Interest Rate Models - Theory and Practice

With Smile, Inflation and Credit

Author: Damiano Brigo,Fabio Mercurio

Publisher: Springer Science & Business Media

ISBN: 354034604X

Category: Mathematics

Page: 982

View: 1532

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.
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Interest Rate Modeling

Theory and Practice

Author: Lixin Wu

Publisher: CRC Press

ISBN: 1420090577

Category: Mathematics

Page: 354

View: 6251

Containing many results that are new or exist only in recent research articles, Interest Rate Modeling: Theory and Practice portrays the theory of interest rate modeling as a three-dimensional object of finance, mathematics, and computation. It introduces all models with financial-economical justifications, develops options along the martingale approach, and handles option evaluations with precise numerical methods. The text begins with the mathematical foundations, including Ito’s calculus and the martingale representation theorem. It then introduces bonds and bond yields, followed by the Heath–Jarrow–Morton (HJM) model, which is the framework for no-arbitrage pricing models. The next chapter focuses on when the HJM model implies a Markovian short-rate model and discusses the construction and calibration of short-rate lattice models. In the chapter on the LIBOR market model, the author presents the simplest yet most robust formula for swaption pricing in the literature. He goes on to address model calibration, an important aspect of model applications in the markets; industrial issues; and the class of affine term structure models for interest rates. Taking a top-down approach, Interest Rate Modeling provides readers with a clear picture of this important subject by not overwhelming them with too many specific models. The text captures the interdisciplinary nature of the field and shows readers what it takes to be a competent quant in today’s market. This book can be adopted for instructional use. For this purpose, a solutions manual is available for qualifying instructors.
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Implementing Models in Quantitative Finance: Methods and Cases

Author: Gianluca Fusai,Andrea Roncoroni

Publisher: Springer Science & Business Media

ISBN: 9783540499596

Category: Business & Economics

Page: 607

View: 5734

This book puts numerical methods in action for the purpose of solving practical problems in quantitative finance. The first part develops a toolkit in numerical methods for finance. The second part proposes twenty self-contained cases covering model simulation, asset pricing and hedging, risk management, statistical estimation and model calibration. Each case develops a detailed solution to a concrete problem arising in applied financial management and guides the user towards a computer implementation. The appendices contain "crash courses" in VBA and Matlab programming languages.
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The SABR/LIBOR Market Model

Pricing, Calibration and Hedging for Complex Interest-Rate Derivatives

Author: Riccardo Rebonato,Kenneth McKay,Richard White

Publisher: John Wiley & Sons

ISBN: 9781119995630

Category: Business & Economics

Page: 296

View: 6150

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
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Efficient Methods for Valuing Interest Rate Derivatives

Author: Antoon Pelsser

Publisher: Springer Science & Business Media

ISBN: 1447138880

Category: Mathematics

Page: 172

View: 7989

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.
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Interest Rate Modeling

Author: Leif B. G. Andersen,Vladimir V. Piterbarg

Publisher: N.A

ISBN: 9780984422104

Category: Business & Economics

Page: 1154

View: 5969

"The three volumes of Interest rate modeling are aimed primarily at practitioners working in the area of interest rate derivatives, but much of the material is quite general and, we believe, will also hold significant appeal to researchers working in other asset classes. Students and academics interested in financial engineering and applied work will find the material particularly useful for its description of real-life model usage and for its expansive discussion of model calibration, approximation theory, and numerical methods."--Preface.
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Stochastic Calculus for Finance II

Continuous-Time Models

Author: Steven E. Shreve

Publisher: Springer Science & Business Media

ISBN: 9780387401010

Category: Business & Economics

Page: 550

View: 8624

This is the second volume in a two-volume sequence on Stochastic calculus models in finance. This second volume, which does not require the first volume as a prerequisite, covers infinite state models and continuous time stochastic calculus. The book is suitable for beginning masters-level students in mathematical finance and financial engineering.
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Discounting, LIBOR, CVA and Funding

Interest Rate and Credit Pricing

Author: Chris Kenyon,Roland Stamm

Publisher: Palgrave Macmillan

ISBN: 1137268514

Category: Business & Economics

Page: 227

View: 6502

Providing the most up-to-date tools and techniques for pricing interest rate and credit products for the new financial world, this book discusses pricing and hedging, funding and regulation, and interpretation, as an essential resource for quantitatively minded practitioners and researchers in finance.
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Credit Derivatives Pricing Models

