FINANCE & TAX CALCULATOR
Black Scholes
A precise tool.
What is the Black Scholes & How does it work?
The Black-Scholes model is a mathematical model for the dynamics of a financial market containing derivative investment instruments, such as stock options. It was developed by Fischer Black and Myron Scholes in 1973.
The model assumes that the price of the underlying asset follows a geometric Brownian motion with constant drift and volatility. This assumption simplifies the derivation of the option pricing formula.
The model assumes that the price of the underlying asset follows a geometric Brownian motion with constant drift and volatility. This assumption simplifies the derivation of the option pricing formula.
C = S_0 N(d_1) – X e^{-rT} N(d_2)
S0 = Current stock price
X = Strike price
r = Risk-free interest rate
T = Time to maturity (in years)
N(x) = Cumulative distribution function of the standard normal distribution
d1 = frac{ln(frac{S_0}{X}) + (r + frac{sigma^2}{2})T}{sigma sqrt{T}}
d2 = d1 – sigma sqrt{T}
sigma = Volatility of the underlying asset
X = Strike price
r = Risk-free interest rate
T = Time to maturity (in years)
N(x) = Cumulative distribution function of the standard normal distribution
d1 = frac{ln(frac{S_0}{X}) + (r + frac{sigma^2}{2})T}{sigma sqrt{T}}
d2 = d1 – sigma sqrt{T}
sigma = Volatility of the underlying asset
Parameters
Result
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Frequently Asked Questions
What is the Black-Scholes Option Pricing Calculator?
It's a tool that uses the Black-Scholes model to calculate theoretical prices of European call and put options.
How does the Black-Scholes model work?
The model assumes stock price follows a geometric Brownian motion, then calculates option prices using current stock price, strike price, risk-free rate, volatility, and time to expiration.
What are the key inputs for the calculator?
You need the current stock price, strike price, risk-free interest rate, volatility of the underlying asset, and time to expiration in years.
Can this calculator be used for American options?
No, the Black-Scholes model is specifically designed for European-style options. It does not account for early exercise features found in American options.
What does N(d1) and N(d2) represent in the formula?
N(d1) and N(d2) are cumulative distribution function values of a standard normal distribution, used to calculate the probability components of the option price.
Why is volatility important in this model?
Volatility represents the expected variation in the underlying asset's price. Higher volatility increases the option's price because it increases the likelihood of a larger move in the stock price.
What does 'risk-free rate' mean in this context?
The risk-free rate is the theoretical rate of return of an investment with zero risk, typically represented by the yield on a government bond.
Results are for informational purposes only and do not constitute professional advice.