Investor's wiki

Black-Scholes Model

Black-Scholes Model

A methodology for esteeming options that considers whether an option is in the money or out of the money, the volatility of the underlying asset, the chance to expiration of the option, whether the option is a put or a call and the current rate of return on a risk-free asset, for example, a Treasury bill.


  • The Black-Scholes model, otherwise known as the Black-Scholes-Merton (BSM) model, is a differential equation widely used to price options contracts.
  • The standard BSM model is simply used to price European options, as it doesn't consider that American options could be practiced before the expiration date.
  • The Black-Scholes model requires five input factors: the strike price of an option, the current stock price, the opportunity to expiration, the risk-free rate, and the volatility.
  • However typically accurate, the Black-Scholes model creates certain assumptions that can lead to prices that digress from this present reality results.


What Are the Inputs for Black-Scholes Model?

The inputs for the Black-Scholes equation are volatility, the price of the underlying asset, the strike price of the option, the time until expiration of the option, and the risk-free interest rate. With these factors, it is theoretically feasible for options merchants to set rational prices for the options that they are selling.

What Assumptions Does Black-Scholes Model Make?

The Black-Scholes model makes certain assumptions. Chief among them is that the option is European and must be practiced at expiration. Different assumptions are that no dividends are paid out during the life of the option; that market developments can't be anticipated; that there are no transaction costs in buying the option; that risk-free rate and volatility of the underlying are known and steady; and that the returns on the underlying asset are log-normally distributed.

How Does the Black-Scholes Model Respond?

Black-Scholes, otherwise called Black-Scholes-Merton (BSM), was the principal widely involved model for option pricing. In view of the assumption that instruments, for example, stock shares or futures contracts, will have a lognormal distribution of prices following a random walk with steady drift and volatility, and figuring in other important factors, the equation determines the price of an European-style call option. It does as such by taking away the net present value (NPV) of the strike price duplicated by the cumulative standard normal distribution from the product of the stock price and the cumulative standard normal likelihood distribution function.

What Are the Limitations of the Black-Scholes Model?

The Black-Scholes model is simply used to price European options and doesn't consider that American options could be practiced before the expiration date. Besides, the model expects dividends, volatility, and risk-free rates stay steady over the option's life.Not considering taxes, commissions or trading costs or taxes can likewise lead to valuations that stray from genuine outcomes.