Models, Pricing and Implementation

Author: Philipp J. Schönbucher

Publisher: John Wiley & Sons

ISBN: 0470868171

Category: Business & Economics

Page: 396

View: 6663

The credit derivatives market is booming and, for the first time, expanding into the banking sector which previously has had very little exposure to quantitative modeling. This phenomenon has forced a large number of professionals to confront this issue for the first time. Credit Derivatives Pricing Models provides an extremely comprehensive overview of the most current areas in credit risk modeling as applied to the pricing of credit derivatives. As one of the first books to uniquely focus on pricing, this title is also an excellent complement to other books on the application of credit derivatives. Based on proven techniques that have been tested time and again, this comprehensive resource provides readers with the knowledge and guidance to effectively use credit derivatives pricing models. Filled with relevant examples that are applied to real-world pricing problems, Credit Derivatives Pricing Models paves a clear path for a better understanding of this complex issue. Dr. Philipp J. Schönbucher is a professor at the Swiss Federal Institute of Technology (ETH), Zurich, and has degrees in mathematics from Oxford University and a PhD in economics from Bonn University. He has taught various training courses organized by ICM and CIFT, and lectured at risk conferences for practitioners on credit derivatives pricing, credit risk modeling, and implementation.
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An Introduction to Mathematical Finance with Applications

Understanding and Building Financial Intuition

Author: Arlie O. Petters,Xiaoying Dong

Publisher: Springer

ISBN: 1493937839

Category: Mathematics

Page: 483

View: 7000

This textbook aims to fill the gap between those that offer a theoretical treatment without many applications and those that present and apply formulas without appropriately deriving them. The balance achieved will give readers a fundamental understanding of key financial ideas and tools that form the basis for building realistic models, including those that may become proprietary. Numerous carefully chosen examples and exercises reinforce the student’s conceptual understanding and facility with applications. The exercises are divided into conceptual, application-based, and theoretical problems, which probe the material deeper. The book is aimed toward advanced undergraduates and first-year graduate students who are new to finance or want a more rigorous treatment of the mathematical models used within. While no background in finance is assumed, prerequisite math courses include multivariable calculus, probability, and linear algebra. The authors introduce additional mathematical tools as needed. The entire textbook is appropriate for a single year-long course on introductory mathematical finance. The self-contained design of the text allows for instructor flexibility in topics courses and those focusing on financial derivatives. Moreover, the text is useful for mathematicians, physicists, and engineers who want to learn finance via an approach that builds their financial intuition and is explicit about model building, as well as business school students who want a treatment of finance that is deeper but not overly theoretical.
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Quantitative Credit Portfolio Management

Practical Innovations for Measuring and Controlling Liquidity, Spread, and Issuer Concentration Risk

Author: Arik Ben Dor,Lev Dynkin,Jay Hyman,Bruce D. Phelps

Publisher: John Wiley & Sons

ISBN: 1118167422

Category: Business & Economics

Page: 416

View: 7050

An innovative approach to post-crash credit portfolio management Credit portfolio managers traditionally rely on fundamental research for decisions on issuer selection and sector rotation. Quantitative researchers tend to use more mathematical techniques for pricing models and to quantify credit risk and relative value. The information found here bridges these two approaches. In an intuitive and readable style, this book illustrates how quantitative techniques can help address specific questions facing today's credit managers and risk analysts. A targeted volume in the area of credit, this reliable resource contains some of the most recent and original research in this field, which addresses among other things important questions raised by the credit crisis of 2008-2009. Divided into two comprehensive parts, Quantitative Credit Portfolio Management offers essential insights into understanding the risks of corporate bonds—spread, liquidity, and Treasury yield curve risk—as well as managing corporate bond portfolios. Presents comprehensive coverage of everything from duration time spread and liquidity cost scores to capturing the credit spread premium Written by the number one ranked quantitative research group for four consecutive years by Institutional Investor Provides practical answers to difficult question, including: What diversification guidelines should you adopt to protect portfolios from issuer-specific risk? Are you well-advised to sell securities downgraded below investment grade? Credit portfolio management continues to evolve, but with this book as your guide, you can gain a solid understanding of how to manage complex portfolios under dynamic events.
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Mathematical Finance

