Dated Options

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. 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×e f TF = S \times e^{\,f\,T}, but Greeks are reported as sensitivities with respect to spot (S) — i.e., a 1% move in SS in the examples below corresponds to $600. With r=0%r = 0\%, the discount factor e−rT=1e^{-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

FactorGreekRaw Greek (definition)Cash Greek (definition)Examples
SpotDeltaSensitivity of option value to a move in the underlyingExpected PnL for a 1% move in spotRaw Delta = 0.5 → 1% of spot = 600→CashDelta=0.5×600 → Cash Delta = 0.5 × 600 = 300→Optiongains 300 → Option gains ~300 if BTC rises 1%
SpotGammaSensitivity of Raw Delta to a move in the underlyingSecond-order PnL for a 1% move in spotRaw Gamma = 0.0002 → Cash Gamma = ½ × 0.0002 × 6002=600² = 36 → Additional ~$36 of convex PnL from a 1% BTC rise
IVVegaSensitivity of option value to a 1% absolute change in IVSame as Raw GreekVega = 80 → If IV moves from 40% to 41% → Option gains ~$80
IV/SpotVannaSensitivity 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 IVVanna = 0.01 → If IV moves from 40% to 41% → Delta shifts such that the position gains an additional ~$6 per subsequent 1% spot move
IVVolgaSensitivity of Vega to a 1% absolute change in IVSame as Raw VolgaVolga = 1.5 → If IV moves from 40% to 41% → Option gains an additional ~$1.50 of convex PnL on top of Vega
Interest RateRhoSensitivity of option value to a 1% absolute change in the risk-free rate (r) used for discounting, holding the forward F constantSame as Raw RhoRho = 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.
TimeThetaSensitivity of option value to 1 day of time decaySame as Raw ThetaTheta = −10 → Option loses ~$10 after 1 day, all else equal