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Black-Scholes Calculator

Model option values, Greeks, and volatility premiums using the standard Black-Scholes-Merton equations.

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Calculation Parameters

Specify your inputs below.

Calculated Result

Call Option Value $9.73
Put Option Value $2.62
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Expert Tip

The Black-Scholes pricing engine assumes European-style options with constant volatility and risk-free rates.

How this Calculator Works

Utilizes normal cumulative distributions to value both options based on stock, strike, time, volatility, and rates.

Formula & Methodology

d1 = [ln(S/K) + (r + v^2 / 2)*t] / (v * sqrt(t)) d2 = d1 - v * sqrt(t) Call = S*N(d1) - K*e^(-r*t)*N(d2)

Step-by-Step Calculation Example

Here is a step-by-step example showing how the calculations are performed:

Stock=$100, Strike=$95, Time=0.5 yrs (180 days), Vol=25%, Rate=4.5%: - Call = $9.73 - Put = $2.62

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Detailed Insights & Expert Guide

โ„น๏ธ About this Calculation

This derivatives and options pricing calculator evaluates theoretical option premiums, implied volatility (IV), option Greeks (Delta, Gamma, Theta, Vega, Rho), multi-leg strategy risk profiles, and futures margin requirements using Black-Scholes and Cox-Ross-Rubinstein binomial models.

Variable Glossary

Input

Option Parameters

Underlying stock price (S), strike price (K), expiration days (T), volatility (ฯƒ %), and risk-free interest rate (r %).

Parameter

Greeks & Premium

Theoretical Call/Put price ($), Delta sensitivity (ฮ”), Theta daily decay (ฮ˜), and maximum profit/loss boundaries.

How to Calculate Step-by-Step

1

Step 1

Input current asset price, option contract strike price, and target expiration date.

2

Step 2

Specify implied or historical volatility percentage, dividend yield %, and risk-free treasury yield.

3

Step 3

Review calculated fair value option price, Greek risk sensitivities, break-even stock price, and payoff diagram matrix.

FAQ

What are the primary Option Greeks and what do they measure?
Delta (ฮ”) measures price sensitivity to underlying asset moves; Gamma (ฮ“) measures rate of Delta change; Theta (ฮ˜) measures daily time decay; Vega (ฮฝ) measures sensitivity to 1% volatility changes.
What is Put-Call Parity?
Put-Call Parity defines the static equilibrium relationship: Call Price - Put Price = Spot Price - Present Value of Strike Price. It prevents arbitrage between options and European spot markets.
Can option pricing models guarantee trading profits?
No. Black-Scholes and Binomial models assume continuous trading, constant volatility, and lognormal price distributions. Options trading involves substantial risk of capital loss due to leverage and volatility expansion.