Overview
The Financial Derivatives project was developed to provide the lowest level of option pricing. Our numerical technique can also serve as a basis for higher level problems like risk management, portfolio management, and so forth.
Background
Stocks, or common shares, have been around for a couple of hundred years. The idea of distributing options, or derivatives, began to be widespread in 1973, although they existed previously on an 'over-the-counter' basis. In 1973 derivatives began to be officially traded on the Chicago Board Options Exchange. In 1992 there was an estimated $10 trillion in derivative investments worldwide.
The holder of a call option has a right, but not an obligation, to buy a stock at a prescribed price (strike price) on a prescribed date (expiry date). If the actual price of the stock is higher than the strike price, the holder may immediately sell the stock and profit from the difference. This is the simplest type of option, known as European Vanilla, and is only one of many kinds of options. Decisions about how and when to correctly exercise the options pose a complex problem.
These decisions present a difficult mathematical problem, to the extent that a new discipline, "Financial Mathematics", has been declared. Options were invented and are used by practicing financiers; they are issued and traded regardless of what theoreticians think. Before 1973, a common approach to model options pricing was through calculation of the expected profit. In 1973 Black-Sholes and Merton proposed an alternative approach to explain option pricing: the so called risk-less approach (which resulted in their Nobel prize). Though not perfect, their approach is a much better approximation of the real prices observed in options markets.
Who needs an option price calculation? All kinds of users (both speculators and hedgers) can gain from option pricing: banks, brokerage firms, pension funds, other funds, and individual investors; although each audience has their own demands. Although many problems can be solved using existing techniques, we believe that our Financial Derivatives technique solves these problems with higher accuracy and speed.