Greeks

Greeks	Symbol	Specification
Delta	Δ	Measures the change in an option's price (premium) resulting from a change in the Underlying Price
Gamma	Γ	Measures the rate of change in Delta
Vega	ν	Measures the change in an option's price (premium) resulting from a change in Implied Volatility

Delta (Δ)

Delta (Δ) is a measure of the change in an option's price (premium of an option) resulting from a change in the underlying asset (such as BTC, ETH or SOL). In layman's terms, if the price of the underlying asset moves $1, how much does the price of my option (premium) move?

In general, the delta of a call option ranges between zero and one, while the delta of a put option ranges between negative one and zero. Furthermore, at-the-money options are most sensitive to changes in various risk factors, so at-the-money options have a delta of ±0.50 (positive if it is a call, negative for a put).

For example, if an at-the-money BTC call option has a delta of 0.5 and BTC price rises by $1, the option's price will increase by approximately $0.5 (0.5 x $1 = $0.5).

In another example, suppose that one out-of-the-money BTC option has a delta of 0.30, and another in-the-money BTC option has a delta of 0.80. A $1 increase in the BTC price will lead to a $0.30 increase in the first option and a $0.80 increase in the second option.

Examples (assume all else equal):

Underlying	Option	Delta	Scenario
BTC	Call	+0.5	Underlying price rises: If the BTC price increases by $1, the BTC Call options price increases by $0.5 (0.5*$1 = $0.5) Underlying price drops: If the BTC price decreases by $1, the BTC Call options price decreases by $0.5 (0.5*-$1 = -$0.5)
BTC	Put	-0.5	Underlying price rises: If the BTC price increases by $1, the BTC Put options price decreases by $0.5 (-0.5*$1 = -$0.5) Underlying price drops: If the BTC price decreases by $1, the BTC Put options price increases by $0.5 (-0.5*-$1 = $0.5)

Gamma (Γ)

Gamma (Γ) measures delta's rate of change over time. Gamma provides traders with an idea of what to expect in the future. In general, Gamma values are highest for at-the-money options and lowest for that deep in-the-money or out-of-the-money options.

For example, suppose that two options have the same delta value, but one option has a high gamma, and another one has a low gamma. The option with the higher gamma will expose a higher risk as an unfavorable move in the underlying asset will generate an oversized impact.

New Delta = Original Delta + (underlying price move x Gamma)

Examples (assume all else equal):

Underlying	Option	Delta	Gamma	Scenario
BTC	Call	+0.5	0.05	Underlying price rises: If the BTC price increases by $1, the delta of BTC Call options increases to 0.55 (0.5+1*0.05 = 0.55) Underlying price drops: If the BTC price decreases by $1, the delta of BTC Call options decreases to 0.45 (0.5-1*0.05 = 0.45)
BTC	Put	-0.5	0.05	Underlying price rises: If the BTC price increases by $1, the delta of BTC Put options increases to -0.45 (-0.5+1*0.05 = -0.45) Underlying price drops: If the BTC price decreases by $1, the delta of BTC Put options decreases to -0.55 (-0.5-1*0.05 = -0.55)

Vega (ν)

Vega (ν) measures the change in an option's price (premium of an option) resulting from a change in the implied volatility of an underlying (such as BTC, ETH or SOL). It's a gauge of how much an option price will increase or decrease given the level of implied volatility.

Long options have a positive vega, and short options have a negative vega, while vega falls as the option gets closer to expiration.

Examples (assume all else equal):

Underlying	Option	Vega	Scenario
BTC	Call	7.00	IV rises: If the BTC IV increases 20bp from 60% to 60.2%, the BTC Call options price increases by $140 (20*$7 = $140) IV drops: If the BTC IV decreases 10bp from 60% to 59.9%, the BTC Call options price decreases by $70 (10*$7 = $70)
BTC	Put	7.00	IV rises: If the BTC IV increases 20bp from 60% to 60.2%, the BTC Put options price increases by $140 (20*$7 = $140) IV drops: If the BTC IV decreases 10bp from 60% to 59.9%, the BTC Put options price decreases by $70 (10*$7 = $70)