Black Scholes Calculator
You can use this Black-Scholes Calculator to determine the fair market value (price) of a European put or call option based on the Black-Scholes pricing model. It also calculates and plots the Greeks – Delta, Gamma, Theta, Vega, Rho.
Enter your own values in the form below and press the "Calculate" button to see the results.
|Option Type: Call Put||Values|
|Expiry Time (Y)||t|
|Div. Yield (%)||d|
Option Type: Call Option
The Black-Scholes Option Pricing Formula
You can compare the prices of your options by using the Black-Scholes formula. It's a well-regarded formula that calculates theoretical values of an investment based on current financial metrics such as stock prices , interest rates, expiration time, and more. The Black-Scholes formula helps investors and lenders to determine the best possible option for pricing.
The Black Scholes Calculator uses the following formulas:
C = SP e -dt N(d 1 ) - ST e -rt N(d 2 )
P = ST e -rt N(-d 2 ) - SP e -dt N(-d 1 )
d 1 = ( ln(SP/ST) + (r - d + (σ 2 /2)) t ) / σ √t
d 2 = ( ln(SP/ST) + (r - d - (σ 2 /2)) t ) / σ √t = d 1 - σ √t
C is the value of the call option,
P is the value of the put option,
N (.) is the cumulative standard normal distribution function,
SP is the current stock price (spot price),
ST is the strike price (exercise price),
e is the exponential constant (2.7182818),
ln is the natural logarithm ,
r is the current risk-free interest rate (as a decimal),
t is the time to expiration in years,
σ is the annualized volatility of the stock (as a decimal),
d is the dividend yield (as a decimal).