European Option Value and Implied Volatility Calculator
Calculate Black–Scholes–Merton call/put values and sensitivities, or solve positive implied volatility from an entered premium.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use the European lognormal model with continuous dividend yield. For implied volatility, bisect the monotonic price function over the explicitly supported positive volatility range.
Call=S exp(−qT)Φ(d1)−K exp(−rT)Φ(d2); d1=[ln(S/K)+(r−q+σ²/2)T]/(σ√T); d2=d1−σ√T
Worked example
Spot=strike=100, one year, continuous rate 5%, no dividends and volatility 20% give call value about 10.4505836 and put value about 5.57352602.
Assumptions and input details
European exercise only, constant parameters, no transaction costs or discrete dividends. 0.001–500% positive annual volatility, positive expiry time up to 50 years. Implied volatility outside that interval or with unidentifiable flat prices is rejected. Delta is per underlying unit; vega/rho are per one percentage point; theta is per calendar day using 365. Normal probabilities use numerical integration. These are model values, not executable prices or forecasts. No live market data or national tax rules are inferred. Enter consistent amounts in one currency unless explicitly stated otherwise.
References: OIC: Greeks and implied volatility · MIT: European Black–Scholes formula
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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