Pricing Interest Rate Caps by Calibrating the Parameters of the Heath-Jarrow-Morton (HJM) Model

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Publisher :
ISBN 13 :
Total Pages : 160 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Pricing Interest Rate Caps by Calibrating the Parameters of the Heath-Jarrow-Morton (HJM) Model by :

Download or read book Pricing Interest Rate Caps by Calibrating the Parameters of the Heath-Jarrow-Morton (HJM) Model written by and published by . This book was released on 2002 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Elementary Introduction to Stochastic Interest Rate Modeling

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Publisher : World Scientific
ISBN 13 : 9812832734
Total Pages : 191 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis An Elementary Introduction to Stochastic Interest Rate Modeling by : Nicolas Privault

Download or read book An Elementary Introduction to Stochastic Interest Rate Modeling written by Nicolas Privault and published by World Scientific. This book was released on 2008 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is written as an accessible introduction to interest rate modeling and related derivatives, which have become increasingly important subjects of interest in financial mathematics. The models considered range from standard short rate to forward rate models and include more advanced topics such as the BGM model and an approach to its calibration. An elementary treatment of the pricing of caps and swaptions under forward measures is also provided, with a focus on explicit calculations and a step-by-step introduction of concepts. Each chapter is accompanied with exercises and their complete solutions, making this book suitable for advanced undergraduate or beginning graduate-level students.

Elementary Introduction To Stochastic Interest Rate Modeling, An (2nd Edition)

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Publisher : World Scientific
ISBN 13 : 9814401641
Total Pages : 243 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Elementary Introduction To Stochastic Interest Rate Modeling, An (2nd Edition) by : Nicolas Privault

Download or read book Elementary Introduction To Stochastic Interest Rate Modeling, An (2nd Edition) written by Nicolas Privault and published by World Scientific. This book was released on 2012-05-04 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest rate modeling and the pricing of related derivatives remain subjects of increasing importance in financial mathematics and risk management. This book provides an accessible introduction to these topics by a step-by-step presentation of concepts with a focus on explicit calculations. Each chapter is accompanied with exercises and their complete solutions, making the book suitable for advanced undergraduate and graduate level students.This second edition retains the main features of the first edition while incorporating a complete revision of the text as well as additional exercises with their solutions, and a new introductory chapter on credit risk. The stochastic interest rate models considered range from standard short rate to forward rate models, with a treatment of the pricing of related derivatives such as caps and swaptions under forward measures. Some more advanced topics including the BGM model and an approach to its calibration are also covered.

The Oxford Guide to Financial Modeling

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Publisher : Oxford University Press
ISBN 13 : 9780199727704
Total Pages : 770 pages
Book Rating : 4.7/5 (277 download)

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Book Synopsis The Oxford Guide to Financial Modeling by : Thomas S. Y. Ho

Download or read book The Oxford Guide to Financial Modeling written by Thomas S. Y. Ho and published by Oxford University Press. This book was released on 2004-01-15 with total page 770 pages. Available in PDF, EPUB and Kindle. Book excerpt: The essential premise of this book is that theory and practice are equally important in describing financial modeling. In it the authors try to strike a balance in their discussions between theories that provide foundations for financial models and the institutional details that provide the context for applications of the models. The book presents the financial models of stock and bond options, exotic options, investment grade and high-yield bonds, convertible bonds, mortgage-backed securities, liabilities of financial institutions--the business model and the corporate model. It also describes the applications of the models to corporate finance. Furthermore, it relates the models to financial statements, risk management for an enterprise, and asset/liability management with illiquid instruments. The financial models are progressively presented from option pricing in the securities markets to firm valuation in corporate finance, following a format to emphasize the three aspects of a model: the set of assumptions, the model specification, and the model applications. Generally, financial modeling books segment the world of finance as "investments," "financial institutions," "corporate finance," and "securities analysis," and in so doing they rarely emphasize the relationships between the subjects. This unique book successfully ties the thought processes and applications of the financial models together and describes them as one process that provides business solutions. Created as a companion website to the book readers can visit www.thomasho.com to gain deeper understanding of the book's financial models. Interested readers can build and test the models described in the book using Excel, and they can submit their models to the site. Readers can also use the site's forum to discuss the models and can browse server based models to gain insights into the applications of the models. For those using the book in meetings or class settings the site provides Power Point descriptions of the chapters. Students can use available question banks on the chapters for studying.

