Option Pricing Calculator 

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An option is worth what the market will pay for it, but every serious trader starts from a theoretical fair value first. This calculator prices European call and put options with the Black-Scholes-Merton model, the same closed-form formula behind most professional pricing tools, and shows the full breakdown: premium, intrinsic value, time value, d1 and d2.

Enter the stock price, strike, time to expiration in years, volatility, the risk-free rate and any dividend yield. The tool is pre-filled with a worked example you can verify line by line below.

Option Pricing Calculator

Black-Scholes-Merton fair value for European calls and puts

Prefilled with the worked example: $100 stock, $100 strike, 1 year, 20% volatility, 5% risk-free rate, no dividends.

Option price

Quick Answer

For a $100 stock, a $100 strike, 1 year to expiration, 20% volatility, a 5% risk-free rate and no dividends, a European call is worth $10.45: $0.00 of intrinsic value plus $10.45 of time value, with d1 = 0.3500 and d2 = 0.1500. The matching put is worth $5.57. The calculator above is pre-filled with this exact example, and every figure here reproduces in the tool.

On this page

How to use the option pricing calculator

Five inputs and one choice stand between you and a theoretical option price. The tool takes about ten seconds once you know where each number comes from.

  1. Pick call or put. A call profits when the stock rises above the strike; a put profits when it falls below. This tool prices European-style options, the standard for index options, which can only be exercised at expiration.
  2. Enter the underlying price and the strike. Use the stock's current market price and the strike of the contract you are evaluating. The gap between the two sets the option's intrinsic value.
  3. Enter time to expiration in years. This is the input people get wrong most often: the model wants years, not days. Use 1 for a year, 0.25 for three months, and about 0.0822 for 30 days.
  4. Enter volatility as a percent. Annualized expected volatility drives the price more than any other input. Most traders plug in the option's implied volatility from their broker; a historical estimate works for what-if analysis.
  5. Enter the risk-free rate and dividend yield, then Calculate. A Treasury yield is the usual stand-in for the risk-free rate. Leave the dividend yield at 0 unless the underlying pays one. The result shows the premium plus the intrinsic/time-value split and d1/d2.

If you only need the total cash outlay for a set number of contracts rather than the model breakdown, the option premium calculator multiplies the per-option price by a contract multiplier.

The Black-Scholes formula this calculator uses

The tool implements the Black-Scholes-Merton model, published by Fischer Black and Myron Scholes in 1973 and extended by Robert Merton, the work that earned Scholes and Merton the 1997 Nobel Memorial Prize in Economic Sciences. For a European call (C) and put (P):

C = S·e−qT·N(d1) − K·e−rT·N(d2)

P = K·e−rT·N(−d2) − S·e−qT·N(−d1)

d1 = [ln(S/K) + (r − q + σ²/2)·T] / (σ·√T), d2 = d1 − σ·√T

S is the stock price, K the strike, T the time to expiration in years, r the risk-free rate, q the continuous dividend yield, σ the volatility, and N(x) the cumulative standard normal distribution. The d1 and d2 terms this page prints come straight from these equations; the tool evaluates N(x) with the standard Abramowitz-Stegun approximation, accurate to about seven decimal places.

Three honest notes about the model. First, it assumes European exercise, constant volatility and interest rates, and lognormal stock returns with no jumps. Second, the dividend yield here is continuous: for a stock paying discrete quarterly dividends, convert the expected annual payout into an equivalent yield. Third, the output is a theoretical fair value, not a prediction of the market quote; real prices also reflect supply, demand, and events the model cannot see.

Worked example: every step verified in the tool

Take the pre-filled example: a call on a $100 stock, $100 strike, 1 year to expiration, 20% volatility, 5% risk-free rate, no dividends.

Step 1: d1. d1 = [ln(100/100) + (0.05 − 0 + 0.20²/2) × 1] / (0.20 × √1) = (0 + 0.07) / 0.20 = 0.3500.

Step 2: d2. d2 = 0.3500 − 0.20 × 1 = 0.1500.

Step 3: the normal probabilities. N(0.3500) ≈ 0.6368 and N(0.1500) ≈ 0.5596. That second number has a plain meaning: about a 56% risk-neutral probability the call finishes in the money.

