Options Pricing Calculator

The Black-Scholes model is a mathematical formula published in 1973 by Fischer Black, Myron Scholes, and Robert Merton. It calculates the theoretical price of European-style options based on the underlying asset price, strike price, time to expiration, risk-free interest rate, and implied volatility.

The Greeks measure how an option's price changes in response to different factors. Delta measures sensitivity to underlying price changes. Gamma measures the rate of change of Delta. Theta measures time decay per day. Vega measures sensitivity to volatility changes. Rho measures sensitivity to interest rate changes.

The Black-Scholes model is designed for European-style options (exercisable only at expiration). It can approximate American call prices on non-dividend-paying stocks, but it may undervalue American puts since they can be exercised early. More advanced models like binomial trees or Bjerksund-Stensland are used for American options.

Implied volatility (IV) is the market's expectation of future price movement, derived by working backwards from an option's market price using the Black-Scholes formula. Higher IV means more expensive options. IV is expressed as an annualised percentage.

Time decay accelerates near expiration because the probability of a large price move decreases as time runs out. At-the-money options experience the most time decay, while deep in-the-money or out-of-the-money options have less Theta exposure.