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Black-Scholes Option Value Calculator — result sheet
Estimate a European call or put option value from price, strike, time, volatility, rates, and dividend yield.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Call = S e^(−qT)N(d₁) − K e^(−rT)N(d₂); put = K e^(−rT)N(−d₂) − S e^(−qT)N(−d₁), with d₁=[ln(S/K)+(r−q+σ²/2)T]/(σ√T) and d₂=d₁−σ√T.
This model gives a theoretical European option value under the supplied continuous-rate and lognormal-volatility assumptions.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Underlying price — currency; minimum 1.0E-6; maximum 1000000000
- Strike price — currency; minimum 1.0E-6; maximum 1000000000
- Time to expiry — years; minimum 1.0E-6; maximum 100
- Volatility — %; minimum 1.0E-6; maximum 1000
- Continuously compounded risk-free rate — %; minimum -100; maximum 1000
- Continuous dividend yield — %; minimum -100; maximum 1000
- Option type — 2 choices
Worked example
| Input | Value |
|---|---|
| Underlying price | 100 |
| Strike price | 100 |
| Time to expiry | 1 |
| Volatility | 20 |
| Continuously compounded risk-free rate | 5 |
| Continuous dividend yield | 0 |
| Option type | call |
Theoretical European call value ≈ 10.45 currency units.
Assumptions and limits
- The option is European and can be exercised only at expiry.
- Volatility, rates, and dividend yield are continuous annual inputs and market prices are not fetched.
- Early exercise, discrete dividends, jumps, bid-ask spreads, liquidity, and model error are not represented.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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