Black-Scholes Option Pricing Calculator

Formula

The Black-Scholes formulas for call and put options are:

Call Option Price: $ C = S_0 e^{-qt} N(d_1) - X e^{-rt} N(d_2) $

Put Option Price: $ P = X e^{-rt} N(-d_2) - S_0 e^{-qt} N(-d_1) $

where:

$ d_1 = \frac{\ln(\frac{S_0}{X}) + (r - q + \frac{v^2}{2})t}{v \sqrt{t}} $
$ d_2 = d_1 - v \sqrt{t} $

Description

The Black-Scholes model is used to determine the fair price of an option. It takes into account the current stock price, the option's strike price, time to maturity, risk-free rate, dividend yield, and volatility.

Example Calculation

Let's assume the following:

Stock Price: $400
Strike Price: $350
Term of Option: 1 year
Dividend Yield: 1%
Volatility: 20%
Risk-Free Interest Rate: 3%

For this example, the call option price is $65.67 and the put option price is $9.30.