Option Pricing Calculator
The fair value of a call or put, and what drives it
Enter the option and see its fair price
Free · No sign-up · Updates as you typeAn option is a contract that gives you the right (not the obligation) to buy or sell a stock at a fixed price by a fixed date. A call profits if the stock rises; a put profits if it falls. This tool estimates what that contract is worth today, using the Black-Scholes model.
$
What one share trades at today, e.g. 155.
$
The fixed price the option locks in, e.g. 150.
Calendar days left, e.g. 30.
How much the stock is expected to swing, e.g. 25.
Government bond yield, e.g. 5.
Fair value of this call
$7.72
per share · one contract = 100 sharesIn plain terms: this call is worth $7.72, made of $5.00 you could pocket by exercising right now (intrinsic value) plus $2.72 for the time and uncertainty still left before expiry (time value). As expiry nears, that time value melts toward zero.
Call price
$7.72
Put price
$2.11
What the option is worth if the stock moves
Everything else held the same, here is the fair value at a range of stock prices.
| Stock price | Call price |
|---|---|
| $139.50 (-10%) | $0.94 |
| $147.25 (-5%) | $3.26 |
| $155.00 (now) | $7.72 |
| $162.75 (+5%) | $14.00 |
| $170.50 (+10%) | $21.26 |
The Greeks (for traders)
Each Greek measures how the price reacts to one thing changing. Full explanations are in the section below.
0.7091
per $1 move in the stock0.0309
how fast Delta changes$0.15
per 1% of volatility$-0.08
lost per day to time$0.08
per 1% of interest rate0.551 / 0.479
model intermediatesThis calculator uses the Black-Scholes model, developed by Fischer Black, Myron Scholes, and Robert Merton in 1973. It gives the theoretical fair value of European-style call and put options and is the foundation of modern options pricing.
C = S·N(d₁) − K·e^(−rT)·N(d₂)
Delta (Δ): How much the option price moves per $1 move in the stock. A delta of 0.60 means the option gains about $0.60 when the stock rises $1.
Gamma (Γ): How fast Delta itself changes as the stock moves. High gamma means Delta swings quickly, common for at-the-money options close to expiry.
Vega (ν): How much the price moves per 1% change in implied volatility. Higher vega means the option reacts more to volatility shifts.
Theta (Θ): Time decay: how much value the option loses each day, all else equal. It works against buyers and for sellers as expiry approaches.
Rho (ρ): How much the price moves per 1% change in the risk-free rate. Usually the smallest effect, and it matters most for long-dated options.
What Is the Black-Scholes Option Pricing Model?
The Black-Scholes model is a mathematical framework for pricing European-style options. Published in 1973 by Fischer Black and Myron Scholes, with key contributions from Robert Merton, it changed financial markets by giving the first widely adopted formula for an option's fair value from observable market inputs.
The model takes five inputs (stock price, strike price, time to expiry, risk-free rate, and implied volatility) and returns a theoretical price for both calls and puts. Despite its simplifying assumptions, it stays the industry standard and the base on which more complex models are built.
The Black-Scholes Formula
C = S·N(d₁) − K·e^(−rT)·N(d₂)
d₁ = [ln(S/K) + (r + σ²/2)T] / (σ√T)
The formula prices the option as the expected stock value (weighted by the chance of exercise) minus the present value of the strike (weighted by the chance the option finishes in the money). N(d₁) and N(d₂) are cumulative standard-normal probabilities.
The put price follows from put-call parity: P = K·e^(−rT)·N(−d₂) − S·N(−d₁). Parity keeps call and put prices consistent, so knowing one gives you the other.
Understanding Implied Volatility
Implied volatility (IV) is the market's forecast of how much the stock will move. Unlike historical volatility, which looks back, IV is forward-looking and baked into the option's market price. Higher IV means the market expects bigger swings, which lifts the premium on both calls and puts.
Traders compare IV to historical volatility to judge whether options look cheap or expensive. When IV sits well above historical volatility, premiums may be rich; when below, they may be a bargain. Run in reverse, this tool doubles as an implied-volatility finder: nudge the volatility input until the model price matches the option's market price, and you have the IV the market is pricing in.
Limitations of the Black-Scholes Model
The model assumes constant volatility and interest rates, a log-normal price distribution, no dividends, no transaction costs, and European exercise only. In reality volatility shifts over time (the "volatility smile"), stocks pay dividends, and many listed options are American-style.
Even so, Black-Scholes is the most common starting point. Practitioners adjust for dividends, switch to a binomial model for American options, and apply volatility surfaces for the smile. Its simplicity and clean formula make it indispensable for fast pricing and risk checks.
How the Greeks Drive Common Options Strategies
This tool prices a single option, but most traders combine several into a strategy. In a covered call you own 100 shares and sell a call against them, collecting premium in exchange for capping your upside. The fair value here tells you whether the call you are selling is richly priced and worth writing.
In a cash-secured put you sell a put while holding enough cash to buy the shares if assigned, earning premium and a chance to buy lower. Implied volatility and Theta tell you whether the premium pays you enough for the risk. Theta, the daily loss of value as expiry nears, works in your favour when you are the seller.
Across every strategy the Greeks are the controls. Delta is your directional exposure, Gamma how fast that exposure shifts, Theta the time decay you earn or pay, Vega your sensitivity to volatility, and Rho your exposure to interest rates. Reading them together is how traders shape and hedge a position.
Frequently Asked Questions
Implied volatility sits in the option chain on your broker or on financial data sites, usually in a column marked "IV". The CBOE VIX index tracks the implied volatility of S&P 500 options and is the popular market-wide gauge. For a single stock, read the IV straight from its option chain.
Black-Scholes prices European options, which you can only exercise at expiry. For American calls on a stock that pays no dividend, the price matches the European call, because exercising early is never worth it. For American puts, or calls on dividend payers, treat this as an approximation; a binomial tree is more accurate.
Delta has three everyday readings: the expected change in the option price for a $1 move in the stock; a rough probability the option finishes in the money; and the equivalent share position (a delta of 0.50 on one contract behaves like 50 shares). It is the Greek traders lean on most for sizing and hedging.
The extra is time value: what buyers pay for the chance the option moves further into profit before expiry. It grows with more time left and higher volatility, and it melts away as expiry nears (that erosion is Theta). At expiry, time value is zero and the option is worth only its intrinsic value.
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