Black-Scholes Option Price Calculator
European call option price, with d₁, d₂, the discounted strike and the intrinsic value.
Results
What this tool does
The gap between the calculated price and the intrinsic value is the time value — what the market pays for the chance the option moves further into the money before it expires. It is largest at the money and shrinks to nothing at expiry, which is the whole reason options decay. Volatility is the only input you cannot look up, and it is the one the answer is most sensitive to.
Formula
C = S N(d₁) − K e^(−rT) N(d₂)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
sp | Current price | — |
kp | Strike price | — |
rr | Risk-free rate | % |
sg | Volatility | % |
tt | Time to expiry | a |
CA | Call option price | — |
D1 | d₁ | — |
D2 | d₂ | — |
PV | Present value | — |
IV | Intrinsic value | — |
Worked example
- Current price100
- Strike price100
- Risk-free rate5 %
- Volatility20 %
- Time to expiry1 a
- Call option price10.4506
- d₁0.350000
- d₂0.150000
- Present value95.1229
- Intrinsic value0.0000
Limitations
- This is an informational calculator, not personalised financial advice. Rates, fees, taxes and contract conditions vary between institutions and countries.
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
Frequently asked questions
How exact is this?
The formula itself is exact for a European option under its own assumptions. The cumulative normal distribution it needs has no closed form, so this uses the rational approximation published as 26.2.17 in Abramowitz and Stegun, whose error is below 7.5 × 10⁻⁸ — far smaller than the uncertainty in the volatility you feed it. The assumptions are the real limitation: constant volatility, no dividends, no transaction costs, and exercise only at expiry.