The Black-Scholes model is a formula designed to perform a wide range of analysis of financial markets.
The Black-Scholes model is an attempt to simplify the financial asset and derivatives markets into a set of mathematical rules. The model serves as the basis for a wide range of market analyses. The best-known example is a formula that can produce a theoretical target price for an options contract, allowing investors to consider where the actual offer price represents good value. The main advantage of the model is that it works entirely on the basis of objective figures rather than human judgment. Another benefit is that, although complex for human calculation, the formula is relatively simple in mathematical terms, so it does not require a sophisticated computer program to do the calculations.
The main use of the model is dealing with option pricing. An option is a financial contract whereby one party buys the right to purchase a designated asset, such as a share, from the other party at a future date at a pre-agreed price. The value of the option arises from the fact that the market price of the asset may be higher than the price agreed on that date. This will allow the buyer to exercise the option, buy the asset and sell it for an immediate profit. This differs from and is much more valuable to the buyer than a futures contract in which the buyer must complete the deal regardless of the market price on the date of completion.
The options contract system means that the buyer of the contract can sell his position in the business to another party before the completion date. This turns the options contract into an asset in its own right, with prices varying according to market supply and demand. The Black-Scholes model attempts to use mathematics to account for the various factors that affect this demand and supply.
The model output is a pricing formula that takes into account five variable factors: the current price of the asset on which the option is based; the price at which the option holder is entitled to purchase the asset; the amount of time remaining until the contract expires; the asset’s price volatility, which determines how predictable its market price will be on the expiration day; and current rates on offer for risk-free investments such as government bonds. The last point is designed to take into account the fact that the higher the available return on risk-free investments, the less impressive the potential return on an options contract will be in comparison.
The main disadvantage of the Black-Scholes model is that it makes a number of assumptions that are not necessarily true in reality. This includes the fact that even so-called risk-free investments, such as government bonds, still have a small chance of default. Another factor is that the price does not take into account transaction costs or taxes. The formula also does not take into account any dividends that the holder of the underlying asset may receive.