Computational Methods in Finance

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Publisher : CRC Press
ISBN 13 : 1466576049
Total Pages : 440 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Computational Methods in Finance by : Ali Hirsa

Download or read book Computational Methods in Finance written by Ali Hirsa and published by CRC Press. This book was released on 2016-04-19 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Helping readers accurately price a vast array of derivatives, this self-contained text explains how to solve complex functional equations through numerical methods. It addresses key computational methods in finance, including transform techniques, the finite difference method, and Monte Carlo simulation. Developed from his courses at Columbia University and the Courant Institute of New York University, the author also covers model calibration and optimization and describes techniques, such as Kalman and particle filters, for parameter estimation.

So This is Financial Engineering: An introduction to financial engineering

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Publisher : Athena Publishing
ISBN 13 :
Total Pages : 666 pages
Book Rating : 4./5 ( download)

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Book Synopsis So This is Financial Engineering: An introduction to financial engineering by : Kizzi Nkwocha

Download or read book So This is Financial Engineering: An introduction to financial engineering written by Kizzi Nkwocha and published by Athena Publishing. This book was released on 2024-08-24 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: So This is Financial Engineering is an authoritative and inspiring book written by Kizzi Nkwocha, the creator of Business Game Changer Magazine, Money and Finance Magazine, and The Property Investor Magazine. This book serves as a comprehensive introduction to the principles and practices of financial engineering, designed specifically for finance professionals seeking to enhance their understanding and skills in this field. Financial engineering is of paramount importance in today's dynamic and complex financial landscape. It involves the application of mathematical and quantitative techniques to design innovative financial products, develop sophisticated risk management strategies, and optimize investment portfolios. This book delves into the significance of financial engineering and explores how it can bring substantial benefits to finance professionals. One of the primary benefits of financial engineering is its ability to provide a systematic framework for decision-making. By employing mathematical models, statistical analysis, and advanced risk assessment techniques, financial engineering equips professionals with the tools to make informed decisions and mitigate risks effectively. It offers a structured approach to tackle complex financial challenges, enabling professionals to optimize their strategies and achieve better outcomes. So This is Financial Engineering serves as a valuable resource for finance professionals as it covers a wide range of topics essential to understanding and implementing financial engineering principles. From option pricing models and portfolio optimization to risk management strategies and market microstructure, the book provides a comprehensive overview of the key concepts and techniques used in financial engineering. By reading So This is Financial Engineering, finance professionals will gain a deeper understanding of the theoretical foundations and practical applications of financial engineering. They will learn how to leverage mathematical models, statistical analysis, and technological advancements to enhance their decision-making capabilities and improve overall financial performance. So This is Financial Engineering not only provides theoretical explanations but also offers practical insights and real-world examples to reinforce learning and encourage practical application. Whether you are a seasoned finance professional or a budding enthusiast looking to expand your knowledge, So This is Financial Engineering is an essential read. It provides a comprehensive and accessible introduction to the principles and practice of financial engineering, empowering you with the tools and insights to excel in the dynamic world of finance.

