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Author : Alberto Ohashi
Publisher :
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.3/5 (91 download)
Download or read book HJM Interest Rate Models with Fractional Brownian Motions written by Alberto Ohashi and published by . This book was released on 2007 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Damir Filipovic
Publisher : Springer Science & Business Media
ISBN 13 : 9783540414933
Total Pages : 148 pages
Book Rating : 4.4/5 (149 download)
Download or read book Consistency Problems for Heath-Jarrow-Morton Interest Rate Models written by Damir Filipovic and published by Springer Science & Business Media. This book was released on 2001-03-27 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bond markets differ in one fundamental aspect from standard stock markets. While the latter are built up to a finite number of trade assets, the underlying basis of a bond market is the entire term structure of interest rates: an infinite-dimensional variable which is not directly observable. On the empirical side, this necessitates curve-fitting methods for the daily estimation of the term structure. Pricing models, on the other hand, are usually built upon stochastic factors representing the term structure in a finite-dimensional state space. Written for readers with knowledge in mathematical finance (in particular interest rate theory) and elementary stochastic analysis, this research monograph has threefold aims: to bring together estimation methods and factor models for interest rates, to provide appropriate consistency conditions and to explore some important examples.
Author : Nicolas Privault
Publisher : World Scientific
ISBN 13 : 9814390860
Total Pages : 243 pages
Book Rating : 4.8/5 (143 download)
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 2012 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.
Author : Maria Krivko
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (86 download)
Download or read book Numerical Methods for Heath-Jarrow-Morton Model of Interest Rates written by Maria Krivko and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The celebrated HJM framework models the evolution of the term structure of interest rates through the dynamics of the forward rate curve. These dynamics are described by a multifactor infinite-dimensional stochastic equation with the entire forward rate curve as state variable. Under no-arbitrage conditions, the HJM model is fully characterized by specifying forward rate volatility functions and the initial forward curve. In short, it can be described as a unifying framework with one of its most striking features being the generality: any arbitrage-free interest rate model driven by Brownian motion can be described as a special case of the HJM model. The HJM model has closed-form solutions only for some special cases of volatility, and valuations under the HJM framework usually require a numerical approximation. We propose and analyze numerical methods for the HJM model. To construct the methods, we first discretize the infinite-dimensional HJM equation in maturity time variable using quadrature rules for approximating the arbitrage-free drift. This results in a finite-dimensional system of stochastic differential equations (SDEs) which we approximate in the weak and mean-square sense. The proposed numerical algorithms are highly computationally efficient due to the use of high-order quadrature rules which allow us to take relatively large discretization steps in the maturity time without affecting overall accuracy of the algorithms. They also have a high degree of flexibility and allow to choose appropriate approximations in maturity and calendar times separately. Convergence theorems for the methods are proved. Results of some numerical experiments with European-type interest rate derivatives are presented.
Author : Nicolas Privault
Publisher : World Scientific
ISBN 13 : 9814401641
Total Pages : 243 pages
Book Rating : 4.8/5 (144 download)
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.
Author : Nicolas Privault
Publisher : World Scientific Publishing Company
ISBN 13 : 9813107308
Total Pages : 191 pages
Book Rating : 4.8/5 (131 download)
Download or read book An Elementary Introduction To Stochastic Interest Rate Modeling written by Nicolas Privault and published by World Scientific Publishing Company. This book was released on 2008-10-13 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.
Author : Nicolas Privault
Publisher : World Scientific
ISBN 13 : 9811226628
Total Pages : 373 pages
Book Rating : 4.8/5 (112 download)
Download or read book Stochastic Interest Rate Modeling With Fixed Income Derivative Pricing (Third Edition) written by Nicolas Privault and published by World Scientific. This book was released on 2021-09-02 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the mathematics of stochastic interest rate modeling and the pricing of related derivatives, based on a step-by-step presentation of concepts with a focus on explicit calculations. The types of interest rates considered range from short rates to forward rates such as LIBOR and swap rates, which are presented in the HJM and BGM frameworks. The pricing and hedging of interest rate and fixed income derivatives such as bond options, caps, and swaptions, are treated using forward measure techniques. An introduction to default bond pricing and an outlook on model calibration are also included as additional topics.This third edition represents a significant update on the second edition published by World Scientific in 2012. Most chapters have been reorganized and largely rewritten with additional details and supplementary solved exercises. New graphs and simulations based on market data have been included, together with the corresponding R codes.This new edition also contains 75 exercises and 4 problems with detailed solutions, making it suitable for advanced undergraduate and graduate level students.
