> For the complete documentation index, see [llms.txt](https://optifi.gitbook.io/optifi/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://optifi.gitbook.io/optifi/option-101/glossary/greeks.md).

# Greeks

<table><thead><tr><th width="107">Greeks</th><th width="91">Symbol</th><th width="593.4285714285713">Specification</th></tr></thead><tbody><tr><td>Delta</td><td>Δ</td><td>Measures the change in an option's price (premium) resulting from a change in the <strong>Underlying Price</strong></td></tr><tr><td>Gamma</td><td>Γ</td><td>Measures the rate of change in <strong>Delta</strong></td></tr><tr><td>Vega</td><td>ν</td><td>Measures the change in an option's price (premium) resulting from a change in <strong>Implied</strong> <strong>Volatility</strong></td></tr></tbody></table>

## **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):&#x20;

<table><thead><tr><th width="132.33333333333331">Underlying</th><th width="85">Option</th><th width="75">Delta</th><th>Scenario</th></tr></thead><tbody><tr><td>BTC</td><td>Call</td><td>+0.5</td><td><strong>Underlying price rises:</strong> If the BTC price increases by $1, the BTC Call options price increases by $0.5 (0.5*$1 = $0.5)<br><br><strong>Underlying price drops:</strong> If the BTC price decreases by $1, the BTC Call options price decreases by $0.5 (0.5*-$1 = -$0.5)</td></tr><tr><td>BTC</td><td>Put</td><td>-0.5</td><td><strong>Underlying price rises:</strong> If the BTC price increases by $1, the BTC Put options price decreases by $0.5 (-0.5*$1 = -$0.5)<br><br><strong>Underlying price drops:</strong> If the BTC price decreases by $1, the BTC Put options price increases by $0.5 (-0.5*-$1 = $0.5)</td></tr></tbody></table>

## **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):&#x20;

<table><thead><tr><th width="132.33333333333331">Underlying</th><th width="86">Option</th><th width="76">Delta</th><th width="94">Gamma</th><th>Scenario</th></tr></thead><tbody><tr><td>BTC</td><td>Call</td><td>+0.5</td><td>0.05</td><td><strong>Underlying price rises:</strong> If the BTC price increases by $1, the delta of BTC Call options increases to 0.55 (0.5+1*0.05 = 0.55)<br><br><strong>Underlying price drops:</strong> If the BTC price decreases by $1, the delta of BTC Call options decreases to 0.45 (0.5-1*0.05 = 0.45)</td></tr><tr><td>BTC</td><td>Put</td><td>-0.5</td><td>0.05</td><td><strong>Underlying price rises:</strong> If the BTC price increases by $1, the delta of BTC Put options increases to -0.45 (-0.5+1*0.05 = -0.45)<br><br><strong>Underlying price drops:</strong> If the BTC price decreases by $1, the delta of BTC Put options decreases to -0.55 (-0.5-1*0.05 = -0.55)</td></tr></tbody></table>

## **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):&#x20;

<table><thead><tr><th width="132.33333333333331">Underlying</th><th width="86">Option</th><th width="73">Vega</th><th>Scenario</th></tr></thead><tbody><tr><td>BTC</td><td>Call</td><td>7.00</td><td><strong>IV rises:</strong> If the BTC IV increases 20bp from 60% to 60.2%, the BTC Call options price increases by $140 (20*$7 = $140)<br><br><strong>IV drops:</strong> If the BTC IV decreases 10bp from 60% to 59.9%, the BTC Call options price decreases by $70 (10*$7 = $70)</td></tr><tr><td>BTC</td><td>Put</td><td>7.00</td><td><strong>IV rises:</strong> If the BTC IV increases 20bp from 60% to 60.2%, the BTC Put options price increases by $140 (20*$7 = $140)<br><br><strong>IV drops:</strong> If the BTC IV decreases 10bp from 60% to 59.9%, the BTC Put options price decreases by $70 (10*$7 = $70)</td></tr></tbody></table>