What is the Black-Scholes calculator?

The Black-Scholes calculator is a financial tool that uses the Black-Scholes model to determine the theoretical price of European call and put options. It requires inputs like stock price, strike price, time to expiration, volatility, and risk-free rate to calculate option premiums and the Greeks (Delta, Gamma, Theta, Vega, Rho).

How do I use the Black-Scholes option calculator?

Enter the current stock price, strike price, days until expiration, implied volatility (as a percentage), and risk-free interest rate. Select whether you want to calculate a call or put option. The calculator instantly displays the option price and all Greeks.

What are the Greeks in options trading?

The Greeks measure how sensitive an option's price is to various factors: Delta measures sensitivity to stock price changes, Gamma measures the rate of Delta change, Theta measures time decay, Vega measures sensitivity to volatility, and Rho measures sensitivity to interest rate changes.

Is the Black-Scholes model accurate?

The Black-Scholes model is highly accurate for European options under normal market conditions. However, it assumes constant volatility and interest rates, no dividends, and efficient markets. Real-world options may deviate due to factors like volatility smile, dividends, and early exercise (for American options).

What is implied volatility in Black-Scholes?

Implied volatility (IV) is the market's expectation of how much the stock price will move. In the Black-Scholes model, it's expressed as an annualized percentage. Higher IV means higher option prices. Typical IV ranges from 15% for stable stocks to 50%+ for volatile stocks.

Black-Scholes Calculator

Calculate option prices and Greeks instantly using the Black-Scholes model.

Stock Price (S)

Strike Price (K)

Expiration

days

Volatility (σ)

Risk-Free Rate (r)

Option Type

Call

Put

Call Price

$0.00

Put Price

$0.00

The Greeks

Delta (Δ) 0.0000

Gamma (Γ) 0.0000

Theta (Θ)/day 0.0000

Vega (ν)/1% 0.0000

Rho (ρ)/1% 0.0000

Greeks Visualization

Want AI-powered options predictions? Try OpPreds

What is the Black-Scholes Model?

The Black-Scholes model (also known as the Black-Scholes-Merton model) is a mathematical model used to calculate the theoretical price of options. Developed by economists Fischer Black, Myron Scholes, and Robert Merton in 1973, it revolutionized options trading and earned Scholes and Merton the Nobel Prize in Economics in 1997.

This Black-Scholes calculator implements the original formula to help traders determine fair option prices and understand the key risk metrics known as "the Greeks." While the model was originally designed for European-style options (exercisable only at expiration), it provides excellent approximations for American-style options on non-dividend paying stocks as well.

The Black-Scholes Formula

The model calculates call and put option prices using these formulas:

Call: C = S × N(d₁) - K × e^-rT × N(d₂)
Put: P = K × e^-rT × N(-d₂) - S × N(-d₁)

Where: d₁ = [ln(S/K) + (r + σ²/2)T] / (σ√T) and d₂ = d₁ - σ√T

S = Stock price
K = Strike price
T = Time to expiration (years)

σ = Implied volatility
r = Risk-free rate
N(x) = Normal CDF

How to Use This Calculator

Using this online Black-Scholes calculator is straightforward:

Stock Price — Current market price of the underlying

Strike Price — Exercise price of the option

Expiration — Days until the option expires

Volatility & Rate — IV and risk-free rate as percentages

Tip: Find implied volatility on your broker platform, Yahoo Finance, or CBOE's option chain.

Understanding the Greeks

The Greeks measure how an option's price changes in response to various factors:

Measures how much the option price changes for every $1 move in the stock. Calls: 0 to 1, Puts: -1 to 0. ATM options typically have delta around ±0.50.

Measures how fast delta changes per $1 stock move. Higher gamma = more volatile option price. Highest for ATM options near expiration.

Measures daily value loss due to time decay. Always negative for long options. Accelerates as expiration approaches.

Measures price change per 1% change in implied volatility. Positive for all options. Critical for earnings plays and volatility trading.

Measures price change per 1% change in interest rates. Calls have positive rho, puts have negative rho. Least significant for short-term options.

Frequently Asked Questions

A financial tool that uses the Black-Scholes model to calculate theoretical option prices and the Greeks (Delta, Gamma, Theta, Vega, Rho). Enter stock price, strike, time to expiration, volatility, and risk-free rate to get instant results.

Highly accurate under normal market conditions. However, it assumes constant volatility and no dividends. Real-world prices may differ due to volatility smile, dividends, and early exercise for American-style options.

The market's expectation of how much a stock will move, expressed as an annualized percentage. Higher IV = higher option prices. Typical range: 15% for stable stocks to 50%+ for volatile ones.

The Black-Scholes model calculates prices for European-style options (exercisable only at expiration). For American options, prices serve as a lower bound—American puts may be worth more due to early exercise value.

Greeks measure option price sensitivity: Delta (price direction), Gamma (delta change rate), Theta (time decay), Vega (volatility sensitivity), and Rho (interest rate sensitivity). Essential for risk management.

Want to reverse-calculate IV from option prices?

Use our Implied Volatility Calculator to find IV when you know the market price.

IV Calculator

This calculator is for educational purposes only. Consult a qualified financial advisor before making investment decisions.

Take Options Trading Further

OpPreds

AI-powered options predictions. Know which calls and puts are likely to profit.

Daily predictions
Option contract details
Trading portfolio simulation

More Apps

SharePreds

Stock predictions

CPreds

Crypto predictions

Black-Scholes Calculator

What is the Black-Scholes Model?

The Black-Scholes Formula

How to Use This Calculator

Understanding the Greeks

Delta (Δ) — Price sensitivity

Gamma (Γ) — Delta's rate of change

Theta (Θ) — Time decay

Vega (ν) — Volatility sensitivity

Rho (ρ) — Interest rate sensitivity

Frequently Asked Questions

What is the Black-Scholes calculator?

How accurate is the Black-Scholes model?

What is implied volatility (IV)?

Does this work for American options?

What are the option Greeks?

Want to reverse-calculate IV from option prices?

Take Options Trading Further

OpPreds

More Apps