Step 4: the price. Call = 100 × 0.6368 − 100 × e−0.05 × 0.5596 = 63.68 − 53.23 = $10.45.

Step 5: the split. Intrinsic value is max(0, 100 − 100) = $0.00; time value is 10.45 − 0.00 = $10.45. An at-the-money option is pure time value, which is exactly what the tool shows. Run the same inputs as a put and you get $5.57, and the two satisfy put-call parity: 10.45 − 5.57 ≈ 100 − 100·e−0.05.

Reading your results: intrinsic value, time value, d1 and d2

Every calculation returns four numbers. The premium is the headline; the other three explain it.

  • Intrinsic value is what the option would be worth if exercised right now: stock minus strike for a call, strike minus stock for a put, floored at zero. It is the only part of the price you can lock in.
  • Time value is everything else: premium minus intrinsic. It reflects the chance the option gains intrinsic value before expiration, and it decays to zero at expiry.
  • d1 feeds the hedge ratio. For a call with no dividends, N(d1) is the option's delta, the number of shares that offset the position.
  • d2 gives the risk-neutral probability of finishing in the money: N(d2) for a call, N(−d2) for a put.

The table below runs four scenarios through the tool. Each cell is a real output, reproducible by entering the inputs above.

ScenarioCallPutd1d2
At the money: $100/$100, 1 yr, 20% vol, 5% rate, 0% div$10.45$5.570.35000.1500
In the money: $120/$100, 0.5 yr, 25% vol, 4% rate, 1.5% div$22.39$1.301.19051.0137
Out of the money: $90/$100, 0.25 yr, 40% vol, 1% rate, 0% div$3.66$13.41−0.4143−0.6143
Zero rate: $100/$100, 1 yr, 20% vol, 0% rate, 0% div$7.97$7.970.1000−0.1000

Notice the patterns the model guarantees. Deeper in the money means a bigger intrinsic slice: the $120/$100 call carries $20.00 of intrinsic value and only $2.39 of time value. Higher volatility inflates time value even when the option is out of the money. And at a zero risk-free rate, the at-the-money call and put cost exactly the same, $7.97, which put-call parity demands when the discounted strike equals the strike.

Volatility deserves its own study: N(d1) is closely tied to the option's delta, the full set of sensitivities lives in the option Greeks calculator, and the premium as a fraction of the stock price is broken out by the call put premium calculator.

What competing calculators get wrong

Six of the best-known Black-Scholes tools were tested against this page's checklist: dividend handling, intrinsic/time-value split, d1/d2 transparency, and numbers you can reproduce.

  • NumericCore Black-Scholes + Greeks: a clean tool with delta readouts and a quick-answer box. Its stated assumptions exclude dividend payouts entirely, so dividend-paying stocks are simply out of scope. This page includes a dividend yield input instead of assuming it away.
  • Calkoo BSOP calculator: the strongest rival, with dividend yield, full Greeks, a payoff chart and an honest worked example. It shows the premium and the Greeks but never decomposes the price into intrinsic versus time value, and its d1/d2 appear without any plain-English interpretation.
  • Calculator.now Black-Scholes: good transparency toggles for formulas, steps and decimal places. The content around the tool is generic template copy, and no worked example ties its numbers to anything verifiable.
  • CtrlCalculator Black-Scholes: an educational strike ladder (strikes 90 through 110 with d1, d2 and call prices) that teaches the shape of the model well. The shown table has no dividend yield, and the explainer and the calculator live on separate pages.
  • OptionsTradingCalculators 10-leg strategiser: twenty Black-Scholes engines for multi-leg P&L, genuinely professional. It is a paid spreadsheet download, not a quick single-option price check, which is a different job.
  • TradingView Black-Scholes indicator: Greeks plotted on the chart where you trade. It needs a TradingView account, shows no intrinsic/time-value split, and never explains d1 or d2.
  • The gap this page fills: a dividend-aware Black-Scholes-Merton pricer that splits every result into intrinsic and time value, prints d1 and d2 with their real meanings (N(d2) is the risk-neutral probability of finishing in the money), and pre-fills a worked example whose every digit reproduces in the tool above.

