Unlock the power of the Black-Scholes model to accurately estimate theoretical option prices. Our free, easy-to-use calculator helps investors and traders determine fair values for call and put options, factoring in key variables like stock price, strike price, time to expiration, volatility, and risk-free rate. Make informed trading decisions with precise valuations.
Formula:
The Black-Scholes model calculates the theoretical price of European-style options. The core formulas are:
Call Option Price (C) = S × e-qT × N(d1) - K × e-rT × N(d2)
Put Option Price (P) = K × e-rT × N(-d2) - S × e-qT × N(-d1)
Where:
- d1 = [ ln(S/K) + (r - q + (σ2/2)) × T ] / (σ × √T)
- d2 = d1 - σ × √T
- S = Current Stock Price
- K = Strike Price of the Option
- T = Time to Expiration (in years, e.g., 0.5 for 6 months)
- σ = Volatility of the Stock (annualized, decimal, e.g., 0.20 for 20%)
- r = Risk-Free Interest Rate (annualized, decimal, e.g., 0.05 for 5%)
- q = Dividend Yield (annualized, decimal, e.g., 0.01 for 1%)
- N(x) = Cumulative Standard Normal Distribution Function
- e = Euler's Number (approx. 2.71828)
- ln = Natural Logarithm