Check the units before comparing prices
A Black-Scholes calculator estimates a European option price from explicit assumptions. Match the underlying, strike, expiry and quote timestamp to the contract you are reviewing on TradingView or with your broker. An underlying chart does not supply a missing option quote or dividend forecast.
| Input | This calculator expects | Common mismatch |
|---|---|---|
| Spot and strike | Prices in the same currency, per underlying unit | Entering a contract total as a per-share price |
| Volatility | Annual standard deviation in percent: enter 20 for 20% | Entering 0.20 or an unannualized daily estimate |
| Risk-free rate | Continuously compounded annual percent | Using an effective yield without conversion |
| Dividend yield | Constant continuous annual percent; zero only when assumed | Treating a known cash dividend as a continuous yield |
| Expiry | Calendar days / 365, months / 12, or years directly | Using trading days with a 365-day divisor |
| Market price for IV | A per-share premium observed at the same time as spot | Using a stale last trade or a wide-spread midpoint as a firm quote |
For a 5% effective annual yield, the continuous input is 100 × ln(1.05) = 4.8790%. A 30-day expiry is 0.082192 years here; one month is 0.083333 years. Use fractional calendar days when the remaining hours matter. The calculator does not infer exchange settlement times.
Reproduce a dividend-adjusted example
Set spot = $100, strike = $100, expiry = 1 year, annual volatility = 20%, continuous rate = 5% and continuous dividend yield = 2%. These are hypothetical inputs, not market observations.
d1 = [ln(S/K) + (r − q + σ²/2)T] / (σ√T) = 0.25
d2 = d1 − σ√T = 0.05
C = S exp(−qT) N(d1) − K exp(−rT) N(d2) = $9.2270
P = K exp(−rT) N(−d2) − S exp(−qT) N(−d1) = $6.3301
The formula uses decimals (σ = 0.20, r = 0.05, q = 0.02), and N is the standard normal cumulative distribution. Check put-call parity: C − P = 100 exp(−0.02) − 100 exp(−0.05) = $2.8969. With q = 0 and the other inputs unchanged, the call is $10.4506. Ignoring dividends changes this estimate by about $1.2236 per share.
The model price of a contract with a confirmed 100-share multiplier would be $922.70. Adjusted contracts can have different deliverables. Verify the multiplier before scaling the result. For actual trade profit, use the premium paid or received and fees in an options profit calculator.
Where the estimate can fail
The model assumes European exercise, constant volatility, rates and continuous dividend yield. It omits early exercise, discrete dividend dates, jumps, transaction costs and liquidity. A volatility smile means one volatility assumption will not fit every strike. Short expiries are particularly sensitive to time and quote errors.
The IV solver searches from 0% to 1,000% annualized volatility. It rejects prices at or outside the European bounds, expired options and inputs outside its numerical range. A failed solve displays no fallback price. For calls the bounds are max(S exp(−qT) − K exp(−rT), 0) and S exp(−qT); for puts they are max(K exp(−rT) − S exp(−qT), 0) and K exp(−rT).
At zero time the calculator returns intrinsic payoff. At zero volatility it returns the discounted deterministic payoff. Greeks and d1/d2 are marked N/A at these boundaries. For positive time and volatility, theta is per calendar day; vega and rho are per one percentage-point change. Sensitivities are local approximations, not forecasts.
Model prices and IV can differ from a broker because inputs, exercise models and conventions differ. An apparent discount to this price does not establish an executable trade or expected profit. This tool is educational and does not provide investment advice.
Sources and next steps
Formula and model assumptions: Martin Haugh, Black-Scholes and the Volatility Surface, sections 1 to 3. Input meanings and Greek units: Options Industry Council, Volatility & the Greeks. Reviewed October 18, 2026. Numerical examples were independently recalculated from the displayed inputs.
Continue with TradingView workflows to connect chart review with a documented contract scenario. Keep missing inputs explicit; this calculator does not fetch or invent them.