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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.
Modeling the Term Structure of Interest Rates provides a comprehensive review of the continuous-time modeling techniques of the term structure applicable to value and hedge default-free bonds and other interest rate derivatives.
"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.
Praise for Dynamic Term Structure Modeling "This book offers the most comprehensive coverage of term-structure models I have seen so far, encompassing equilibrium and no-arbitrage models in a new framework, along with the major solution techniques using trees, PDE methods, Fourier methods, and approximations. It is an essential reference for academics and practitioners alike." --Sanjiv Ranjan Das Professor of Finance, Santa Clara University, California, coeditor, Journal of Derivatives "Bravo! This is an exhaustive analysis of the yield curve dynamics. It is clear, pedagogically impressive, well presented, and to the point." --Nassim Nicholas Taleb author, Dynamic Hedging and The Black Swan "Nawalkha, Beliaeva, and Soto have put together a comprehensive, up-to-date textbook on modern dynamic term structure modeling. It is both accessible and rigorous and should be of tremendous interest to anyone who wants to learn about state-of-the-art fixed income modeling. It provides many numerical examples that will be valuable to readers interested in the practical implementations of these models." --Pierre Collin-Dufresne Associate Professor of Finance, UC Berkeley "The book provides a comprehensive description of the continuous time interest rate models. It serves an important part of the trilogy, useful for financial engineers to grasp the theoretical underpinnings and the practical implementation." --Thomas S. Y. Ho, PHD President, Thomas Ho Company, Ltd, coauthor, The Oxford Guide to Financial Modeling
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.
This paper discusses the estimation of models of the term structure of interest rates. After reviewing the term structure models, specifically the Nelson-Siegel Model and Affine Term- Structure Model, this paper estimates the terms structure of Treasury bond yields for the United States with pre-crisis data. This paper uses a software developed by Fund staff for this purpose. This software makes it possible to estimate the term structure using at least nine models, while opening up the possibility of generating simulated paths of the term structure.
Nominal yields on government debt in several countries have fallen very near their zero lower bound (ZLB), causing a liquidity trap and limiting the capacity to stimulate economic growth. This book provides a comprehensive reference to ZLB structure modeling in an applied setting.
We investigate the possibility of an arbitrage free model for the term structure of interest rates where the yield curve only changes through a parallel shift. We consider HJM type forward rate models driven by a multidimensionalWiener process as well as by a general marked point process. Within this general framework we show that there does indeed exist a large variety of nontrivial parallel shift term structure models, and we also describe these in detail. We also show that there exists no nontrivial flat term structure model. The same analysis is repeated for the similar case, where the yield curve only changes through proportional shifts. Key words: bond market, term structure of interest rates, flat term structures.
The paper assesses estimates of term structure models for the United States. To this end, this paper first describes the mathematics underlying two types of term structure models, namely the Nelson-Siegel and Cox, Ingersoll and Ross family of models, and the estimation techniques. It then presents estimations of some of specific models within these families of models?three-factor Nelson-Siegel Model, four-factor Svensson model, and preference-free, two-factor Cox, Ingersoll and Roll model?for the United States from 1972 to mid 2011. It subsequently provides an assessment of the estimations. It concludes that these estimations of the term structure models successfully capture the dynamics of the term structure in the United States.