The application of mathematics to important problems related to financial derivatives and risk management has expanded rapidly in recent years. The general area of this book is the application of mathematics to understanding properties of options. Options, in turn, are examples of what are referred to as derivative securities, or simply, derivatives. A derivative is a financial contract written on an underlying asset and it's value is derived from the value of this asset. The underlying asset might be a stock, a foreign currency, a treasury bill, a commodity, such as aviation fuel, or even another derivative. The two major types of derivatives are futures (or forwards) and options. They are traded on organized exchanges around the world, in which case the contracts are standardized with respect to most or all of the key variables. They can also be bought and sold through major banks and financial institutions in which case they are referred to as over-the counter derivatives.