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Computational finance is increasingly important in the financial industry, as a necessary instrument for applying theoretical models to real-world challenges. Indeed, many models used in practice involve complex mathematical problems, for which an exact or a closed-form solution is not available. Consequently, we need to rely on computational techniques and specific numerical algorithms. This book combines theoretical concepts with practical implementation. Furthermore, the numerical solution of models is exploited, both to enhance the understanding of some mathematical and statistical notions, and to acquire sound programming skills in MATLAB®, which is useful for several other programming languages also. The material assumes the reader has a relatively limited knowledge of mathematics, probability, and statistics. Hence, the book contains a short description of the fundamental tools needed to address the two main fields of quantitative finance: portfolio selection and derivatives pricing. Both fields are developed here, with a particular emphasis on portfolio selection, where the author includes an overview of recent approaches. The book gradually takes the reader from a basic to medium level of expertise by using examples and exercises to simplify the understanding of complex models in finance, giving them the ability to place financial models in a computational setting. The book is ideal for courses focusing on quantitative finance, asset management, mathematical methods for economics and finance, investment banking, and corporate finance.
List of contents
Part I: Programming techniques for financial calculus 1. An introduction to MATLAB with applications Part II: Portfolio Selection 2. Preliminary elements in Probability Theory and Statistics 3. Linear and Non-linear Programming 4. Portfolio Optimization Part III: Derivatives pricing 5. Further elements on Probability Theory and Statistics 6. Pricing of derivatives with an underlying security
About the author
Francesco Cesarone is an Assistant Professor of Computational Finance at the Department of Business Studies of the Roma Tre University, Italy.
Summary
The theoretical aspects of the book are based on an essential introduction to the building blocks of the two topics under consideration: mathematical programming and stochastic processes. It also includes a primer on MATLAB, as a tool to help students, scholars and practitioners use the concepts in the book.
