Black-Scholes Option Pricing Calculator

Calculate theoretical option prices, Greeks, and analyze risk metrics

Input Parameters

Current market price
Option exercise price
Annual rate in %
Annual yield in % (optional)
Days to Expiry
365
Select the option expiration date
Annual volatility in %
Volatility data from Aswath Damodaran

Option Prices

ATM

Call Option

0.00
Intrinsic Value0.00
Time Value0.00
ATM

Put Option

0.00
Intrinsic Value0.00
Time Value0.00
Call Break-Even
0.00
+0.00%
Put Break-Even
0.00
-0.00%
Call Prob. of Profit
0.0%
N(d2)
Put Prob. of Profit
0.0%
N(-d2)

The Greeks

Delta (Δ) Measures how much the option price changes for a $1 move in the underlying stock.
0
Call
0
Put
Gamma (Γ) Measures the rate of change in Delta for a $1 move in the stock. Higher near ATM options.
0
Both
Theta (Θ) Time decay - how much value the option loses each day. Usually negative (options lose value over time).
0
Call
0
Put
Vega (ν) Sensitivity to volatility. Shows price change for a 1% change in implied volatility.
0
Both
Rho (ρ) Sensitivity to interest rates. Shows price change for a 1% change in the risk-free rate.
0
Call
0
Put

Visualization

Implied Volatility Calculator

Enter the market price of an option to calculate its implied volatility.

Implied Volatility: --

Understanding the Inputs

S Stock Price (Spot Price)

The current market price of the underlying asset (stock, index, ETF, etc.) on which the option is written.

Example: If Apple (AAPL) is trading at $150.00, enter 150.

K Strike Price (Exercise Price)

The predetermined price at which the option holder can buy (calls) or sell (puts) the underlying asset.

Example: A $155 strike call gives you the right to buy at $155.

T Time to Expiry

The remaining time until the option expires. Select the expiration date using the calendar, and the calculator automatically computes the time in years.

Example: 6 months = 0.5 years, 30 days ≈ 0.082 years

r Risk-Free Interest Rate

The theoretical return on a zero-risk investment, typically represented by government treasury bonds.

Example: If 1-year Treasury yield is 5.25%, enter 5.25.

σ Volatility (Implied Volatility)

A measure of expected price fluctuation. You can enter it manually or select from industry averages calculated by Prof. Aswath Damodaran based on historical data.

Example: 20% volatility means the stock may move ±20% annually (1 std dev).

q Dividend Yield

Annual dividend payments as a percentage of stock price. Dividends reduce call values and increase put values.

Example: A $100 stock paying $2/year has 2% dividend yield.

The Black-Scholes 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) and d₂ = d₁ - σ√T

Model Assumptions & Limitations: The Black-Scholes model assumes constant volatility, no dividends during the option's life (unless adjusted), efficient markets, no transaction costs, European-style options (exercise only at expiration), and log-normal distribution of returns. Real market conditions may differ significantly. This calculator is for educational purposes only and should not be used as the sole basis for trading decisions.