Estimate the theoretical price of European call and put options using the foundational Black-Scholes model. Input stock price, strike, time, rate, and volatility to get instant results based on this foundational option pricing formula.

Estimate Option Prices with the Black Scholes Calculator

The Black-Scholes model, also known as the Black-Scholes-Merton (BSM) model, is a cornerstone of modern financial theory, providing a mathematical framework for estimating the theoretical fair value of options. This calculator allows you to apply the model to find the theoretical price for European-style call and put options based on key inputs.

What This Calculator Provides:

This tool calculates the theoretical fair value for:

• European Call Option Price: The estimated price for the right to buy the underlying asset at the strike price on the expiration date.
• European Put Option Price: The estimated price for the right to sell the underlying asset at the strike price on the expiration date.

Understanding the theoretical price can help traders identify potential mispricings in the market and inform trading strategies.

How to Use the Calculator:

1. Enter Current Stock Price (S): The current market price of the underlying asset.
2. Enter Strike Price (K): The price at which the option can be exercised.
3. Enter Days to Expiration: The number of calendar days remaining until the option expires.
4. Enter Risk-Free Interest Rate (%): The current annualized risk-free rate (e.g., Treasury bill rate), entered as a decimal (e.g., 0.05 for 5%).
5. Enter Volatility (%): The expected future volatility (implied volatility) of the underlying stock, entered as a decimal (e.g., 0.20 for 20%).
6. View Results: The calculated theoretical prices for the European call and put options will be displayed.

Model Assumptions & Limitations:

The Black-Scholes model provides a theoretical benchmark and relies on several important assumptions:

• The option is European style (can only be exercised at expiration).
• No dividends are paid by the underlying stock during the option’s life. (The basic BSM model assumes this; dividend yields require adjustments to the formula).
• Implied volatility and the risk-free rate are constant and known throughout the option’s life.
• The underlying stock price follows a lognormal distribution (meaning returns are normally distributed).
• There are no transaction costs or commissions.
• The market allows for frictionless borrowing and lending at the risk-free rate.

Due to these assumptions, the price generated by the Black Scholes calculator is theoretical and may differ from the actual market price of the option. It’s a valuable tool for analysis but should be used in conjunction with other market information and trading strategies.

See my preferred options broker IBKR here.

See my Black Scholes calculator in Excel here.

See my Black Scholes calculator in Python here.