Interest Rate, Term Structure, and Valuation Modeling

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Publisher : John Wiley & Sons
ISBN 13 : 9780471220947
Total Pages : 536 pages
Book Rating : 4.2/5 (29 download)

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Book Synopsis Interest Rate, Term Structure, and Valuation Modeling by : Frank J. Fabozzi, CFA

Download or read book Interest Rate, Term Structure, and Valuation Modeling written by Frank J. Fabozzi, CFA and published by John Wiley & Sons. This book was released on 2002-11-01 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ultimate guide contains an excellent blend of theory and practice This comprehensive guide covers various aspects of model building for fixed income securities and derivatives. Filled with expert advice, valuable insights, and advanced modeling techniques, Interest Rate, Term Structure, and Valuation Modeling is a book that all institutional investors, portfolio managers, and risk professionals should have. John Wiley & Sons, Inc. is proud to be the publisher of the esteemed Frank J. Fabozzi Series. Comprising nearly 100 titles-which include numerous bestsellers—The Frank J. Fabozzi Series is a key resource for finance professionals and academics, strategists and students, and investors. The series is overseen by its eponymous editor, whose expert instruction and presentation of new ideas have been at the forefront of financial publishing for over twenty years. His successful career has provided him with the knowledge, insight, and advice that has led to this comprehensive series. Frank J. Fabozzi, PhD, CFA, CPA, is Editor of the Journal of Portfolio Management, which is read by thousands of institutional investors, as well as editor or author of over 100 books on finance for the professional and academic markets. Currently, Dr. Fabozzi is an adjunct Professor of Finance at Yale University's School of Management and on the board of directors of the Guardian Life family of funds and the Black Rock complex of funds.

Calibrating the Non-gaussian HJM Model

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Publisher :
ISBN 13 :
Total Pages : 264 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Calibrating the Non-gaussian HJM Model by :

Download or read book Calibrating the Non-gaussian HJM Model written by and published by . This book was released on 2002 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Term-Structure Models

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Publisher : Springer Science & Business Media
ISBN 13 : 3540680152
Total Pages : 259 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Term-Structure Models by : Damir Filipovic

Download or read book Term-Structure Models written by Damir Filipovic and published by Springer Science & Business Media. This book was released on 2009-07-28 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Changing interest rates constitute one of the major risk sources for banks, insurance companies, and other financial institutions. Modeling the term-structure movements of interest rates is a challenging task. This volume gives an introduction to the mathematics of term-structure models in continuous time. It includes practical aspects for fixed-income markets such as day-count conventions, duration of coupon-paying bonds and yield curve construction; arbitrage theory; short-rate models; the Heath-Jarrow-Morton methodology; consistent term-structure parametrizations; affine diffusion processes and option pricing with Fourier transform; LIBOR market models; and credit risk. The focus is on a mathematically straightforward but rigorous development of the theory. Students, researchers and practitioners will find this volume very useful. Each chapter ends with a set of exercises, that provides source for homework and exam questions. Readers are expected to be familiar with elementary Itô calculus, basic probability theory, and real and complex analysis.

Interest Rate, Term Structure, and Valuation Modeling

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Publisher : John Wiley & Sons
ISBN 13 : 047144698X
Total Pages : 530 pages
Book Rating : 4.4/5 (714 download)

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Book Synopsis Interest Rate, Term Structure, and Valuation Modeling by : Frank J. Fabozzi

Download or read book Interest Rate, Term Structure, and Valuation Modeling written by Frank J. Fabozzi and published by John Wiley & Sons. This book was released on 2002-11-29 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ultimate guide contains an excellent blend of theory and practice This comprehensive guide covers various aspects of model building for fixed income securities and derivatives. Filled with expert advice, valuable insights, and advanced modeling techniques, Interest Rate, Term Structure, and Valuation Modeling is a book that all institutional investors, portfolio managers, and risk professionals should have. John Wiley & Sons, Inc. is proud to be the publisher of the esteemed Frank J. Fabozzi Series. Comprising nearly 100 titles-which include numerous bestsellers—The Frank J. Fabozzi Series is a key resource for finance professionals and academics, strategists and students, and investors. The series is overseen by its eponymous editor, whose expert instruction and presentation of new ideas have been at the forefront of financial publishing for over twenty years. His successful career has provided him with the knowledge, insight, and advice that has led to this comprehensive series. Frank J. Fabozzi, PhD, CFA, CPA, is Editor of the Journal of Portfolio Management, which is read by thousands of institutional investors, as well as editor or author of over 100 books on finance for the professional and academic markets. Currently, Dr. Fabozzi is an adjunct Professor of Finance at Yale University's School of Management and on the board of directors of the Guardian Life family of funds and the Black Rock complex of funds.

