What is the Black-Scholes model?

Black-Scholes (1973) is a mathematical model that gives a closed-form price for European-style options assuming the underlying follows geometric Brownian motion with constant volatility and no dividends. It remains the most widely used benchmark for option pricing.

What inputs does the model need?

Five inputs: (S) current stock price, (K) strike price, (T) time to expiry in years, (σ) annualized volatility as a decimal, and (r) annualized risk-free rate as a decimal. This tool converts percentage inputs to decimals automatically.

The Greeks measure option price sensitivity: Delta (change per $1 move in stock), Gamma (change in Delta), Theta (daily time decay in dollars), Vega (change per 1% vol move), and Rho (change per 1% rate move).

Does this work for American options?

No. Black-Scholes prices European options only (exercisable at expiry). American options, which can be exercised early, typically require a binomial tree or finite-difference method and are worth slightly more for puts.

How do I enter time to expiry?

Enter years as a decimal. For example: 3 months = 0.25, 6 months = 0.5, 1 year = 1.0. A quick way: divide calendar days to expiry by 365.

What is a reasonable volatility input?

Implied volatility (IV) varies by stock and market conditions. Blue-chip stocks often sit between 15%–30% annualized. High-growth or small-cap stocks can exceed 50%–80%. Check your broker or an options chain for the current IV.

Black-Scholes Option Price Calculator

Compute European call and put option prices with the Black-Scholes formula — instant results with Greeks (Delta, Gamma, Theta, Vega, Rho).

Option Parameters

Stock Price (S) — current underlying price

Strike Price (K)

Time to Expiry (T) — in years

Implied Volatility (σ) — annualized %

Risk-Free Rate (r) — annualized %

Option Prices

Call Price

—

Right to buy

Put Price

—

Right to sell

Put-Call Parity check: —

Option Greeks

Delta

Call

—

Put

—

$/$ move

Gamma

—

same for both

Theta

Call / day

—

Put / day

—

$/day

Vega

—

$/1% vol

Rho

Call

—

Put

—

$/1% rate

Model Inputs Summary

S = —

K = —

T = — yr

σ = —%

r = —%

d₁ = —

Summary

The Black-Scholes model is the industry-standard formula for pricing European-style call and put options. It takes five inputs — current stock price, strike price, time to expiration, implied volatility, and the risk-free interest rate — and produces theoretical fair-value prices along with the five Greeks. This tool performs all calculations client-side in real time, so no data leaves your browser.

How it works

Enter the current stock or underlying asset price.
Set the option strike price and time to expiration in years (e.g. 0.25 = 3 months).
Input the annualized implied volatility as a percentage (e.g. 25 for 25%).
Enter the annualized risk-free interest rate as a percentage.
Results update instantly: call price, put price, and all five Greeks.

Use cases

Price European call or put options before placing a trade.
Compare theoretical value against market price to spot mispricings.
Understand how changing volatility affects option premium (Vega).
Estimate daily time decay on a position (Theta).
Assess directional exposure with Delta before hedging.
Study how the Greeks change as inputs move with live sliders.
Verify option pricing homework or CFA exam practice problems.
Quickly check put-call parity relationships.

Frequently Asked Questions

Last updated: 2026-06-04 · Reviewed by Nham Vu