The Greeks — Delta, Theta, Gamma, Vega
Why do you need the Greeks?
An option's price depends on a lot of things: the underlying's price, time, and volatility. The Greeks — indicators that show you exactly how the option's price will react to each of those changes. Once you understand them, you can look at any position and immediately say where its sensitivity lies.
A car's dashboard
The Greeks are like a car's dashboard. Speedometer, RPM, temperature — each one shows a single thing. The Greeks work the same way: each one shows a single aspect of the option. You don't need to know them all at once — start with the two most important.
Delta — how far your portfolio will move
Delta shows: how much the option's price will change when the underlying's price moves $1.
PutPutAn option type that grants the right to SELL at a set price. Used as insurance.Read the lesson → simply: delta = the sensitivity gauge.
| Position | Delta range | What it means |
|---|---|---|
| Long CallCallAn option type that grants the right to BUY at the strike price. The opposite of a put.Read the lesson → | 0 to +1.0 | When SOLSOLSolana's native token. Used to pay gas and as collateral.Read the lesson → +$1, the option +$0.50 (if delta is 0.50) |
| Long PutPutAn option type that grants the right to SELL at a set price. Used as insurance.Read the lesson → | -1.0 to 0 | When SOLSOLSolana's native token. Used to pay gas and as collateral.Read the lesson → -$1, the option +$0.42 (if delta is -0.42) |
| Short CallCallAn option type that grants the right to BUY at the strike price. The opposite of a put.Read the lesson → | 0 to -1.0 | When SOLSOLSolana's native token. Used to pay gas and as collateral.Read the lesson → +$1, you lose $0.08 |
| Short PutPutAn option type that grants the right to SELL at a set price. Used as insurance.Read the lesson → | 0 to +1.0 | When SOLSOLSolana's native token. Used to pay gas and as collateral.Read the lesson → +$1, you make $0.18 |
Our portfolio's delta:
When SOLSOLSolana's native token. Used to pay gas and as collateral.Read the lesson → rises $1, the options positions lose $58 by these Greeks, while the 126 SOLSOLSolana's native token. Used to pay gas and as collateral.Read the lesson → collateral gains $126.
A note on the base amounts. The options quantities and the spot quantity don't match: the Long PutPutAn option type that grants the right to SELL at a set price. Used as insurance.Read the lesson → is written on a 200 SOL notional, while the collateral is 126 SOL. That's an intentional difference in size — but both deltas are measured in the same SOLSOLSolana's native token. Used to pay gas and as collateral.Read the lesson → units, so they can be added together.
The final portfolio number also folds in the LPLPLiquidity Provider — deposits tokens into a pool and earns a share of trading fees.Read the lesson → position (+11.5 SOLSOLSolana's native token. Used to pay gas and as collateral.Read the lesson →) and an effective hedge adjustment on the options (in practice -81 instead of -58 — why, is explained in Module 6's "Portfolio DeltaDeltaAn option's price sensitivity to the underlying price. Delta 0.50 means: if the underlying rises $1, the option price rises about $0.50.Read the lesson →" lesson). Result: **+56.5 SOLSOLSolana's native token. Used to pay gas and as collateral.Read the lesson →** net delta. A managed situation.
Delta = probability
DeltaDeltaAn option's price sensitivity to the underlying price. Delta 0.50 means: if the underlying rises $1, the option price rises about $0.50.Read the lesson → also gives you a rough read on the probability that an option finishes in the money. A PutPutAn option type that grants the right to SELL at a set price. Used as insurance.Read the lesson → with delta -0.42 has roughly a 42% chance of finishing ITMITMIn The Money — an option that has intrinsic value.Read the lesson →. A Short PutPutAn option type that grants the right to SELL at a set price. Used as insurance.Read the lesson → with delta +0.18 — about an 18% chance you'll have to pay up. The probability is small, but it's only a rough estimate, and the amount you'd owe if it happens isn't small — so the strike is chosen where you'd be willing to buy SOLSOLSolana's native token. Used to pay gas and as collateral.Read the lesson → anyway.
Theta — what the insurance costs you per day
Theta shows: how much the option's value drops in one day. Think of it as a daily rental fee for the insurance.
| Who you are | Theta effect | Typically |
|---|---|---|
| Buyer (Long) | Negative theta | You lose value every day |
| Seller (Short) | Positive theta | You earn every day |
Our portfolio's theta:
| Position | Theta per day | Good or bad for you? |
|---|---|---|
| Long PutPutAn option type that grants the right to SELL at a set price. Used as insurance.Read the lesson → $90 | -$3.25 | Bad — you pay daily |
| Short PutPutAn option type that grants the right to SELL at a set price. Used as insurance.Read the lesson → $65 | +$1.50 | Good — you earn |
| Short PutPutAn option type that grants the right to SELL at a set price. Used as insurance.Read the lesson → $60 | +$1.00 | Good — you earn |
| Short CallCallAn option type that grants the right to BUY at the strike price. The opposite of a put.Read the lesson → $160 | +$0.75 | Good — you earn |
| Total | ~$0.00 | Almost neutral! |
That means: the theta from the sold options almost exactly offsets the time decay on the bought PutPutAn option type that grants the right to SELL at a set price. Used as insurance.Read the lesson →, so the net daily time cost is close to zero. It's worth understanding what you're paying for that: the theta cost doesn't disappear, it gets swapped for risk — the sold PutsPutAn option type that grants the right to SELL at a set price. Used as insurance.Read the lesson → obligate you to buy SOLSOLSolana's native token. Used to pay gas and as collateral.Read the lesson → at $65 and $60, and the sold CallCallAn option type that grants the right to BUY at the strike price. The opposite of a put.Read the lesson → caps your upside above $160.