Statistical Models and Methods for Financial Markets

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Publisher : Springer Science & Business Media
ISBN 13 : 0387778276
Total Pages : 363 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Statistical Models and Methods for Financial Markets by : Tze Leung Lai

Download or read book Statistical Models and Methods for Financial Markets written by Tze Leung Lai and published by Springer Science & Business Media. This book was released on 2008-09-08 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea of writing this bookarosein 2000when the ?rst author wasassigned to teach the required course STATS 240 (Statistical Methods in Finance) in the new M. S. program in ?nancial mathematics at Stanford, which is an interdisciplinary program that aims to provide a master’s-level education in applied mathematics, statistics, computing, ?nance, and economics. Students in the programhad di?erent backgroundsin statistics. Some had only taken a basic course in statistical inference, while others had taken a broad spectrum of M. S. - and Ph. D. -level statistics courses. On the other hand, all of them had already taken required core courses in investment theory and derivative pricing, and STATS 240 was supposed to link the theory and pricing formulas to real-world data and pricing or investment strategies. Besides students in theprogram,thecoursealso attractedmanystudentsfromother departments in the university, further increasing the heterogeneity of students, as many of them had a strong background in mathematical and statistical modeling from the mathematical, physical, and engineering sciences but no previous experience in ?nance. To address the diversity in background but common strong interest in the subject and in a potential career as a “quant” in the ?nancialindustry,thecoursematerialwascarefullychosennotonlytopresent basic statistical methods of importance to quantitative ?nance but also to summarize domain knowledge in ?nance and show how it can be combined with statistical modeling in ?nancial analysis and decision making. The course material evolved over the years, especially after the second author helped as the head TA during the years 2004 and 2005.

The LIBOR Market Model in Practice

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Publisher : John Wiley & Sons
ISBN 13 : 0470060417
Total Pages : 290 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis The LIBOR Market Model in Practice by : Dariusz Gatarek

Download or read book The LIBOR Market Model in Practice written by Dariusz Gatarek and published by John Wiley & Sons. This book was released on 2007-01-30 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: The LIBOR Market Model (LMM) is the first model of interest rates dynamics consistent with the market practice of pricing interest rate derivatives and therefore it is widely used by financial institution for valuation of interest rate derivatives. This book provides a full practitioner's approach to the LIBOR Market Model. It adopts the specific language of a quantitative analyst to the largest possible level and is one of first books on the subject written entirely by quants. The book is divided into three parts - theory, calibration and simulation. New and important issues are covered, such as various drift approximations, various parametric and nonparametric calibrations, and the uncertain volatility approach to smile modelling; a version of the HJM model based on market observables and the duality between BGM and HJM models. Co-authored by Dariusz Gatarek, the 'G' in the BGM model who is internationally known for his work on LIBOR market models, this book offers an essential perspective on the global benchmark for short-term interest rates.

Continuous-Time Asset Pricing Theory

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Publisher : Springer Nature
ISBN 13 : 3030744108
Total Pages : 470 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Continuous-Time Asset Pricing Theory by : Robert A. Jarrow

Download or read book Continuous-Time Asset Pricing Theory written by Robert A. Jarrow and published by Springer Nature. This book was released on 2021-07-30 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asset pricing theory yields deep insights into crucial market phenomena such as stock market bubbles. Now in a newly revised and updated edition, this textbook guides the reader through this theory and its applications to markets. The new edition features ​new results on state dependent preferences, a characterization of market efficiency and a more general presentation of multiple-factor models using only the assumptions of no arbitrage and no dominance. Taking an innovative approach based on martingales, the book presents advanced techniques of mathematical finance in a business and economics context, covering a range of relevant topics such as derivatives pricing and hedging, systematic risk, portfolio optimization, market efficiency, and equilibrium pricing models. For applications to high dimensional statistics and machine learning, new multi-factor models are given. This new edition integrates suicide trading strategies into the understanding of asset price bubbles, greatly enriching the overall presentation and further strengthening the book’s underlying theme of economic bubbles. Written by a leading expert in risk management, Continuous-Time Asset Pricing Theory is the first textbook on asset pricing theory with a martingale approach. Based on the author’s extensive teaching and research experience on the topic, it is particularly well suited for graduate students in business and economics with a strong mathematical background.

