Financial Option Pricing Calculator
Financial Option Pricing Calculator computes the price of a European call or put option using the Black-Scholes model. Enter stock price \\( S \\), strike price \\( K \\), time to maturity \\( T \\), risk-free rate \\( r \\), volatility \\( \sigma \\), and option type.
Black-Scholes Model
The Black-Scholes model prices European options. For a call option:
\\[
C = S \cdot N(d_1) – K e^{-rT} \cdot N(d_2)
\\]
For a put option:
\\[ P = K e^{-rT} \cdot N(-d_2) – S \cdot N(-d_1) \\]Where:
- \\( S \\): Stock price
- \\( K \\): Strike price
- \\( T \\): Time to maturity (years)
- \\( r \\): Risk-free rate (annual, as a decimal)
- \\( \sigma \\): Volatility (annual, as a decimal)
- \\( N(x) \\): Cumulative distribution function of the standard normal distribution
- \\( d_1 = \frac{\ln(S/K) + (r + \sigma^2/2)T}{\sigma \sqrt{T}} \\)
- \\( d_2 = d_1 – \sigma \sqrt{T} \\)