# Black Scholes Calculator

Calculate option prices using our Black-Scholes Calculator. Accurately price stock options with ease. Try our free calculator now and make informed investment decisions.

Result Call Price \$0 Put Price \$0

## Black-Scholes Formula

The Black-Scholes formula is a mathematical model used to calculate the theoretical value of European-style stock options, assuming that the underlying stock prices follow a lognormal distribution with constant volatility and that there are no transaction costs or taxes.

The formula takes into account six variables: the current stock price, the option strike price, the time until expiration, the risk-free interest rate, the implied volatility of the stock price, and the dividend yield of the stock.

The formula is as follows:

```S = current stock price
K = option strike price
t = time until expiration (in years)
r = risk-free interest rate
σ = implied volatility
q = dividend yield

d1 = (ln(S/K) + (r - q + σ²/2)t) / (σ * √t)
d2 = d1 - σ * √t

Call option price = S * e^(-q*t) * N(d1) - K * e^(-r*t) * N(d2)
Put option price = K * e^(-r*t) * N(-d2) - S * e^(-q*t) * N(-d1)```

Where N() is the standard normal cumulative distribution function.

More Articles