The Black–Scholes model is a mathematical description of financial markets and derivative investment instruments. The model develops partial differential equations whose solution, the Black–Scholes formula, is widely used in the pricing of European-style options.A model of price variation over time of financial instruments such as stocks that can, among other things, be used to determine the price of a European call option. The model assumes that the price of heavily traded assets follow a geometric Brownian motion with constant drift and volatility. When applied to a stock option, the model 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.
Also known as the Black-Scholes-Merton Model.
The Black Scholes Model is one of the most important concepts in modern financial theory. It was developed in 1973 by Fisher Black, Robert Merton and Myron Scholes and is still widely used today, and regarded as one of the best ways of determining fair prices of options.
There are a number of variants of the original Black-Scholes model. The Black–Scholes model of the market for a particular equity makes the following explicit assumptions:
- It is possible to borrow and lend cash at a known constant risk-free interest rate. This restriction has been removed in later extensions of the model.
- The price follows a Geometric Brownian motion with constant drift and volatility. It follows from this that the return is a Log-normal distribution. This often implies the validity of the efficient-market hypothesis.
- There are no transaction costs or taxes.
- The stock does not pay a dividend (see below for extensions to handle dividend payments).
- All securities are perfectly divisible (i.e. it is possible to buy any fraction of a share).
- There are no restrictions on short selling.
- There is no arbitrage opportunity
- Options use the European exercise terms, which dictate that options may only be exercised on the day of expiration.