With an introduction to the needed mathematical financial theory, this book presents statistical and quantitative methods to implement and apply state-of-the-art financial models. It details the necessary steps for implementation of the models in MATLAB and provides the code; discusses the affine transform formalism; focuses on developing and utilizing the Kalman filter; and exploits the extended, Gauss-Hermite, unscented, Monte Carlo, and particle Kalman filters for nonlinear and non-Gaussian models.