What is the Black-Scholes option pricing model?

The Black-Scholes model is the most famous option pricing formula in finance, developed by Fischer Black and Myron Scholes in 1973. Based on the no-arbitrage principle, it uses five parameters — underlying asset price, strike price, time to expiration, risk-free rate, and volatility — to calculate the theoretical price of European options.

What is the difference between call and put options?

A Call option gives the buyer the right to buy the underlying asset at the strike price, suitable for bullish markets. A Put option gives the buyer the right to sell the underlying asset at the strike price, suitable for bearish markets. European options can only be exercised at expiration; American options can be exercised any time before expiration.

What does implied volatility mean?

Implied volatility reflects the market's expectation of future price fluctuations of the underlying asset. Higher volatility means higher option prices. Individual stocks typically have volatility of 20-60%, while major indices range from 15-25%. This calculator supports custom volatility parameters.

Is the calculator data safe?

Completely safe. All calculations are performed locally in your browser and are never uploaded to any server. This tool is for educational reference only and does not constitute investment advice.

Option Price Calculator - Black-Scholes Model

Calculate European call/put option theoretical prices using the Black-Scholes model. Enter spot price, strike, time to expiry and other parameters to get fair value and Greeks.

Financial Analysis · Investment Reference

📊 Input Parameters

Spot Price ($)

Current market price of the underlying asset

Strike Price ($)

The strike price specified in the option contract

Days to Expiry

Remaining days until option expiration

Risk-Free Rate (%)

Typically the treasury yield, e.g. 3.5%

Volatility (%)

Annualized volatility, typically 20-60% for stocks

Dividend Yield (%)

Annualized dividend yield of the underlying (optional)

📖 About the Black-Scholes Model

The Black-Scholes model is the classic option pricing formula for calculating theoretical prices of European options. It assumes log-normal distribution of the underlying, frictionless markets, and continuous trading.

Core Formula

Call: C = S·e^(-qT)·N(d₁) - K·e^(-rT)·N(d₂)

Put: P = K·e^(-rT)·N(-d₂) - S·e^(-qT)·N(-d₁)

where d₁ = [ln(S/K) + (r - q + σ²/2)T] / (σ√T)，d₂ = d₁ - σ√T

Disclaimer

This calculator is for educational reference only and does not constitute investment advice. Options trading carries extremely high risk and may result in total loss of principal. Actual market prices may differ from model theoretical values due to liquidity, supply/demand and other factors.

📈 Option Price Calculator

📊 Input Parameters

💰 Option Prices

🔢 Greeks

📖 About the Black-Scholes Model

Core Formula

Disclaimer