Black-Scholes Calculator
Price European call/put options with Black-Scholes from spot, strike, time to expiry, annual volatility and risk-free rate.
Results
Fill in the inputs and click Calculate.
- Option Price
- –
- Intrinsic Value
- –
Risk disclaimer
This calculator provides theoretical reference prices, not investment advice. The model assumes constant volatility and rates; real prices reflect supply/demand, dividends and early exercise.
What is Black-Scholes?
Black-Scholes is the classic analytical model for European options. Price comes from the probability-weighted time value: higher volatility and longer time raise the price.
Crypto options often mix European/American features; this tool outputs a standard European theoretical reference, not an executable quote.
How to use
- Choose call or put.
- Enter spot, strike and time to expiry in years (e.g. 90 days ≈ 0.2466).
- Enter annual volatility % (e.g. 60 = 60%) and risk-free rate % (default 0).
- Click Calculate to get the theoretical price and intrinsic value.
Formula
- C = S·N(d1) − K·e^(−rT)·N(d2)
- P = K·e^(−rT)·N(−d2) − S·N(−d1)
- d1 = [ln(S/K) + (r + σ²/2)T] ÷ (σ√T), d2 = d1 − σ√T
Example
Spot 100, strike 100, 1 year, vol 20%, rate 5%: Call ≈ 10.45.
At 60% vol the same call is noticeably pricier, showing volatility's effect on time value.
FAQ
How well does it fit crypto options?
Crypto options are volatile and often near-European settlement. Treat this as a theoretical reference; quotes also depend on supply and demand.
How do I enter time?
In years: 3 months ≈ 0.25, 90 days ≈ 0.2466, or divide remaining days by 365.