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Author: Patrick S. Hagan
Publisher: Cambridge University Press
ISBN: 1009339303
Category : Business & Economics
Languages : en
Pages : 85
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Book Description
In this Element the authors review the technique of the change of numeraire in the martingale approach to option pricing. Their intention is to present a reader friendly explanation of the technique itself, and illustrate how it is applied in various fields of quantitative finance as the basis for building option valuation models. They start with an informal review of Girsanov's theorem, followed by a brief summary of the basic concepts of the arbitrage free pricing, and the technique of change of numeraire. This is followed by a number of applications of the change of numeraire technique including interest rate models, FX quanto adjustments, credit risk modeling, mortgage backed securities, and CMS rates.
Author: Patrick S. Hagan
Publisher: Cambridge University Press
ISBN: 1009339303
Category : Business & Economics
Languages : en
Pages : 85
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Book Description
In this Element the authors review the technique of the change of numeraire in the martingale approach to option pricing. Their intention is to present a reader friendly explanation of the technique itself, and illustrate how it is applied in various fields of quantitative finance as the basis for building option valuation models. They start with an informal review of Girsanov's theorem, followed by a brief summary of the basic concepts of the arbitrage free pricing, and the technique of change of numeraire. This is followed by a number of applications of the change of numeraire technique including interest rate models, FX quanto adjustments, credit risk modeling, mortgage backed securities, and CMS rates.
Author: Glenn Shafer
Publisher: John Wiley & Sons
ISBN: 1118548027
Category : Business & Economics
Languages : en
Pages : 559
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Book Description
Game-theoretic probability and finance come of age Glenn Shafer and Vladimir Vovk’s Probability and Finance, published in 2001, showed that perfect-information games can be used to define mathematical probability. Based on fifteen years of further research, Game-Theoretic Foundations for Probability and Finance presents a mature view of the foundational role game theory can play. Its account of probability theory opens the way to new methods of prediction and testing and makes many statistical methods more transparent and widely usable. Its contributions to finance theory include purely game-theoretic accounts of Ito’s stochastic calculus, the capital asset pricing model, the equity premium, and portfolio theory. Game-Theoretic Foundations for Probability and Finance is a book of research. It is also a teaching resource. Each chapter is supplemented with carefully designed exercises and notes relating the new theory to its historical context. Praise from early readers “Ever since Kolmogorov's Grundbegriffe, the standard mathematical treatment of probability theory has been measure-theoretic. In this ground-breaking work, Shafer and Vovk give a game-theoretic foundation instead. While being just as rigorous, the game-theoretic approach allows for vast and useful generalizations of classical measure-theoretic results, while also giving rise to new, radical ideas for prediction, statistics and mathematical finance without stochastic assumptions. The authors set out their theory in great detail, resulting in what is definitely one of the most important books on the foundations of probability to have appeared in the last few decades.” – Peter Grünwald, CWI and University of Leiden “Shafer and Vovk have thoroughly re-written their 2001 book on the game-theoretic foundations for probability and for finance. They have included an account of the tremendous growth that has occurred since, in the game-theoretic and pathwise approaches to stochastic analysis and in their applications to continuous-time finance. This new book will undoubtedly spur a better understanding of the foundations of these very important fields, and we should all be grateful to its authors.” – Ioannis Karatzas, Columbia University
Author: Tomas Björk
Publisher: Oxford University Press
ISBN: 019153384X
Category : Arbitrage
Languages : en
Pages : 486
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Book Description
The second edition of this popular introduction to the classical underpinnings of the mathematics behind finance continues to combine sounds mathematical principles with economic applications. Concentrating on the probabilistics theory of continuous arbitrage pricing of financial derivatives, including stochastic optimal control theory and Merton's fund separation theory, the book is designed for graduate students and combines necessary mathematical background with a solid economic focus. It includes a solved example for every new technique presented, contains numerous exercises and suggests further reading in each chapter. In this substantially extended new edition, Bjork has added separate and complete chapters on measure theory, probability theory, Girsanov transformations, LIBOR and swap market models, and martingale representations, providing two full treatments of arbitrage pricing: the classical delta-hedging and the modern martingales. More advanced areas of study are clearly marked to help students and teachers use the book as it suits their needs.
Author: Antoon Pelsser
Publisher: Springer Science & Business Media
ISBN: 1447138880
Category : Mathematics
Languages : en
Pages : 177
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Book Description
This book provides an overview of the models that can be used for valuing and managing interest rate derivatives. Split into two parts, the first discusses and compares the traditional models, such as spot- and forward-rate models, while the second concentrates on the more recently developed Market models. Unlike most of his competitors, the author's focus is not only on the mathematics: Antoon Pelsser draws on his experience in industry to explore a host of practical issues.
