Black Scholes Calculator
This Black Scholes calculator uses the Black-Scholes option pricing methodOption Pricing ModelsOption Pricing Models are mathematical models that use certain variables to calculate the theoretical value of an option. The theoretical value of an to help you calculate the fair value of a callCall OptionA call option, commonly referred to as a "call," is a form of a derivatives contract that gives the call option buyer the right, but not the obligation, to buy a stock or other financial instrument at a specific price - the strike price of the option - within a specified time frame. or put optionPut OptionA put option is an option contract that gives the buyer the right, but not the obligation, to sell the underlying security at a specified price (also known as strike price) before or at a predetermined expiration date. It is one of the two main types of options, the other type being a call option..
Here is a brief preview of CFI’s Black Scholes calculator.
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Option Pricing
CFI’s Black Scholes calculator uses the Black-Scholes option pricing method. Other option pricing methods include the binomial option pricing model and the Monte-Carlo simulationMonte Carlo SimulationMonte Carlo simulation is a statistical method applied in modeling the probability of different outcomes in a problem that cannot be simply solved due to the interference of a random variable. The simulation relies on the repetition of random samples to achieve numerical results. It can be used to understand the effect.
The Black-Scholes option pricing method focuses purely on European options on stocks. European options, which can only be exercised on the expiry date of the option. American options, which can be exercised early, cannot be priced using the Black-Scholes option pricing method.
Using this method, the Black Scholes calculator makes a few assumptions that you will need to remember:
- The stock pays no dividendsStock DividendA stock dividend, a method used by companies to distribute wealth to shareholders, is a dividend payment made in the form of shares rather than cash. Stock dividends are primarily issued in lieu of cash dividends when the company is low on liquid cash on hand.
- Continuously compounded returnsContinuously Compounded ReturnContinuously compounded return is what happens when the interest earned on an investment is calculated and reinvested back into the account for an infinite number of periods. The interest is calculated on the principal amount and the interest accumulated are independent over time and are normally distributedNormal DistributionThe normal distribution is also referred to as Gaussian or Gauss distribution. This type of distribution is widely used in natural and social sciences. The
- The volatilityVolatilityVolatility is a measure of the rate of fluctuations in the price of a security over time. It indicates the level of risk associated with the price changes of a security. Investors and traders calculate the volatility of a security to assess past variations in the prices of continuously compounded returns is constant and given
- Risk-free rateRisk-Free RateThe risk-free rate of return is the interest rate an investor can expect to earn on an investment that carries zero risk. In practice, the risk-free rate is commonly considered to equal to the interest paid on a 3-month government Treasury bill, generally the safest investment an investor can make. is constant and given
- Transaction costs or taxes are 0
- Short-selling is possible at no cost
- Borrowing is done at the risk-free rate
The main variables calculated and used in the Black Scholes calculator are:
- Stock PriceStock PriceThe term stock price refers to the current price that a share of stock is trading for on the market. Every publicly traded company, when its shares are (S): the price of the underlying asset or stock
- Strike PriceStrike PriceThe strike price is the price at which the holder of the option can exercise the option to buy or sell an underlying security, depending on whether they hold a call option or put option. An option is a contract with the right to exercise the contract at a specific price, which is known as the strike price. (K): the exercise price of the option
- Time to Maturity (t): the time in years until the exercise/maturity date of the option
- Risk-free Rate (r): the risk-free interest rate
- Volatility (σ): the measure of how much the underlying asset’s prices will move over time. This calculator uses annualized volatility
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