Adjust parameters, watch Greeks change in real time. Based on the Black-Scholes model, this calculator covers first-order Greeks (Delta, Gamma, Theta, Vega, Rho) and second-order Greeks (Vanna, Charm, Volga). Drag any slider and both the numbers and the curve update instantly.
For formula derivations, see the Option Greeks Guide. For second-order Greeks, see Vanna, Charm, Volga Explained. For trading applications, see Greeks in Practice.
Formula Basics
The calculator uses the Black-Scholes model. The core intermediaries are \(d_1\) and \(d_2\):
$$d_1 = \frac{\ln(S/K) + (r + \sigma^2/2) \cdot T}{\sigma\sqrt{T}}, \quad d_2 = d_1 - \sigma\sqrt{T}$$All first-order and second-order Greeks are functions of \(d_1\), \(d_2\), and the standard normal distribution functions \(N(\cdot)\) and \(n(\cdot)\). For full derivations, see the Option Greeks Guide.
Second-order Greeks: Vanna measures Delta’s sensitivity to volatility, Charm measures how Delta decays over time, and Volga measures Vega’s convexity with respect to volatility. Detailed explanations at Second-Order Greeks Explained.
Usage Tips
Drag the spot price \(S\) slider and watch Delta trace its characteristic S-curve from 0 to 1 (for calls). Switch to the Gamma view and notice the peak at ATM, which gets dramatically sharper as expiry approaches. This is why market makers get most nervous near expiry: short-dated ATM options carry the highest Gamma risk.
Reduce T (days to expiry) below 5 days and look at Theta: time decay accelerates in the final days. This is the nonlinear Theta decay discussed in Greeks in Practice.