Author: Kerry Back
Publisher: Springer Science & Business Media
ISBN: 3540279008
Category : Business & Economics
Languages : en
Pages : 358
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Book Description
"Deals with pricing and hedging financial derivatives.... Computational methods are introduced and the text contains the Excel VBA routines corresponding to the formulas and procedures described in the book. This is valuable since computer simulation can help readers understand the theory....The book...succeeds in presenting intuitively advanced derivative modelling... it provides a useful bridge between introductory books and the more advanced literature." --MATHEMATICAL REVIEWS
Author: Patrice Poncet
Publisher: Springer Nature
ISBN: 3030846008
Category : Business & Economics
Languages : en
Pages : 1385
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Book Description
This book offers a comprehensive and coherent presentation of almost all aspects of Capital Market Finance, providing hands-on knowledge of advanced tools from mathematical finance in a practical setting. Filling the gap between traditional finance textbooks, which tend to avoid advanced mathematical techniques used by professionals, and books in mathematical finance, which are often more focused on mathematical refinements than on practical uses, this book employs advanced mathematical techniques to cover a broad range of key topics in capital markets. In particular, it covers all primitive assets (equities, interest and exchange rates, indices, bank loans), most vanilla and exotic derivatives (swaps, futures, options, hybrids and credit derivatives), portfolio theory and management, and risk assessment and hedging of individual positions as well as portfolios. Throughout, the authors emphasize the methodological aspects and probabilistic foundations of financial asset valuation, risk assessment and measurement. Background in financial mathematics, particularly stochastic calculus, is provided as needed, and over 200 fully worked numerical examples illustrate the theory. Based on the authors' renowned master's degree courses, this book is written for students in business and finance, as well as practitioners in quantitative finance. Apart from an undergraduate-level knowledge of calculus, linear algebra and probability, the book is self-contained with no prior knowledge of market finance required.
Author: Amir Sadr
Publisher: John Wiley & Sons
ISBN: 0470443944
Category : Business & Economics
Languages : en
Pages : 276
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Book Description
An up-to-date look at the evolution of interest rate swaps and derivatives Interest Rate Swaps and Derivatives bridges the gap between the theory of these instruments and their actual use in day-to-day life. This comprehensive guide covers the main "rates" products, including swaps, options (cap/floors, swaptions), CMS products, and Bermudan callables. It also covers the main valuation techniques for the exotics/structured-notes area, which remains one of the most challenging parts of the market. Provides a balance of relevant theory and real-world trading instruments for rate swaps and swap derivatives Uses simple settings and illustrations to reveal key results Written by an experienced trader who has worked with swaps, options, and exotics With this book, author Amir Sadr shares his valuable insights with practitioners in the field of interest rate derivatives-from traders and marketers to those in operations.
Author: Jiongmin Yong
Publisher: World Scientific
ISBN: 9814489697
Category : Mathematics
Languages : en
Pages : 286
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Book Description
The book deals with topics such as the pricing of various contingent claims within different frameworks, risk-sensitive problems, optimal investment, defaultable term structure, etc. It also reflects on some recent developments in certain important aspects of mathematical finance.
Author: Jiongmin Yong
Publisher: World Scientific
ISBN: 9810247974
Category : Mathematics
Languages : en
Pages : 286
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Book Description
The book deals with topics such as the pricing of various contingent claims within different frameworks, risk-sensitive problems, optimal investment, defaultable term structure, etc. It also reflects on some recent developments in certain important aspects of mathematical finance.
Author: Hanno Damm
Publisher: GRIN Verlag
ISBN: 3638709140
Category :
Languages : en
Pages : 89
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Book Description
Diploma Thesis from the year 2002 in the subject Business economics - Investment and Finance, grade: 1,0, University of Bonn (Institut f r Gesellschafts- und Wirtschaftswissenschaften, Statistische Abteilung), 48 entries in the bibliography, language: English, abstract: The growing importance of credit derivatives creates the need to price them in a market consistent manner. In this thesis the well known and accepted Libor Market Model is extended following Sch nbucher (2000). The thesis consists of two main parts: one describing and explaining the theoretical framework that will yield the pricing formulae for credit derivatives, and a second part explaining how to practically implement and calibrate the model. The second part also reports results of our implementation. We show that approximations introduced by Sch nbucher (2000) hold and that the model can be used to price defaultable bonds, credit default swaps as well as options on credit default swaps. The thesis has been written at the Department of Statistics, University of Bonn in cooperation with Deutsche Postbank AG Credit Risk Management.
