# 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.

## 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(d1) - ST e-rt N(d2)

P = ST e-rt N(-d2) - SP e-dt N(-d1)

d1 = ( ln(SP/ST) + (r - d + (σ2/2)) t ) / σ √t

d2 = ( ln(SP/ST) + (r - d - (σ2/2)) t ) / σ √t = d1 - 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).

Black-Scholes Option Calculator

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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

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.

## 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(d1) - ST e-rt N(d2)

P = ST e-rt N(-d2) - SP e-dt N(-d1)

d1 = ( ln(SP/ST) + (r - d + (σ2/2)) t ) / σ √t

d2 = ( ln(SP/ST) + (r - d - (σ2/2)) t ) / σ √t = d1 - 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).

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