenly behave much more like ATM options.
At 30% IV, a 10% OTM call has ~5 delta. At 150% IV (common in crypto crises), the same option has ~25 delta. Your "safe" far-OTM position just became 5x more exposed. Always check your Greeks at elevated vol levels, not just current vol.
Delta Is NOT Probability
A common misconception: "delta equals the probability of finishing in-the-money." This is approximately true for ATM options at low vol, but breaks down badly for OTM options, at high vol, and when skew is steep. Delta is a hedge ratio, not a probability. In crypto, where vol is high and skew is steep, the two can diverge significantly.
Gamma (Γ): How Delta Changes
Gamma measures how much delta changes when spot moves.
Gamma is why short-dated ATM options feel "twitchy."
Why gamma matters: If you're short options, gamma works against you. Large spot moves cause your delta exposure to grow in the wrong direction.
Gamma isn't symmetric. For multi-leg positions (like risk reversals), you can have positive gamma if spot rallies but negative gamma if it drops. Always ask: "What's my gamma in each direction?" — a single aggregate gamma number can hide dangerous asymmetry.
See Gamma In Action
Notice how gamma peaks at ATM and explodes near expiry:
Theta (Θ): Time Decay
Theta measures how much the option loses per day from time passing.
Theta accelerates near expiry: An ATM option loses more per day in its final week than in its first month.
See Theta In Action
Drag the slider to simulate time passing. Notice how decay accelerates near expiry:
Vega (ν): Volatility Sensitivity
Vega measures how much the option price changes when IV moves.
Interpretation: Vega of 50 means the option price moves $50 for a 1% (1 vol point) change in IV.
See Vega In Action
Notice how vega peaks at ATM and increases with time to expiry:
Greeks Summary Table
The Greeks Trade-Off
There's no free lunch in options. Each Greek represents a trade-off:
| If You Want... | You Accept... |
|---|---|
| Long gamma (delta moves in your favor) | Negative theta (pay time decay) |
| Positive theta (collect premium) | Short gamma (delta moves against you) |
| Long vega (profit from IV rise) | Pay more premium upfront |
Long options have negative theta but positive gamma (you pay for convexity). Short options have positive theta but negative gamma (you collect premium but face blow-up risk).
Common Mistakes
| Mistake | Correction |
|---|---|
| Believing delta is constant | Delta changes as spot moves. That's what gamma measures. |
| Ignoring gamma near expiry | Short-dated ATM options have extreme gamma. Small moves cause big delta changes. |
| Treating theta as linear | Theta accelerates near expiry. The last week decays fastest. |
| Thinking Greeks are independent | They interact. Gamma affects how delta changes, which affects P&L. |
| Delta = probability of ITM | Delta is a hedge ratio, not a probability. They diverge at high vol and with steep skew. |
| Ignoring delta at high vol | At extreme vol (common in crypto), all deltas compress toward 0.5. Your "5-delta" OTM option can become 25-delta. |
💡 Tip: Try answering each question yourself before revealing the answer.
See Also
Navigation: ← Lesson 5: Implied Volatility | Lesson 7: Basic Strategies →