Black Scholes Calculator


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.

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

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).

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