Black–Scholes Option Pricer (Educational)
Educational Black–Scholes European call and put values with Greeks (delta, gamma, theta, vega, rho) — assumes continuous dividend yield.
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Educational Black–Scholes–Merton
Closed-form pricing assumes log-normal returns, constant volatility and rate, no jumps, and frictionless markets. Real markets violate these assumptions. This is not trading, valuation, or accounting advice.
Inputs
European call & put (continuous yield)
Continuous dividend yield q enters d1/d2 in the standard Merton extension; toggle it in advanced mode.
Advanced mode
Continuous dividend / carry yield on the underlying.
Outputs
Model prices
Call value
10.94
Put value
6.54
d1
0.3145
d2
0.0945
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Perspective
Models assume frictionless markets
Real markets have bid-ask spreads, discrete dividends, early exercise for Americans, and volatility smiles.
Use for learning; never as the sole basis for trades.
FAQ
Common questions
European vs American?
Black–Scholes here is European (no early exercise). American options may be worth more.
What units for time and volatility?
Time in years (e.g. 0.25 = 3 months); volatility as annualized decimal (e.g. 0.20 for 20%).
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