This Black Scholes calculator uses the Black-Scholes option pricing method to calculate the fair market value of an option. This calculator can be used for both call or put options. Additionally, the Black-Scholes option pricing method only works with European options. European options are options that can only be exercised at the expiry date. Conversely, American options can be exercised at any time before the exercise date.

Option Pricing

CFI's Black Scholes calculator uses the Black-Scholes option pricing method. This is one method out of several common methods which include the binomial option pricing model and the Monte Carlo simulation. The Black-Scholes option pricing method, as previously mentioned, assumes that the option being evaluated is a European option. In addition to this assumption, this Black Scholes calculator also makes several more assumptions:

• the stock does not pay any dividends
• continuously compounded returns are independent over time and are normally distributed
• the volatility of these continuously compounded returns is given and does not change
• the risk-free rate is also given and remains constant
• there are no transaction costs or taxes
• short-selling can be done at no cost
• money is borrowed at the risk-free rate

This Black Scholes calculator uses several inputs to calculate the option price:

• Stock Price (S): the price of the stock of the option
• Strike Price (K): the price that the option can be exercised at
• Time to Maturity (t): number of years until the exercise date of the option
• Risk-free Rate (r): the risk-free interest rate (usually the interest rate of U.S. Treasury Bills)
• Volatility (σ): the measure of how much the stock's price moves over time. This Black Scholes calculator uses annualized volatility

To learn more about option pricing models, check out CFI's article on the Monte Carlo Simulation! As well, take a look at CFI's Fixed Income Fundamentals course to learn more about other types of financial instruments!