Black Scholes Calculator

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.