Theory, Modeling, Implementation

Author: Christian Fries

Publisher: John Wiley & Sons

ISBN: 9780470179772

Category: Mathematics

Page: 512

View: 1948

A balanced introduction to the theoretical foundations and real-world applications of mathematical finance The ever-growing use of derivative products makes it essential for financial industry practitioners to have a solid understanding of derivative pricing. To cope with the growing complexity, narrowing margins, and shortening life-cycle of the individual derivative product, an efficient, yet modular, implementation of the pricing algorithms is necessary. Mathematical Finance is the first book to harmonize the theory, modeling, and implementation of today's most prevalent pricing models under one convenient cover. Building a bridge from academia to practice, this self-contained text applies theoretical concepts to real-world examples and introduces state-of-the-art, object-oriented programming techniques that equip the reader with the conceptual and illustrative tools needed to understand and develop successful derivative pricing models. Utilizing almost twenty years of academic and industry experience, the author discusses the mathematical concepts that are the foundation of commonly used derivative pricing models, and insightful Motivation and Interpretation sections for each concept are presented to further illustrate the relationship between theory and practice. In-depth coverage of the common characteristics found amongst successful pricing models are provided in addition to key techniques and tips for the construction of these models. The opportunity to interactively explore the book's principal ideas and methodologies is made possible via a related Web site that features interactive Java experiments and exercises. While a high standard of mathematical precision is retained, Mathematical Finance emphasizes practical motivations, interpretations, and results and is an excellent textbook for students in mathematical finance, computational finance, and derivative pricing courses at the upper undergraduate or beginning graduate level. It also serves as a valuable reference for professionals in the banking, insurance, and asset management industries.
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Interest Rate Modelling

Author: Jessica James,Nick Webber

Publisher: Wiley

ISBN: N.A

Category: Business & Economics

Page: 676

View: 7712

As interest rate markets continue to innovate and expand it is becoming increasingly important to remain up-to-date with the latest practical and theoretical developments. This book covers the latest developments in full, with descriptions and implementation techniques for all the major classes of interest rate models-both those actively used in practice as well as theoretical models still 'waiting in the wings'. Interest rate models, implementation methods and estimation issues are discussed at length by the authors as are important new developments such as kernel estimation techniques, economic based models, implied pricing methods and models on manifolds. Providing balanced coverage of both the practical use of models and the theory that underlies them, Interest Rate Modelling adopts an implementation orientation throughout, making it an ideal resource for both practitioners and researchers.
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Counterparty Credit Risk, Collateral and Funding

With Pricing Cases For All Asset Classes

Author: Damiano Brigo,Massimo Morini,Andrea Pallavicini

Publisher: John Wiley & Sons

ISBN: 047066178X

Category: Business & Economics

Page: 464

View: 3196

The book’s content is focused on rigorous and advanced quantitative methods for the pricing and hedging of counterparty credit and funding risk. The new general theory that is required for this methodology is developed from scratch, leading to a consistent and comprehensive framework for counterparty credit and funding risk, inclusive of collateral, netting rules, possible debit valuation adjustments, re-hypothecation and closeout rules. The book however also looks at quite practical problems, linking particular models to particular ‘concrete’ financial situations across asset classes, including interest rates, FX, commodities, equity, credit itself, and the emerging asset class of longevity. The authors also aim to help quantitative analysts, traders, and anyone else needing to frame and price counterparty credit and funding risk, to develop a ‘feel’ for applying sophisticated mathematics and stochastic calculus to solve practical problems. The main models are illustrated from theoretical formulation to final implementation with calibration to market data, always keeping in mind the concrete questions being dealt with. The authors stress that each model is suited to different situations and products, pointing out that there does not exist a single model which is uniformly better than all the others, although the problems originated by counterparty credit and funding risk point in the direction of global valuation. Finally, proposals for restructuring counterparty credit risk, ranging from contingent credit default swaps to margin lending, are considered.
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Monte Carlo Methods in Financial Engineering

