Black-Scholes Option Pricing Calculator

Calculate European call and put theoretical prices with full Delta, Gamma, Theta, Vega, and Rho Greeks using the Black-Scholes-Merton formula.

Black-Scholes European Option Pricing & Greeks Calculator

Compute real-time Call and Put option theoretical values with complete first and second-order Greeks (Delta, Gamma, Theta, Vega, Rho).

Underlying Stock Price ($S)

Strike Price ($K)

Days to Expiration (DTE)

Implied Volatility (IV, %)

Risk-Free Rate (%r)

Dividend Yield (%q)

Call Option

$3.04

Delta: 0.535

Put Option

$2.67

Delta: -0.465

The Greeks Analysis

Gamma (Γ): 0.0554

Vega (ν): $0.114/1% IV

Call Theta (Θ): $-0.054/day

Put Theta (Θ): $-0.041/day

Call Rho (ρ): $0.041

Put Rho (ρ): $-0.040

The Mathematics of Option Valuation

The Black-Scholes formula revolutionized global modern financial markets. It proves that a riskless hedge can be established between an option and its underlying stock, yielding an exact theoretical fair value based on lognormal asset price distributions.

Key Features

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Complete First & Second-Order Greeks

Instantly outputs Delta, Gamma, Theta (per calendar day), Vega, and Rho.

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Continuous Dividend Yield Extension

Incorporates the Merton dividend yield extension for index and dividend-paying stocks.

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Arbitrage-Free Theoretical Modeling

Implements standard cumulative normal distribution calculations for precise Wall Street pricing.

Common Use Cases

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Derivatives Traders & Analysts
Price European call and put options and stress-test Greek sensitivities to volatility and time decay.
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Quantitative Finance Students & CFA Candidates
Master the mathematical dynamics of the Nobel-prize winning Black-Scholes-Merton model.

Frequently Asked Questions

What is the Black-Scholes option pricing model?

The Black-Scholes model is a mathematical model for pricing European-style option contracts, developed by Fischer Black and Myron Scholes in 1973. It calculates theoretical option value based on stock price, strike price, time to expiration, volatility, and risk-free interest rates.

What are the Option Greeks?

The Greeks measure the sensitivity of an option's price to various market factors: Delta (price change per $1 move in stock), Gamma (change in Delta), Theta (time decay per day), Vega (sensitivity to 1% change in implied volatility), and Rho (sensitivity to interest rates).