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 | ||||
---|---|---|---|---|---|
x | Variable | Symbol | Input Value | From | To |
Spot Price | SP | ||||
Strike Price | ST | ||||
Expiry Time (Y) | t | ||||
Volatility (%) | v | ||||
Rate (%) | r | ||||
Div. Yield (%) | d |
Option Type: Call Option
y | Axis | Symbol | Result |
---|---|---|---|
Value | |||
d1 | |||
d2 | |||
Delta | |||
Gamma | |||
Theta | |||
Vega | |||
Rho |
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
Where:
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).