The SABR/LIBOR Market Model

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Publisher : John Wiley & Sons
ISBN 13 : 1119995639
Total Pages : 308 pages
Book Rating : 4.1/5 (199 download)

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Book Synopsis The SABR/LIBOR Market Model by : Riccardo Rebonato

Download or read book The SABR/LIBOR Market Model written by Riccardo Rebonato and published by John Wiley & Sons. This book was released on 2011-03-01 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a major innovation in the interest rate space. It explains a financially motivated extension of the LIBOR Market model which accurately reproduces the prices for plain vanilla hedging instruments (swaptions and caplets) of all strikes and maturities produced by the SABR model. The authors show how to accurately recover the whole of the SABR smile surface using their extension of the LIBOR market model. This is not just a new model, this is a new way of option pricing that takes into account the need to calibrate as accurately as possible to the plain vanilla reference hedging instruments and the need to obtain prices and hedges in reasonable time whilst reproducing a realistic future evolution of the smile surface. It removes the hard choice between accuracy and time because the framework that the authors provide reproduces today's market prices of plain vanilla options almost exactly and simultaneously gives a reasonable future evolution for the smile surface. The authors take the SABR model as the starting point for their extension of the LMM because it is a good model for European options. The problem, however with SABR is that it treats each European option in isolation and the processes for the various underlyings (forward and swap rates) do not talk to each other so it isn't obvious how to relate these processes into the dynamics of the whole yield curve. With this new model, the authors bring the dynamics of the various forward rates and stochastic volatilities under a single umbrella. To ensure the absence of arbitrage they derive drift adjustments to be applied to both the forward rates and their volatilities. When this is completed, complex derivatives that depend on the joint realisation of all relevant forward rates can now be priced. Contents THE THEORETICAL SET-UP The Libor Market model The SABR Model The LMM-SABR Model IMPLEMENTATION AND CALIBRATION Calibrating the LMM-SABR model to Market Caplet prices Calibrating the LMM/SABR model to Market Swaption Prices Calibrating the Correlation Structure EMPIRICAL EVIDENCE The Empirical problem Estimating the volatility of the forward rates Estimating the correlation structure Estimating the volatility of the volatility HEDGING Hedging the Volatility Structure Hedging the Correlation Structure Hedging in conditions of market stress

Fixed Income Quant

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Publisher : HiTeX Press
ISBN 13 :
Total Pages : 346 pages
Book Rating : 4.:/5 (661 download)

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Book Synopsis Fixed Income Quant by : William Johnson

Download or read book Fixed Income Quant written by William Johnson and published by HiTeX Press. This book was released on 2024-10-16 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Fixed Income Quant: Strategies for Modeling Bonds and Interest Rates" offers a comprehensive guide to the world of fixed income securities, blending theoretical insights with practical approaches to modeling and analysis. This book delves into the fundamental components of fixed income markets, providing readers with essential knowledge on bond pricing, interest rate structures, and yield curves. By mastering these foundational topics, investors and financial professionals gain the tools necessary to navigate the complex landscape of fixed income investments with confidence and precision. Through detailed exploration of risk and return, duration and convexity, and credit risk analysis, this book equips readers with a robust framework for managing and optimizing fixed income portfolios. Advanced topics such as interest rate models, fixed income derivatives, and algorithmic trading underscore the integration of quantitative methods and technology in modern financial strategies. With insights into global fixed income markets and machine learning applications, "Fixed Income Quant" serves as both a comprehensive reference and a forward-looking guide, empowering readers to achieve strategic financial goals in an ever-evolving market environment.

