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The Black-Scholes model is an attempt to simplify the markets for both financial assets and derivatives into a set of mathematical rules. The model serves as the basis for a wide range of analysis of markets. The best known example is a formula that can produce a theoretical objective price for an options contract, allowing investors to consider where the actual price on offer represents good value. The main advantage of the model is that it works entirely on 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 make calculations.
The main use of the model is to deal with options pricing. An option is a financial contract by which one party buys the right to purchase a designated asset, such as a stock, from the other party on a future date at a price agreed in advance. The option's value comes from the fact that the market price for the asset may be higher than the agreed price on this date. This will allow the buyer to exercise the option, buy the asset, and sell it at an immediate profit. This differs from, and is far more valuable to the buyer than, a futures contract in which the buyer must complete the deal regardless of the market price on the completion date.
The options contract system means that the buyer of the contract can sell his position in the deal to another party before the completion date. This turns the options contract into an asset in its own right, with prices varying due to market demand and supply. The Black-Scholes model attempts to use mathematics to take account of the various factors that affect this demand and supply.
The result of the model is a pricing formula that takes account of five variable factors: the current price of the asset on which the option is based; the price at which the option holder has the right to buy the asset; the amount of time left until the contract expires; the volatility of the asset price, which determines how predictable its market price will be on expiry day; and the current rates on offer for risk-free investments such as government bonds. The last point is designed to take account of the fact that the higher the return available from risk-free investments, the less impressive the potential return on an options contract looks in comparison.
The main disadvantage of the Black-Scholes model is that it makes several assumptions that are not necessarily true in reality. This includes the fact that even so-called risk-free investments, such as government bonds, still carry a slim possibility of default. Another factor is that the pricing doesn't take account of transaction costs or taxes. The formula also fails to take account of any dividends the holder of the underlying asset may receive.