how the black scholes model works
black scholes posits that instruments such as stock shares or futures contracts will have a lognormal distribution of prices following a random walk with constant drift and volatility the equation uses this assumption and factors in other important variables to derive the price of a european style call option the black scholes equation requires six variables volatility the price of the underlying asset the strike price of the option the time until the expiration of the option the risk free interest rate and the type of option whether it s call or put it s theoretically possible for options sellers to set rational prices with these variables for the options that they re selling the model predicts that the price of heavily traded assets follows a geometric brownian motion with constant drift and volatility it incorporates the constant price variation of the stock the time value of money the option s strike price and the time to the option s expiry when it s applied to a stock option the black scholes model is often contrasted against the binomial model or a monte carlo simulation the black scholes model makes certain assumptions the original black scholes model didn t consider the effects of dividends paid during the life of the option but the model is frequently adapted to account for dividends by determining the ex dividend date value of the underlying stock the model is also modified by many option selling market makers to account for the effect of options that can be exercised before expiration firms will alternatively use a binomial or trinomial model or the bjerksund stensland model for the pricing of the more commonly traded american style options the black scholes model formulathe mathematics involved in the formula are complicated and can be intimidating but you don t have to know or even understand the math to use black scholes modeling in your strategies options traders have access to a variety of online options calculators and many trading platforms boast robust options analysis tools that include indicators and spreadsheets that perform the calculations and output the options pricing values the black scholes call option formula is calculated by multiplying the stock price by the cumulative standard normal probability distribution function the net present value npv of the strike price multiplied by the cumulative standard normal distribution is then subtracted from the resulting value of the previous calculation 