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
- \( d_1 = \frac{\ln(S/K) + (r + \sigma^2/2)T}{\sigma \sqrt{T}} \)
- \( d_2 = d_1 – \sigma \sqrt{T} \)