Options
Black-Scholes Calculator
Theoretical European option price with continuous dividend yield.
How the calculation works
Uses the Black–Scholes–Merton formula with continuous dividend yield q. d₁ and d₂ are the usual standardized terms; the call is S e^{-qT} N(d₁) − K e^{-rT} N(d₂) (put via put-call parity form). Intrinsic is separated so you can see time value.
Formula & example
Call = S e^{-qT} N(d₁) − K e^{-rT} N(d₂); put via corresponding formula
ATM S=K=100, T=1y, r=5%, q=0, σ=20% → call price ≈ $10.45 (model).
Why use this calculator
Market premiums embed IV; comparing model price to market (off-platform) helps separate intrinsic from time value under explicit assumptions.
When to use it
Use for educational European-style fair value estimates when you have spot, strike, time, rates, and an IV assumption.
Background
Fischer Black and Myron Scholes (1973), with Robert Merton’s continuous-dividend extension, established the canonical European option pricing PDE and closed form used here.
Tips for accurate results
- Ignores early exercise, discrete dividends, and fees.
- Very small T or σ are floored internally to keep math stable.
FAQ
Is this the same as the market price?
No. It is a model value for your inputs. Markets can and do trade away from model prices.
American options?
This tool is European-style. American puts (and calls on dividends) can be worth more due to early exercise.