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. 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.
Об авторе
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 Math Consult Gmb H, 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.
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