European-style call and put pricing, implied volatility, and Greeks. An educational Black-Scholes-Merton lab for finance students and self-taught options learners — not investment advice, not a broker, and not a DLOM or WACC toolkit.
Input the five required variables: stock price (S) — the current market price; strike price (K) — the exercise price; time to expiration (T) in years (e.g., 0.25 for 3 months); risk-free rate (r) — typically a matching Treasury yield; and implied volatility (σ) — the annualized expected movement. Optionally enter a dividend yield (q).
The calculator instantly shows the theoretical call and put price, plus all five Greeks: Delta, Gamma, Theta (per day), Vega (per 1% vol), and Rho (per 1% rate).
Know the market price but not the IV? Scroll to the Implied Volatility Solver, enter the observed price, select call or put, and the Newton-Raphson solver will find the volatility that matches.
The Payoff Diagram charts profit and loss at expiration across stock prices, accounting for the premium paid. Toggle between long call, long put, or both.
Enter observed call and put market prices with the same strike and expiry to verify whether the fundamental pricing relationship holds. Deviations may signal mispricings.
This calculator uses the generalized Black-Scholes-Merton model supporting continuous dividend yield. It assumes European-style exercise, constant volatility, and log-normal returns. All calculations run entirely in your browser — no data is transmitted.
| Greek | Call | Put | Meaning |
|---|---|---|---|
| Δ Delta | — | — | Price sensitivity to S |
| Γ Gamma | — | — | Delta sensitivity to S |
| Θ Theta | — | — | Price decay per day |
| V Vega | — | — | Sensitivity to vol (1%) |
| ρ Rho | — | — | Sensitivity to rate (1%) |
Enter an observed market price for a call or put option. The solver uses Newton-Raphson iteration to reverse-engineer the implied volatility. Uses the same S, K, T, r, q inputs from above.
Visualize profit and loss at expiration. Uses the current S, K, and calculated premiums from the calculator above.
The Black-Scholes model (1973) provides a closed-form solution for pricing European-style options. It assumes the underlying asset follows geometric Brownian motion with constant volatility.
C = Call price, P = Put price, N() = cumulative normal distribution
σ = volatility, T = time in years, r = risk-free rate, q = dividend yield
Enter observed market prices for a call and put with the same strike and expiry to check if parity holds.
Uses the same S, K, T, r, q inputs from the calculator above.