Tools / Black–Scholes pricer & Greeks
Black–Scholes pricer & Greeks
Price European calls and puts, see every Greek, and watch the payoff bend as time and volatility change.
C = S·N(d₁) − K·e^(−rT)·N(d₂)
- Price
- Delta Δ
- Gamma Γ
- Vega (per vol pt)
- Theta (per day)
- Rho (per 1%)
- P(ITM), risk-neutral
Value vs spot. Solid: value today. Dashed: payoff at expiry. The gap between them is time value.
How to read it
Move days to expiry towards zero and watch the curve collapse onto the payoff, with gamma spiking at the strike. Raise volatility and every option gets more expensive — the curve lifts away from the payoff. Theta is quoted per calendar day and vega per one volatility point, the way traders quote them.
The implied-volatility solver inverts the formula with a safeguarded Newton method. If it reports no solution, the price you entered is outside the no-arbitrage bounds for the other inputs.
The theory is in the lesson.
Turn this into a tool you own
Want this on live option chains, with a volatility surface and risk across a whole book? Paste this into your coding agent.
/agenkit build an options analytics service with Black–Scholes pricing, Greeks, an implied-volatility solver, and a volatility-surface fit from live Deribit option chains, with unit tests against known values- npx agenkit install engineering-kit in your project
- Paste the command into your agent and approve each phase
- Get tests, backtest, risk controls and a paper-trading switch