Gamma — how fast delta changes
Gamma shows: how much delta will change when the price moves $1. It's a "speed of change" indicator.
- High gamma = delta changes fast. The position is unstable
- Low gamma = delta changes slowly. The position is stable
| Situation | Gamma |
|---|---|
| ATMATMAt The Money — an option whose strike sits at the current price.Read the lesson → options (price = strike) | High — unstable |
| Deep OTMOTMOut of The Money — an option with no intrinsic value, only time value.Read the lesson →/ITMITMIn The Money — an option that has intrinsic value.Read the lesson → options | Low — stable |
| Long option | Positive — works for you |
| Short option | Negative — works against you |
Gamma and the LP connection
A Concentrated LiquidityConcentrated LiquidityProviding liquidity within a specific price range instead of from 0 to infinity. Uses capital more efficiently.Read the lesson → position (OrcaOrcaA Solana DEX with concentrated liquidity (Whirlpool). The basis of our LP strategy on the Solana network.Read the lesson →) has negative gamma. That means when the price moves sharply, the LPLPLiquidity Provider — deposits tokens into a pool and earns a share of trading fees.Read the lesson → position suffers (impermanent loss). It's very similar to selling options. Both suffer from large price jumps.
Vega — sensitivity to volatility
Vega shows: how much the option's price will change when market volatility moves 1%.
| Position | Vega effect |
|---|---|
| Long option | Earns when volatility rises |
| Short option | Earns when volatility falls |
Why are crypto options expensive?
SOLSOLSolana's native token. Used to pay gas and as collateral.Read the lesson →'s volatility runs ~70-80% a year. A typical stock — only ~20-30%. Bigger swings = pricier protection:
| Asset | Volatility | Insurance cost |
|---|---|---|
| Apple stock ($200) | ~25% | ~$5.00 (2.5% of price) |
| SOLSOLSolana's native token. Used to pay gas and as collateral.Read the lesson → ($88) | ~74% | ~$6.50 (7.4% of price) |
Crypto insurance is ~3x more expensive than for stocks. That's why our strategy needs a spread (Long + Short together) to bring the cost down.
Delta and Theta — the core trade-off
This is the most important trade-off in options:
| Want more... | You have to accept... |
|---|---|
| Protection (more delta hedge) | A bigger theta cost per day |
| ThetaThetaAn option's change in value from the passage of time. Negative for the buyer (a cost), positive for the seller (income).Read the lesson → income | Less protection |
Our strategy balances both:
- Long PutPutAn option type that grants the right to SELL at a set price. Used as insurance.Read the lesson → $90 — strong protection, but expensive
- Short PutPutAn option type that grants the right to SELL at a set price. Used as insurance.Read the lesson → $65 + $60 — theta income, but you take on risk
- Short CallCallAn option type that grants the right to BUY at the strike price. The opposite of a put.Read the lesson → $160 — extra theta
The bottom line:
- Net delta: ~+56.5 SOLSOLSolana's native token. Used to pay gas and as collateral.Read the lesson → (56.5 / 126 = ~45% exposure to price)
- Net theta: ~$0.00 per day (the daily time cost is close to neutral)
- The options hedge ~64% of the spot exposure (81 of 126 SOLSOLSolana's native token. Used to pay gas and as collateral.Read the lesson →)
What to watch every day
The three most important indicators:
- Net Delta — how much you're exposed to price (target zone: 40-55% of the 126 SOLSOLSolana's native token. Used to pay gas and as collateral.Read the lesson → collateral, i.e. ~50-69 SOLSOLSolana's native token. Used to pay gas and as collateral.Read the lesson →)
- Theta — what time costs you per day (target: close to zero)
- Gamma — whether the position is stable
GammaGammaThe rate of change of delta. High gamma means delta shifts quickly as the price moves.Read the lesson → is strongest right before an option's expiry — that's when delta changes fastest. That's why we roll positions when 30 days remain: a simple rule that steps around this period in advance, before it even starts.
Next step: Understood the Greeks? Now let's look at where to actually trade options — on the Deribit exchange.
The Greeks stop being scary once you see them in a live table. This paper exercise (~15 min) is pure observation and interpretation — no trading.
We only watch and take notes — DO NOT BUY ANYTHING. We're learning to read the indicators, not to trade.
This is learning, not investing — use only small amounts you treat as tuition.
You just read a real option's delta and IV in a live table and understood what they're telling you — most people never do that.