Black-Scholes Option Pricing Calculator
Compute theoretical call and put prices plus all five Greeks (Delta, Gamma, Theta, Vega) using the Black-Scholes model. Enter stock price, strike, days to expiry, rate, and IV.
What is the Black-Scholes Model?
The Black-Scholes model (1973) is the foundational formula for pricing European-style options on non-dividend-paying stocks. It assumes stock prices follow a geometric Brownian motion with constant volatility, and derives a closed-form solution for the fair value of a call or put option given five inputs: the current stock price, the strike price, time to expiry, the risk-free interest rate, and the implied volatility of the underlying. Despite its simplifying assumptions (constant volatility, no dividends, no early exercise), Black-Scholes remains the universal benchmark for option pricing and is the basis for all five Greeks that traders use to manage options risk. The model won the 1997 Nobel Prize in Economics for Myron Scholes and Robert Merton (Fischer Black passed away in 1995).
Formula
Call = S × N(d₁) - K × e^(-rT) × N(d₂)
Put = K × e^(-rT) × N(-d₂) - S × N(-d₁)
d₁ = [ ln(S/K) + (r + σ²/2) × T ] / (σ × √T)
d₂ = d₁ - σ × √T
N(·) = cumulative standard normal CDF
S = stock price, K = strike, T = time (years), r = risk-free rate, σ = volatility
Calculator
How to Use
- 1Stock Price (S): The current market price of the underlying. For equities, use the last trade price.
- 2Strike Price (K): The price at which the holder can buy (call) or sell (put) the underlying at expiry.
- 3Days to Expiry: Calendar days until expiration. The model divides by 365 to convert to years. For weekly options, this might be 7; for a LEAPS, 365-730.
- 4Risk-Free Rate: Use the current annualised 3-month US T-bill yield. Enter as a percentage (e.g. 5 for 5%).
- 5Implied Volatility: The market's expected annualised volatility. Find it from your broker's option chain. Enter as a percentage (e.g. 25 for 25% IV).
Worked Example
Example: 30-day ATM Call
Stock Price
$150.00
Strike
$150.00
Days to Expiry
30
Risk-Free Rate
5%
IV
25%
An at-the-money 30-day call on a $150 stock with 25% IV and a 5% risk-free rate prices at approximately $4.65. The put prices at approximately $3.98 (reflecting the rate premium in calls). Delta is ~0.52, meaning the call moves ~$0.52 for every $1 move in the stock. Theta is ~-$0.08/day: the option loses about 8 cents in time value each calendar day.
Auto-fill Volatility from EDGAR
Beat Index members can load historical volatility metrics from EDGAR filings to inform their IV baseline.