FinanceCalcs
Options Calculator
Price any stock option using the Black-Scholes model — the industry-standard formula used by professional traders worldwide. Enter the stock price, strike, days to expiration, and volatility to get the theoretical option price, all five Greeks, break-even price, and a profit/loss chart at expiration.
Black-Scholes gives the theoretical fair value of an option. The market price may differ — that difference is what traders call edge.
Options Pricing — Black-Scholes
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Theoretical Price: $0
Option Details
The Greeks
| Greek | Value | Meaning |
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Greeks Sensitivity — Stock Price ±20%
| Stock Price | Option Price | Delta | Gamma | Theta/day | Vega/1% |
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"An option’s price is not what you pay. It’s what you get: the right to participate in upside without unlimited downside. Understanding the Greeks tells you exactly what you’re buying."
— Options Trading Fundamentals
The Black-Scholes model
Black-Scholes (1973) gives the theoretical fair value of a European option. The model assumes stock prices follow a log-normal distribution, volatility is constant, there are no transaction costs, and the risk-free rate is known and constant. Despite these simplifying assumptions, it remains the foundational benchmark for options pricing.
The formula requires five inputs: stock price (S), strike price (K), time to expiration (T in years), volatility (σ), and the risk-free rate (r). It outputs the theoretical price and five sensitivity measures (the Greeks) that describe how the price changes with each input.
Black-Scholes is most accurate for at-the-money options with moderate time to expiration. It tends to underestimate the probability of large moves (fat tails), which is why market participants often pay more for out-of-the-money options than Black-Scholes predicts — the “volatility smile.”
Options FAQs
What does delta mean?
Delta measures how much the option price changes for every $1 move in the stock. A delta of 0.50 means a $1 stock move changes the option price by $0.50. Delta also approximates the probability the option expires in-the-money. Deep in-the-money options approach delta 1.0; far out-of-the-money options approach 0.
What is theta and why does it matter?
Theta is daily time decay — how much value the option loses each day just from the passage of time, all else equal. Option buyers pay theta; sellers collect it. Theta accelerates as expiration approaches, especially in the final 30 days. A theta of −$0.05 means the option loses $0.05 per day per contract ($5 per standard 100-share contract).
What is implied volatility?
Implied volatility (IV) is the market’s expectation of future volatility, derived by solving Black-Scholes backwards from the market option price. High IV means the market expects large moves; low IV means small moves. IV often spikes before earnings announcements and drops after — the “IV crush” that can hurt option buyers even when the stock moves in the right direction.
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