Read more
Informationen zum Autor MICHAEL AICHINGER obtained his Ph.D. in Theoretical Physics from the Johannes Kepler University Linz with a thesis on numerical methods in density functional theory and their application to 2D finite electron systems. A mobility grant led him to the Texas A&M University (2003) and to the Helsinki University of Technology (2004). In 2007 Michael Aichinger joined the Industrial Mathematics Competence Center where he has been working as a senior researcher and consultant in the field of quantitative finance for the last five years. He also works for the Austrian Academy of Sciences at the Radon Institute for Computational and Applied Mathematics where he is involved in several industrial mathematics and computational physics projects. Michael has (co-) authored around 20 journal articles in the fields of computational physics and quantitative finance. ANDREAS BINDER obtained his Ph.D. in Industrial Mathematics from the Johannes Kepler University Linz with a thesis on continuous casting of steel. A research grant led him to the Oxford Center for Industrial and Applied Mathematics, UK, in 1991, where he got in touch with mathematical finance for the first time. After some years being an assistant professor at the Industrial Mathematics Institute, in 1996, he left university and became managing director of MathConsult GmbH, where he heads also the Computational Finance Group. Andreas has authored two introductory books on mathematical finance and 25 journal articles in the fields of industrial mathematics and of mathematical finance. Klappentext A comprehensive introduction to various numerical methods used in computational finance todayQuantitative skills are a prerequisite for anyone working in finance or beginning a career in the field, as well as risk managers. A thorough grounding in numerical methods is necessary, as is the ability to assess their quality, advantages, and limitations. This book offers a thorough introduction to each method, revealing the numerical traps that practitioners frequently fall into. Each method is referenced with practical, real-world examples in the areas of valuation, risk analysis, and calibration of specific financial instruments and models. It features a strong emphasis on robust schemes for the numerical treatment of problems within computational finance. Methods covered include PDE/PIDE using finite differences or finite elements, fast and stable solvers for sparse grid systems, stabilization and regularization techniques for inverse problems resulting from the calibration of financial models to market data, Monte Carlo and Quasi Monte Carlo techniques for simulating high dimensional systems, and local and global optimization tools to solve the minimization problem. Zusammenfassung A comprehensive introduction to various numerical methods used in computational finance today Quantitative skills are a prerequisite for anyone working in finance or beginning a career in the field, as well as risk managers. Inhaltsverzeichnis Acknowledgements xiii About the Authors xv 1 Introduction and Reading Guide 1 2 Binomial Trees 7 2.1 Equities and Basic Options 7 2.2 The One Period Model 8 2.3 The Multiperiod Binomial Model 9 2.4 Black-Scholes and Trees 10 2.5 Strengths and Weaknesses of Binomial Trees 12 2.5.1 Ease of Implementation 12 2.5.2 Oscillations 12 2.5.3 Non-recombining Trees 14 2.5.4 Exotic Options and Trees 14 2.5.5 Greeks and Binomial Trees 15 2.5.6 Grid Adaptivity and Trees 15 2.6 Conclusion 16 3 Finite Differences and the Black-Scholes PDE 17 3.1 A Continuous Time Model for Equity Prices 17 3.2 Black-Scholes Model: From the SDE to the PDE 19 3.3 Finite Differences 23 3.4 Time Discretization 27 3.5 Stability Considerations 30 ...
