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"This edition contains more material. The largest addition is a new section on jump processes (Section 1.9). The derivation of a related partial integro differential equation is included in Appendix A3. More material is devoted to Monte Carlo simulation. An algorithm for the standard workhorse of in verting the normal distribution is added to Appendix A7. New figures and more exercises are intended to improve the clarity at some places. Several further references give hints on more advanced material and on important developments. Many small changes are hoped to improve the readability of this book. Further I have made an effort to correct misprints and errors that I knew about. A new domain is being prepared to serve the needs of the computational finance community, and to provide complementary material to this book. The address of the domain is www.compfin.de The domain is under construction; it replaces the website address www . mi. uni koeln.de/numerik/compfin/. Suggestions and remarks both on this book and on the domain are most welcome."@en
"Computational and numerical methods are used in a number of ways across the field of finance. It is the aim of this book to explain how such methods work in financial engineering. By concentrating on the field of option pricing, a core task of financial engineering and risk analysis, this book explores a wide range of computational tools in a coherent and focused manner and will be of use to the entire field of computational finance. Starting with an introductory chapter that presents the financial and stochastic background, the remainder of the book goes on to detail computational methods using both stochastic and deterministic approaches.Now in its fifth edition, Tools for Computational Finance has been significantly revised and contains:A new chapter on incomplete markets, which links to new appendices on viscosity solutions and the Dupire equation;Several new parts throughout the book such as that on the calculation of sensitivities (Sect. 3.7) and the introduction of penalty methods and their application to a two-factor model (Sect. 6.7)Additional material in the field of analytical methods including Kim's integral representation and its computationGuidelines for comparing algorithms and judging their efficiencyAn extended chapter on finite elements that now includes a discussion of two-asset optionsAdditional exercises, figures and referencesWritten from the perspective of an applied mathematician, all methods are introduced for immediate and straightforward application. A 'learning by calculating' approach is adopted throughout this book enabling readers to explore several areas of the financial world.Interdisciplinary in nature, this book will appeal to advanced undergraduate and graduate students in mathematics, engineering, and other scientific disciplines as well as professionals in financial engineering."
"Presents computational issues arising in financial mathematics. This guide to the financial engineering features revisions that concern topics like calibration, Monte Carlo Methods, American options, exotic options and Algorithms for Bermuda Options. It includes various figures, exercises, background material of financial engineering."
"This book is very easy to read and one can gain a quick snapshot of computational issues arising in financial mathematics. Researchers or students of the mathematical sciences with an interest in finance will find this book a very helpful and gentle guide to the world of financial engineering. SIAM review (46, 2004). The fourth edition is thoroughly revised and extended. Major revisions concern topics like calibration, Monte Carlo Methods, American options, exotic options and Algorithms for Bermuda Options. New figures, more exercises, more background material make this guide to the world of financial engineering a real must-to-have for everyone working in FE."@en
"Basic principles underlying the transactions of ?nancial markets are tied to probability and statistics. Accordingly it is natural that books devoted to mathematical ?nance are dominated by stochastic methods. Only in recent years, spurred by the enormous economical success of ?nancial derivatives, a need for sophisticated computational technology has developed. For - ample, to price an American put, quantitative analysts have asked for the numerical solution of a free-boundary partial di?erential equation. Fast and accurate numerical algorithms have become essential tools to price ?nancial derivatives and to manage portfolio risks. The required methods aggregate to the new ?eld of Computational Finance. This discipline still has an aura of mysteriousness; the ?rst specialists were sometimes called rocket scientists. So far, the emerging ?eld of computational ?nance has hardly been discussed in the mathematical ?nance literature. This book attempts to ?ll the gap. Basic principles of computational ?nance are introduced in a monograph with textbook character. The book is divided into four parts, arranged in six chapters and seven appendices. The general organization is Part I (Chapter 1): Financial and Stochastic Background Part II (Chapters 2, 3): Tools for Simulation Part III (Chapters 4, 5, 6): Partial Di?erential Equations for Options PartIV(AppendicesA1...A7):FurtherRequisitsandAdditionalMaterial."
"Basic principles underlying the transactions of ?nancial markets are tied to probability and statistics. Accordingly it is natural that books devoted to mathematical ?nance are dominated by stochastic methods. Only in recent years, spurred by the enormous economical success of ?nancial derivatives, a need for sophisticated computational technology has developed. For - ample, to price an American put, quantitative analysts have asked for the numerical solution of a free-boundary partial di?erential equation. Fast and accurate numerical algorithms have become essential tools to price ?nancial derivatives and to manage portfolio risks. The required methods aggregate to the new ?eld of Computational Finance. This discipline still has an aura of mysteriousness; the ?rst specialists were sometimes called rocket scientists. So far, the emerging ?eld of computational ?nance has hardly been discussed in the mathematical ?nance literature. This book attempts to ?ll the gap. Basic principles of computational ?nance are introduced in a monograph with textbook character. The book is divided into four parts, arranged in six chapters and seven appendices. The general organization is Part I (Chapter 1): Financial and Stochastic Background Part II (Chapters 2, 3): Tools for Simulation Part III (Chapters 4, 5, 6): Partial Di?erential Equations for Options PartIV(AppendicesA1...A7):FurtherRequisitsandAdditionalMaterial."@en

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