Options
Black-Scholes Option Calculator: Price, Greeks and IV
Enter the stock price, strike, days to expiration, volatility and interest rate to get a call or put’s theoretical price and all five Greeks, or enter the option’s price to solve for its implied volatility.
Option price and Greeks calculator
- Theoretical price
- $3.59
- $359.11 per contract
- Delta
- 0.5324
- Gamma
- 0.0462
- Theta per day
- −0.0624
- Vega per 1 vol point
- 0.1140
- Rho per 1 rate point
- 0.0408
- Chance of expiring in the money
- 49.8%
- Breakeven at expiration
- $103.59
Intrinsic value $0.00 + time value $3.59
Black-Scholes prices European options; US stock options can be exercised early, so a put or a call before a dividend may be worth a little more. Greeks are per share: multiply by 100 for one contract. The chance of expiring in the money uses the model’s own assumptions, not a forecast.
The calculator runs in your browser. Nothing you type is saved or sent anywhere.
Educational tool, not financial advice. The results only reflect the numbers you enter and say nothing about future returns. Trading involves a substantial risk of loss.
How to use the Black-Scholes calculator
- Choose call or put, and what to calculate: the price from a volatility, or the implied volatility from a price.
- Enter the stock price, the strike and the calendar days left to expiration.
- Enter the implied volatility from your options chain, or the option’s price per share (the mid between bid and ask) to solve for it.
- Add the interest rate, roughly the yield on a short-term Treasury bill, and the dividend yield if the stock pays one.
- Read the price per share and per contract, the Greeks and the breakeven, and use the chart to see how the value changes with the stock today and at expiration.
The Black-Scholes formula in plain words
The model prices an option as the expected payoff at expiration, discounted to today, assuming the stock moves randomly with a constant volatility. Two numbers, d1 and d2, measure how far the stock sits from the strike in units of volatility over the time left; N() turns them into probabilities from the normal distribution.
The Greeks are the slopes of that price: delta for the stock, gamma for delta, theta for one calendar day, vega for one point of volatility and rho for one point of interest. Implied volatility runs the formula backwards: it is the volatility that makes the model price equal the market price.
T = days ÷ 365; d1 = [ln(S ÷ K) + (r − q + σ² ÷ 2) × T] ÷ (σ × √T); d2 = d1 − σ × √T
Call = S × e^(−qT) × N(d1) − K × e^(−rT) × N(d2)
Put = K × e^(−rT) × N(−d2) − S × e^(−qT) × N(−d1)
Call delta = e^(−qT) × N(d1); put delta = call delta − e^(−qT)
Breakeven at expiration: call = strike + price; put = strike − price
Worked example
A 30-day call with a $100 strike on a $100.00 stock, implied volatility of 30%, an interest rate of 4% and no dividend.
- Theoretical price: $3.59 per share, or $359.11 for a 100-share contract, all of it time value because the call is at the money.
- Delta 0.5324: the call gains about $0.53 if the stock rises $1. Gamma 0.0462: delta then rises to about 0.58.
- Theta −0.0624: about $6 per contract lost each day with nothing else changing. Vega 0.1140: about $11 per contract for each point of volatility.
- Breakeven at expiration: $100 + $3.59 = $103.59. The model puts the chance of finishing in the money at 49.8%, and the chance of reaching the breakeven is lower still.
- The same option with one day left is worth about $0.63, with a gamma of about 0.25: short-dated options swing much harder on the same move.
Questions
Is the Black-Scholes price what I will pay?
No. The market sets the price; the model shows what that price implies. If the model price at your volatility differs from the quote, the market is using a different volatility. Switch to implied volatility mode and enter the quote to see which one.
Does it work for American options?
Black-Scholes prices European options, which can only be exercised at expiration. For a call on a stock with no dividend the American price is the same; for puts, and for calls just before a dividend, early exercise can make the American option worth a little more.
Why is theta negative?
An option buyer pays for time. With the stock and volatility unchanged, the option loses a little value every day, and the decay speeds up near expiration. The options Greeks lesson shows how it adds up.
What is implied volatility?
It is the volatility that makes the model price match the market price: the move the market is pricing in. It rises before events like earnings and often falls right after, which can cut an option’s value even if the stock moves your way. See implied volatility.
UpTickFlow is our product. These guides are education, not financial advice. Trading involves a substantial risk of loss.