Model assumptions and limits, stated plainly

Black-Scholes assumes European exercise, constant volatility and interest rates over the option's life, lognormal returns with no jumps, frictionless markets, and no arbitrage. Real markets violate all of these at times: volatility smiles and skews, rates move, and stocks gap on news. Treat the output as the model's fair value under its assumptions, a starting point for comparing against the market quote, not a prediction of where the quote will go. For American-style options that can be exercised early, especially deep in-the-money puts and calls on dividend payers, a binomial or other early-exercise model is the honest choice; this tool does not price those.

Frequently asked questions

A closed-form formula for the theoretical value of European call and put options, published by Fischer Black and Myron Scholes in 1973 and extended by Robert Merton. It takes the stock price, strike, time to expiration, volatility, risk-free rate and dividend yield, and returns a single fair value. Scholes and Merton received the 1997 Nobel Memorial Prize in Economic Sciences for it.

Intrinsic value is what the option would be worth if exercised immediately: stock minus strike for a call, strike minus stock for a put, never below zero. Time value is everything else in the premium, the market's payment for the chance the option gains intrinsic value before expiration. Time value always decays to zero at expiration.

d1 and d2 are the two standardized inputs to the normal distribution inside the formula. Practically, N(d1) is closely tied to the call's delta, the hedge ratio, and N(d2) is the risk-neutral probability the option finishes in the money. In the worked example above, N(0.1500) is about 0.5596, roughly a 56% risk-neutral chance the call ends in the money.

Yes. It uses the Black-Scholes-Merton extension with a continuous dividend yield, which lowers call values and raises put values because dividends drag the forward stock price. Leave the yield at 0 for stocks that pay no dividend; a blank entry is treated as 0. For lumpy quarterly payouts, convert the expected annual dividend into an equivalent yield first.

Choose the contract you are evaluating. A call gives the right to buy at the strike and gains when the stock rises; a put gives the right to sell at the strike and gains when the stock falls. The badge on the result also tells you whether the option is in the money, at the money, or out of the money at the prices you entered.

The formula annualizes everything: volatility is quoted per year and the rate compounds per year, so time must be in years for the units to work. Divide days by 365. Thirty days is about 0.0822, three months is 0.25. Entering 30 when you mean 30 days prices a 30-year option, which is the most common input mistake.

Only the stock price, strike, time and volatility are required to be positive; the rate is only checked for being numeric. That is deliberate: zero and negative rates are economically meaningful in some markets, and the formula handles them. At a zero rate, an at-the-money call and put cost exactly the same, which put-call parity requires.

Not necessarily. It is the model's theoretical fair value under its assumptions: European exercise, constant volatility and rates, lognormal returns. Market quotes also reflect supply and demand, the volatility smile, and event risk. Traders use the model price as a baseline and read the difference between it and the quote as information about what the market expects.

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References

  1. Stanford Graduate School of Business. Professor Myron Scholes Shares 1997 Nobel Prize in Economic Sciences. Accessed October 23, 2026.
  2. Cboe. The Options Institute: Learn Options Trading from the Experts. Accessed October 23, 2026.
  3. Cboe. Cboe European-Style Options Implied Volatility Calculation Methodology (PDF). Accessed October 23, 2026.
  4. Federal Reserve Bank of St. Louis, FRED. Market Yield on U.S. Treasury Securities at 10-Year Constant Maturity (DGS10). Accessed October 23, 2026.
  5. Financial Industry Regulatory Authority. Regulatory Notice 22-08: Options Account Approval and Risk Disclosures. Accessed October 23, 2026.
  6. The Options Clearing Corporation. Publications: Characteristics and Risks of Standardized Options. Accessed October 23, 2026.
  7. The Options Industry Council. Options Basics FAQ. Accessed October 23, 2026.
  8. CME Group. Options Analytics: Greeks and Implied Volatility Data. Accessed October 23, 2026.
  9. CME Group. Understanding the CVOL Index: Implied Volatility Curves. Accessed October 23, 2026.
  10. CME Group. Options on Futures: Short-Dated Options and QuikStrike Strategy Tools. Accessed October 23, 2026.

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