Financial Engineering

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Publisher : John Wiley & Sons
ISBN 13 : 0470889837
Total Pages : 616 pages
Book Rating : 4.4/5 (78 download)

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Book Synopsis Financial Engineering by : Tanya S. Beder

Download or read book Financial Engineering written by Tanya S. Beder and published by John Wiley & Sons. This book was released on 2011-05-16 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: FINANCIAL ENGINEERING Financial engineering is poised for a great shift in the years ahead. Everyone from investors and borrowers to regulators and legislators will need to determine what works, what doesn't, and where to go from here. Financial Engineering part of the Robert W. Kolb Series in Finance has been designed to help you do just this. Comprised of contributed chapters by distinguished experts from industry and academia, this reliable resource will help you focus on established activities in the field, developing trends and changes, as well as areas of opportunity. Divided into five comprehensive parts, Financial Engineering begins with an informative overview of the discipline, chronicling its complete history and profiling potential career paths. From here, Part II quickly moves on to discuss the evolution of financial engineering in major markets fixed income, foreign exchange, equities, commodities and credit and offers important commentary on what has worked and what will change. Part III then examines a number of recent innovative applications of financial engineering that have made news over the past decade such as the advent of securitized and structured products and highly quantitative trading strategies for both equities and fixed income. Thoughts on how risk management might be retooled to reflect what has been learned as a result of the recent financial crisis are also included. Part IV of the book is devoted entirely to case studies that present valuable lessons for active practitioners and academics. Several of the cases explore the risk that has instigated losses across multiple markets, including the global credit crisis. You'll gain in-depth insights from cases such as Countrywide, Société Générale, Barings, Long-Term Capital Management, the Florida Local Government Investment Pool, AIG, Merrill Lynch, and many more. The demand for specific and enterprise risk managers who can think outside the box will be substantial during this decade. Much of Part V presents new ways to be successful in an era that demands innovation on both sides of the balance sheet. Chapters that touch upon this essential topic include Musings About Hedging; Operational Risk; and The No-Arbitrage Condition in Financial Engineering: Its Use and Mis-Use. This book is complemented by a companion website that includes details from the editors' survey of financial engineering programs around the globe, along with a glossary of key terms from the book. This practical guide puts financial engineering in perspective, and will give you a better idea of how it can be effectively utilized in real- world situations.

Interest Rate Models - Theory and Practice

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Publisher : Springer Science & Business Media
ISBN 13 : 354034604X
Total Pages : 1016 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Interest Rate Models - Theory and Practice by : Damiano Brigo

Download or read book Interest Rate Models - Theory and Practice written by Damiano Brigo and published by Springer Science & Business Media. This book was released on 2007-09-26 with total page 1016 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2nd edition of this successful book has several new features. The calibration discussion of the basic LIBOR market model has been enriched considerably, with an analysis of the impact of the swaptions interpolation technique and of the exogenous instantaneous correlation on the calibration outputs. A discussion of historical estimation of the instantaneous correlation matrix and of rank reduction has been added, and a LIBOR-model consistent swaption-volatility interpolation technique has been introduced. The old sections devoted to the smile issue in the LIBOR market model have been enlarged into a new chapter. New sections on local-volatility dynamics, and on stochastic volatility models have been added, with a thorough treatment of the recently developed uncertain-volatility approach. Examples of calibrations to real market data are now considered. The fast-growing interest for hybrid products has led to a new chapter. A special focus here is devoted to the pricing of inflation-linked derivatives. The three final new chapters of this second edition are devoted to credit. Since Credit Derivatives are increasingly fundamental, and since in the reduced-form modeling framework much of the technique involved is analogous to interest-rate modeling, Credit Derivatives -- mostly Credit Default Swaps (CDS), CDS Options and Constant Maturity CDS - are discussed, building on the basic short rate-models and market models introduced earlier for the default-free market. Counterparty risk in interest rate payoff valuation is also considered, motivated by the recent Basel II framework developments.