Financial Mathematics

This textbook provides complete coverage of discrete-time financial models that form the cornerstones of financial derivative pricing theory. Unlike similar texts in the field, this one presents multiple problem-solving approaches, linking related comprehensive techniques for pricing different types of financial derivatives. Key features: In-depth coverage of discrete-time theory and methodology. Numerous, fully worked out examples and exercises in every chapter. Mathematically rigorous and consistent yet bridging various basic and more advanced concepts. Judicious balance of financial theory, mathematical, and computational methods. Guide to Material. This revision contains: Almost 200 pages worth of new material in all chapters. A new chapter on elementary probability theory. An expanded the set of solved problems and additional exercises. Answers to all exercises. This book is a comprehensive, self-contained, and unified treatment of the main theory and application of mathematical methods behind modern-day financial mathematics. Table of Contents List of Figures and Tables Preface I Introduction to Pricing and Management of Financial Securities 1 Mathematics of Compounding 2 Primer on Pricing Risky Securities 3 Portfolio Management 4 Primer on Derivative Securities II Discrete-Time Modelling 5 Single-Period ArrowDebreu Models 6 Introduction to Discrete-Time Stochastic Calculus 7 Replication and Pricing in the Binomial Tree Model 8 General Multi-Asset Multi-Period Model Appendices A Elementary Probability Theory B Glossary of Symbols and Abbreviations C Answers and Hints to Exercises References Index Biographies Giuseppe Campolieti is Professor of Mathematics at Wilfrid Laurier University in Waterloo, Canada. He has been Natural Sciences and Engineering Research Council postdoctoral research fellow and university research fellow at the University of Toronto. In 1998, he joined the Masters in Mathematical Finance as an instructor and later as an adjunct professor in financial mathematics until 2002. Dr. Campolieti also founded a financial software and consulting company in 1998. He joined Laurier in 2002 as Associate Professor of Mathematics and as SHARCNET Chair in Financial Mathematics. Roman N. Makarov is Associate Professor and Chair of Mathematics at Wilfrid Laurier University. Prior to joining Laurier in 2003, he was an Assistant Professor of Mathematics at Siberian State University of Telecommunications and Informatics and a senior research fellow at the Laboratory of Monte Carlo Methods at the Institute of Computational Mathematics and Mathematical Geophysics in Novosibirsk, Russia.