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# Greeks

Greeks measure the sensitivity of an option's price to changes in underlying factors such as spot price, implied volatility, interest rates, and time. Paradex provides both **Raw Greeks** and **Cash Greeks**.

Raw Greeks are available on the API via the [markets summary endpoint](/api/prod/markets/get-markets-summary). On the UI, users can choose to display Cash Greeks by changing their Greeks preference setting from **Raw** to **Cash**.

## Assumptions for examples

The examples below use the following assumptions:

* BTC spot price (S) = \$60,000
* Annualized forward rate (f) = 10%
* Implied volatility (IV) = 40%
* Risk-free rate (r) = 0% *(current platform setting; used only for discounting)*
* Position size = 1 BTC

Under Black-76, the option is priced against the synthetic forward $F = S \times e^{\,f\,T}$, but Greeks are reported as sensitivities with respect to **spot (S)** — i.e., a 1% move in $S$ in the examples below corresponds to \$600. With $r = 0\%$, the discount factor $e^{-rT} = 1$, so option values equal the undiscounted Black-76 payoff. The Rho example uses a non-zero rate purely to illustrate the sensitivity.

## Definitions and examples

| Factor        | Greek | Raw Greek (definition)                                                                                                             | Cash Greek (definition)                                                | Examples                                                                                                                                                                 |
| ------------- | ----- | ---------------------------------------------------------------------------------------------------------------------------------- | ---------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------ |
| Spot          | Delta | Sensitivity of option value to a move in the underlying                                                                            | Expected PnL for a 1% move in spot                                     | Raw Delta = 0.5 → 1% of spot = $600 → Cash Delta = 0.5 × $600 = $300 → Option gains ~$300 if BTC rises 1%                                                                |
| Spot          | Gamma | Sensitivity of Raw Delta to a move in the underlying                                                                               | Second-order PnL for a 1% move in spot                                 | Raw Gamma = 0.0002 → Cash Gamma = ½ × 0.0002 × $600² = $36 → Additional \~\$36 of convex PnL from a 1% BTC rise                                                          |
| IV            | Vega  | Sensitivity of option value to a 1% absolute change in IV                                                                          | Same as Raw Greek                                                      | Vega = 80 → If IV moves from 40% to 41% → Option gains \~\$80                                                                                                            |
| IV/Spot       | Vanna | Sensitivity of Raw Delta to a 1% absolute change in IV (equivalently, sensitivity of Vega to a move in spot)                       | Additional expected PnL assuming 1% move in spot and 1% increase in IV | Vanna = 0.01 → If IV moves from 40% to 41% → Delta shifts such that the position gains an additional \~\$6 per subsequent 1% spot move                                   |
| IV            | Volga | Sensitivity of Vega to a 1% absolute change in IV                                                                                  | Same as Raw Volga                                                      | Volga = 1.5 → If IV moves from 40% to 41% → Option gains an additional \~\$1.50 of convex PnL on top of Vega                                                             |
| Interest Rate | Rho   | Sensitivity of option value to a 1% absolute change in the risk-free rate (r) used for discounting, holding the forward F constant | Same as Raw Rho                                                        | Rho = 25 → If r moves from 0% to 1% → Option value changes by \~\$25 through the discount factor. Sensitivities to the underlying level are captured by Delta and Gamma. |
| Time          | Theta | Sensitivity of option value to 1 day of time decay                                                                                 | Same as Raw Theta                                                      | Theta = −10 → Option loses \~\$10 after 1 day, all else equal                                                                                                            |