Implementing models in quantitative finance

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This book presents major numerical methods used in quantitative finance, divided into two parts. Part I focuses on methodology, offering a comprehensive toolkit that includes Monte Carlo simulation, numerical schemes for partial differential equations, stochastic optimization in discrete time, copula functions, transform-based methods, and quadrature techniques. Part II is practical, featuring self-contained cases that introduce specific problems along with detailed, step-by-step solutions. Included are computer codes that implement these cases and their outputs. The cases address a range of quantitative issues in equity, interest rates, credit risk, energy, and exotic derivatives, covering model simulation, derivative valuation, dynamic hedging, portfolio selection, risk management, statistical estimation, and model calibration. Algorithms are provided in Matlab and Visual Basic for Applications (VBA), with several codes accessible via a link on the Editor’s website. This work originated from class notes and problems developed for courses on Numerical Methods in Finance and Exotic Derivatives at Bocconi University, part of the Master in Quantitative Finance and Insurance and the Master of Quantitative Finance and Risk Management programs.