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Derivatives in financial market play an important and useful role in hedging and managing risk. Derivative securities, when used correctly, can help investors increase their expected returns and minimize their exposure to risk. Options offer leverage and insurance for risk-averse investors. For the risk-alike investors, they can be ways of speculation. However, the values of option depend on a number of different variables in addition to the underlying asset, which makes them hard to value. This book explored some commonly used pricing models and compared their accuracy for the valuation. In the last section, it introduced a new numerical scheme --- the Radial Basis Function Method (RBF), particularly Hardy s multiquadric (MQ) as a spatial approximation for the numerical solution of the option value and its derivatives.