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A Workout in Computational Finance: with Website (The Wiley Finance Series)

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<p>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.</p><br/><p>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.</p><br/><p>Acknowledgements xiiiAbout the Authors xv1 Introduction and Reading Guide 12 Binomial Trees 72.1 Equities and Basic Options 72.2 The One Period Model 82.3 The Multiperiod Binomial Model 92.4 Black-Scholes and Trees 102.5 Strengths and Weaknesses of Binomial Trees 122.6 Conclusion 163 Finite Differences and the Black-Scholes PDE 173.1 A Continuous Time Model for Equity Prices 173.2 Black-Scholes Model: From the SDE to the PDE 193.3 Finite Differences 233.4 Time Discretization 273.5 Stability Considerations 303.6 Finite Differences and the Heat Equation 303.7 Appendix: Error Analysis 364 Mean Reversion and Trinomial Trees 394.1 Some Fixed Income Terms 394.2 Black76 for Caps and Swaptions 434.3 One-Factor Short Rate Models 454.3.1 Prominent Short Rate Models 454.4 The Hull-White Model in More Detail 464.5 Trinomial Trees 475 Upwinding Techniques for Short Rate Models 555.1 Derivation of a PDE for Short Rate Models 555.2 Upwind Schemes 565.3 A Puttable Fixed Rate Bond under the Hull-White One Factor Model 636. Boundary, Terminal and Interface Conditions and their Influence 716.1 Terminal Conditions for Equity Options 716.2 Terminal Conditions for Fixed

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