A mathematical model used to calculate the theoretical price of an option.
The Black and Scholes model was published in 1973 by Fisher Black and Myron Scholes. It is one of the most popular, relative simple and fast modes of calculation. Unlike the binomial model, it does not rely on calculation by iteration.
This model is used to calculate a theoretical call price (ignoring the dividends paid during the life of the option) using the five key determinants of an option’s price: stock price, strike price, volatility, time to expiration, and short-term (risk free) interest rate.
The original formula for calculating the theoretical Option Price (OP) is: OP = SN(d1)-XertN(d2) Where, D1=[In(s/n)+(r+(v2/2)t]/ vvt D2
• S = stock price = d1-vvt And the variables are
• X = strike price
• t = time remaining until expiration, expressed in years
• r = current continuously compounded risk-free interest rate
• v = annual volatility of stock price (the standard deviation of the short-term returns over one year)
• In = natural logarithm
• N(x) = standard normal cumulative distribution function
• e = the exponential function