Options Pricing Calculator: 17 Models and 17 Greeks

Free options pricing calculator that runs the chain through 17 models simultaneously: Black-Scholes, Heston stochastic volatility, Monte Carlo, SABR, Jump Diffusion, Variance Gamma, Local Volatility, Binomial, FFT, PDE, plus seven exotic models (Asian, Barrier, Lookback, Digital, Compound, Chooser, Multi-Asset). Compute all 17 Greeks across every model: delta, gamma, theta, vega, rho, vanna, charm, vomma, zomma, color, speed, ultima, lambda, epsilon, phi, plus the model-parameter Greeks for stochastic-volatility models. Black-Scholes plus the full Greek set is free; the full multi-model surface unlocks on the paid tier.

How the Calculator Is Different

Most retail options calculators run one model and report one price. This calculator runs the full multi-model surface and shows the prices side by side. The point is not to declare one model right and the others wrong: each model captures a different facet of the market (constant vol vs stochastic vol, log-normal returns vs jumps vs mean-reverting variance). When the models agree, the price has consensus. When they diverge, the disagreement is itself information, often signaling a regime shift, an unusually rich tail, or a calibration problem on one of the models. The model-divergence dashboard surfaces these gaps directly.

Inputs the Calculator Accepts

For European-style options, the standard six inputs are spot price (S), strike (K), time to expiration (T, in years), implied volatility (sigma), risk-free rate (r), and continuous dividend yield (q). For American-style options the binomial and PDE engines additionally require an early-exercise grid; for stochastic-volatility models you can either supply pre-calibrated parameters or let the calibration job fit Heston, SABR, Variance Gamma, Jump Diffusion, or Local Vol against the live surface. For Monte Carlo, you can choose path count, antithetic sampling, and control-variate seeds; for FFT you can choose damping factor and grid resolution.

Greeks the Calculator Returns

First-order Greeks (delta, gamma, theta, vega, rho) come back per share in standard units. Theta is per year by default; divide by 365 for the per-calendar-day decay commonly cited by retail platforms. Vega is per unit move in the IV decimal; divide by 100 for a one-vol-point move. The higher-order Greeks (vanna, charm, vomma, zomma, color, speed, ultima, lambda, epsilon, phi) are returned in their canonical mathematical form; the documentation pages cover the units and the trading interpretation for each.

3D Volatility Surface and Calibration

The 3D volatility surface visualizes implied vol across both strike and expiration in a single rotatable view. Surfaces are fit using eSSVI parameterization, which is designed to be arbitrage-free under standard parameter constraints; butterfly arbitrage and calendar arbitrage are both checked at fit time so violations are flagged rather than silently emitted. For markets where the static fit is not the right tool (illiquid wings, extreme regime events), the platform also exposes Dupire local volatility extraction so you can see where a state-dependent vol function would project the surface to evolve. Calibrated parameters export through the Python SDK if you want to roll the same fit into a backtest or research notebook.

When to Use Which Model

For European-style equity options under normal market conditions, Black-Scholes is the natural starting point because it is fast, parsimonious, and well-understood. Heston is the standard upgrade once you need to capture smile and term-structure dynamics in a single calibration. SABR is preferred when you want the per-expiration smile shape without the full-surface dynamics (commodity desks and rate-options desks typically prefer SABR). Jump Diffusion and Variance Gamma earn their keep when fat tails are the primary risk: they price the wings more accurately than continuous-diffusion models. Monte Carlo and PDE are the right tools when path-dependence (Asian, Barrier, Lookback) matters or when you need flexibility on early-exercise mechanics.

Common Workflow

The most common workflow is: start on a per-ticker page, look at the volatility skew and dealer-gamma exposure to frame the regime, jump to the calculator with the same chain pre-loaded, run the multi-model surface to see the price dispersion, and use the calibrated parameters to drive a strategy in the strategy builder. The calibration objects produced here can be exported and re-used programmatically through the Python SDK.