Black-Scholes Model Calculator
What is the Black-Scholes Model?
The Black-Scholes model is a mathematical framework used to determine the fair market price of stock options. Developed by Fischer Black, Myron Scholes, and Robert Merton in the early ’70s, it provides a way to calculate the theoretical value of European-style options based on six key variables:
- Stock Price (S₀): The current price of the underlying stock.
- Strike Price (X): The agreed-upon price at which the option can be exercised.
- Time to Maturity (T): The duration until the option expires.
- Risk-Free Rate (r): The return on a risk-free investment like government bonds.
- Volatility (σ): The expected fluctuation in the stock’s price.
- Dividend Yield (q): The annual dividend payout as a percentage of the stock price.
How to Use the Black-Scholes Model Calculator?
This calculator allows you to compute the fair prices of call and put options using the Black-Scholes formula. Follow these steps:
- Input Stock Price: Enter the current market price of the stock.
- Add Strike Price: Provide the agreed-upon strike price for your option contract.
- Select Time to Maturity: Specify how long until the option expires, measured in years.
- Set Risk-Free Rate: Enter the annualized risk-free interest rate as a percentage.
- Add Volatility: Provide an estimate of the stock’s annualized volatility as a percentage.
- Add Dividend Yield: Include any expected dividend yield as a percentage of the stock’s value.
- Click Calculate: Press “Calculate” to generate call and put option prices based on your inputs.
The results will show you both call and put prices, helping you make informed trading decisions based on theoretical valuations derived from market data.