Author: Paul Glasserman

Publisher: Springer Science & Business Media

ISBN: 0387216170

Category: Mathematics

Page: 596

View: 4363

From the reviews: "Paul Glasserman has written an astonishingly good book that bridges financial engineering and the Monte Carlo method. The book will appeal to graduate students, researchers, and most of all, practicing financial engineers [...] So often, financial engineering texts are very theoretical. This book is not." --Glyn Holton, Contingency Analysis
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Term-Structure Models

A Graduate Course

Author: Damir Filipovic

Publisher: Springer Science & Business Media

ISBN: 3540680152

Category: Mathematics

Page: 256

View: 4781

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.
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An Introduction to Credit Risk Modeling

Author: Christian Bluhm,Ludger Overbeck,Christoph Wagner

Publisher: CRC Press

ISBN: 9781420057362

Category: Mathematics

Page: 297

View: 7599

In today's increasingly competitive financial world, successful risk management, portfolio management, and financial structuring demand more than up-to-date financial know-how. They also call for quantitative expertise, including the ability to effectively apply mathematical modeling tools and techniques. An Introduction to Credit Risk Modeling supplies both the bricks and the mortar of risk management. In a gentle and concise lecture-note style, it introduces the fundamentals of credit risk management, provides a broad treatment of the related modeling theory and methods, and explores their application to credit portfolio securitization, credit risk in a trading portfolio, and credit derivatives risk. The presentation is thorough but refreshingly accessible, foregoing unnecessary technical details yet remaining mathematically precise. Whether you are a risk manager looking for a more quantitative approach to credit risk or you are planning a move from the academic arena to a career in professional credit risk management, An Introduction to Credit Risk Modeling is the book you've been looking for. It will bring you quickly up to speed with information needed to resolve the questions and quandaries encountered in practice.
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Synthetic CDOs

Modelling, Valuation and Risk Management

Author: C. C. Mounfield

Publisher: Cambridge University Press

ISBN: 0521897882

Category: Business & Economics

Page: 369

View: 9922

Details the latest models and techniques in quantitative and computational modelling of synthetic Collateralised Debt Obligations.
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Volatility and Correlation

The Perfect Hedger and the Fox

Author: Riccardo Rebonato

Publisher: John Wiley & Sons

ISBN: 0470091401

Category: Business & Economics

Page: 864

View: 2778

In Volatility and Correlation 2nd edition: The Perfect Hedger and the Fox, Rebonato looks at derivatives pricing from the angle of volatility and correlation. With both practical and theoretical applications, this is a thorough update of the highly successful Volatility & Correlation – with over 80% new or fully reworked material and is a must have both for practitioners and for students. The new and updated material includes a critical examination of the ‘perfect-replication’ approach to derivatives pricing, with special attention given to exotic options; a thorough analysis of the role of quadratic variation in derivatives pricing and hedging; a discussion of the informational efficiency of markets in commonly-used calibration and hedging practices. Treatment of new models including Variance Gamma, displaced diffusion, stochastic volatility for interest-rate smiles and equity/FX options. The book is split into four parts. Part I deals with a Black world without smiles, sets out the author’s ‘philosophical’ approach and covers deterministic volatility. Part II looks at smiles in equity and FX worlds. It begins with a review of relevant empirical information about smiles, and provides coverage of local-stochastic-volatility, general-stochastic-volatility, jump-diffusion and Variance-Gamma processes. Part II concludes with an important chapter that discusses if and to what extent one can dispense with an explicit specification of a model, and can directly prescribe the dynamics of the smile surface. Part III focusses on interest rates when the volatility is deterministic. Part IV extends this setting in order to account for smiles in a financially motivated and computationally tractable manner. In this final part the author deals with CEV processes, with diffusive stochastic volatility and with Markov-chain processes. Praise for the First Edition: “In this book, Dr Rebonato brings his penetrating eye to bear on option pricing and hedging.... The book is a must-read for those who already know the basics of options and are looking for an edge in applying the more sophisticated approaches that have recently been developed.” —Professor Ian Cooper, London Business School “Volatility and correlation are at the very core of all option pricing and hedging. In this book, Riccardo Rebonato presents the subject in his characteristically elegant and simple fashion...A rare combination of intellectual insight and practical common sense.” —Anthony Neuberger, London Business School
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