Black Scholes Calculator
You can use this BlackScholes Calculator to determine the fair market value (price) of a European put or call option based on the BlackScholes pricing model. It also calculates and plots the Greeks – Delta, Gamma, Theta, Vega, Rho.
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 BlackScholes Option Pricing Formula
You can compare the prices of your options by using the BlackScholes formula. It's a wellregarded formula that calculates theoretical values of an investment based on current financial metrics such as stock prices, interest rates, expiration time, and more. The BlackScholes 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 riskfree 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).
What is Black Scholes Calculator
A BlackScholes calculator is a tool used to estimate the price of options contracts using the BlackScholes model. The BlackScholes model is a mathematical model developed by economists Fisher Black and Myron Scholes in 1973 to calculate the theoretical value of Europeanstyle options.
Here's how a BlackScholes calculator typically works:

Inputs: The calculator requires several inputs to estimate the option price:
 Underlying Asset Price: The current market price of the underlying asset (e.g., stock, index).
 Strike Price: The predetermined price at which the option can be exercised.
 Time to Expiration: The length of time until the option contract expires.
 RiskFree Interest Rate: The riskfree interest rate over the option's term.
 Volatility: The standard deviation of the underlying asset's returns, representing its price fluctuation.

Calculation: Using the provided inputs, the BlackScholes calculator applies the following formula to estimate the option price:
 For a call option: C = S * N(d1)  X * e^(rt) * N(d2)
 For a put option: P = X * e^(rt) * N(d2)  S * N(d1)
where:
 C/P = Call/Put option price
 S = Underlying asset price
 X = Strike price
 t = Time to expiration
 r = Riskfree interest rate
 N() = Cumulative standard normal distribution function
 d1 = (ln(S/X) + (r + σ²/2)t) / (σ * sqrt(t))
 d2 = d1  σ * sqrt(t)
 σ = Volatility

Displaying the Result: The calculator provides the estimated price of the call or put option based on the BlackScholes model as the output.
It's important to note that the BlackScholes model assumes certain factors, such as constant volatility, no dividends, and efficient markets. Therefore, the calculated option price may not perfectly match the market price due to realworld complexities and assumptions.
BlackScholes calculators are widely used in financial markets, options trading, risk management, and quantitative finance for pricing and evaluating options contracts. They provide a useful tool for investors, traders, and analysts to assess the fair value of options and make informed investment decisions.
Black Scholes Calculator Example
Certainly! The BlackScholes model is used to calculate the theoretical price of options. Let's consider an example of using the BlackScholes formula to calculate the value of a call option.
Assume the following parameters:
 Stock price (S): $100
 Strike price (K): $105
 Time to expiration (T): 1 year
 Riskfree interest rate (r): 0.05 (5%)
 Volatility (σ): 0.2 (20%)
Using these parameters, we can calculate the value of the call option using the BlackScholes formula:
d1 = (ln(S/K) + (r + σ^2/2) * T) / (σ * sqrt(T)) = (ln(100/105) + (0.05 + 0.2^2/2) * 1) / (0.2 * sqrt(1)) ≈ 0.0889
d2 = d1  σ * sqrt(T) = 0.0889  0.2 * sqrt(1) ≈ 0.2889
Using a standard normal cumulative distribution function, we can calculate N(d1) and N(d2). Let's assume N(d1) = 0.4641 and N(d2) = 0.3805.
Call option value (C) = S * N(d1)  K * e^(rT) * N(d2) = 100 * 0.4641  105 * e^(0.05 * 1) * 0.3805 = 46.41  105 * 0.9753 * 0.3805 ≈ 46.41  39.90 ≈ $6.51
Therefore, using the BlackScholes formula, the value of the call option in this example is approximately $6.51.
Please note that this is a simplified example for illustrative purposes, and the BlackScholes model has assumptions and limitations. In practice, option pricing can be more complex, and there are variations and refinements to the basic model to consider.