Estimate European call and put values under entered Black-Scholes assumptions.
It makes the prices, cash flows, rates, time periods, weights, and model conventions explicit so you can inspect an entered scenario without hidden live-market assumptions.
Calculation structure
Follow the stated model and units
Call = Se^(−qT)N(d1) − Ke^(−rT)N(d2); put follows put-call parity.
Visual explanation
See how the inputs become the result
Capital and cash flowstime and rate→entered modelScenario resultChanging one assumption changes the model—not the marketCall = Se^(−qT)N(d1) − Ke^(−rT)N(d2); put follows put-call parity.
Read the estimate correctly
Use the result within its boundaries
Spot 100, strike 100, one year, 5% rate, 0% yield, and 20% volatility produce call value about 10.45 and put about 5.57.
European exercise, constant continuous rates/yield/volatility, lognormal prices, and no transaction costs are assumed.
Quick guide
How to use this calculator
Enter the contract, market, expiry, rate, and position assumptions named by the fields.
Keep premiums, prices, multipliers, contract counts, and time conventions consistent.
Read the exact expiry-payoff or model assumptions before interpreting the result.
Calculation method
Calculation method
Call = Se^(−qT)N(d1) − Ke^(−rT)N(d2); put follows put-call parity.
Expiry-payoff arithmetic uses the entered terminal underlying price. Model-derived values are explicitly estimates and reject unsupported domains.
Worked example
Worked example
Spot 100, strike 100, one year, 5% rate, 0% yield, and 20% volatility produce call value about 10.45 and put about 5.57.
Call = Se^(−qT)N(d1) − Ke^(−rT)N(d2); put follows put-call parity.
Supported inputs
Precision and limits
Visible input limits
Fixed decimals accept up to 30 digits and 12 decimal places with absolute values capped at 1e12. General rates are bounded from −100% through 1000% where signed rates are meaningful.
No contract or market feed
No exchange specification, live quote, exercise style, dividend schedule, settlement rule, margin model, or contract multiplier is selected automatically.
Decision boundary
Outputs are entered scenarios, not quotes, forecasts, arbitrage findings, risk limits, suitability judgments, or recommendations.
Calculator-specific assumptions
European exercise, constant continuous rates/yield/volatility, lognormal prices, and no transaction costs are assumed.
