Implementing Models in Quantitative Finance

Methods and Cases

By: Gianluca Fusai, Andrea Roncoroni

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eText | 20 December 2007

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Introduction This book presents and develops major numerical methods currently used for solving problems arising in quantitative ?nance. Our presentation splits into two parts. Part I is methodological, and offers a comprehensive toolkit on numerical me- ods and algorithms. This includes Monte Carlo simulation, numerical schemes for partial differential equations, stochastic optimization in discrete time, copula fu- tions, transform-based methods and quadrature techniques. Part II is practical, and features a number of self-contained cases. Each case introduces a concrete problem and offers a detailed, step-by-step solution. Computer code that implements the cases and the resulting output is also included. The cases encompass a wide variety of quantitative issues arising in markets for equity, interest rates, credit risk, energy and exotic derivatives. The corresponding problems cover model simulation, derivative valuation, dynamic hedging, portfolio selection, risk management, statistical estimation and model calibration. R We provide algorithms implemented using either Matlab or Visual Basic for R Applications (VBA). Several codes are made available through a link accessible from the Editor's web site. Origin Necessity is the mother of invention and, as such, the present work originates in class notes and problems developed for the courses "Numerical Methods in Finance" and "Exotic Derivatives" offered by the authors at Bocconi University within the Master in Quantitative Finance and Insurance program (from 2000-2001 to 2003-2004) and the Master of Quantitative Finance and Risk Management program (2004-2005 to present).