Author : René Carmona
Publisher : Springer Science & Business Media
ISBN 13 : 3540270671
Total Pages : 236 pages
Book Rating : 4.5/5 (42 download)
Download or read book Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective written by René Carmona and published by Springer Science & Business Media. This book was released on 2007-05-22 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the mathematical issues that arise in modeling the interest rate term structure by casting the interest-rate models as stochastic evolution equations in infinite dimensions. The text includes a crash course on interest rates, a self-contained introduction to infinite dimensional stochastic analysis, and recent results in interest rate theory. From the reviews: "A wonderful book. The authors present some cutting-edge math." --WWW.RISKBOOK.COM
Author : Takashi Yasuoka
Publisher : Bentham Science Publishers
ISBN 13 : 1681086891
Total Pages : 325 pages
Book Rating : 4.6/5 (81 download)
Download or read book Interest Rate Modeling for Risk Management: Market Price of Interest Rate Risk (Second Edition) written by Takashi Yasuoka and published by Bentham Science Publishers. This book was released on 2018-05-09 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest Rate Modeling for Risk Management presents an economic model which can be used to compare interest rate and perform market risk assessment analyses. The key interest rate model applied in this book is specified under real-world measures, and the result is used as to generate scenarios for interest rates. The book introduces a theoretical framework that allows estimating the market price of interest rate risk. For this, the book starts with a brief explanation of stochastic analysis, and introduces interest rate models such as Heath-Jarrow-Morton, Hull-White and LIBOR models. The real-world model is then introduced in subsequent chapters. Additionally, the book also explains some properties of the real-world model, along with the negative price tendency of the market price for risk and a positive market price of risk (with practical examples). Readers will also find a handy appendix with proofs to complement the numerical methods explained in the book. This book is intended as a primer for practitioners in financial institutions involved in interest rate risk management. It also presents a new perspective for researchers and graduates in econometrics and finance on the study of interest rate models. The second edition features an expanded commentary on real world models as well as additional numerical examples for the benefit of readers.
Author : Alberto Ohashi
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.3/5 (91 download)
Download or read book Invariant Manifolds for Stochastic PDE with Fractional Brownian Motion written by Alberto Ohashi and published by . This book was released on 2007 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Lixin Wu
Publisher : CRC Press
ISBN 13 : 1420090577
Total Pages : 356 pages
Book Rating : 4.4/5 (2 download)
Download or read book Interest Rate Modeling written by Lixin Wu and published by CRC Press. This book was released on 2009-05-14 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 app
Author : Alberto Ohashi
Publisher :
ISBN 13 :
Total Pages : 38 pages
Book Rating : 4.3/5 (91 download)
Download or read book Fractional Term Structure Models written by Alberto Ohashi and published by . This book was released on 2008 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : L. P. Hughston
Publisher :
ISBN 13 :
Total Pages : 408 pages
Book Rating : 4.:/5 (31 download)
Download or read book Vasicek and Beyond written by L. P. Hughston and published by . This book was released on 1996 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Damiano Brigo
Publisher : Springer Science & Business Media
ISBN 13 : 354034604X
Total Pages : 1016 pages
Book Rating : 4.5/5 (43 download)
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.
Author : Andrew J. G. Cairns
Publisher : Princeton University Press
ISBN 13 : 0691187428
Total Pages : 289 pages
Book Rating : 4.6/5 (911 download)
Download or read book Interest Rate Models written by Andrew J. G. Cairns and published by Princeton University Press. This book was released on 2018-06-05 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of financial mathematics has developed tremendously over the past thirty years, and the underlying models that have taken shape in interest rate markets and bond markets, being much richer in structure than equity-derivative models, are particularly fascinating and complex. This book introduces the tools required for the arbitrage-free modelling of the dynamics of these markets. Andrew Cairns addresses not only seminal works but also modern developments. Refreshingly broad in scope, covering numerical methods, credit risk, and descriptive models, and with an approachable sequence of opening chapters, Interest Rate Models will make readers--be they graduate students, academics, or practitioners--confident enough to develop their own interest rate models or to price nonstandard derivatives using existing models. The mathematical chapters begin with the simple binomial model that introduces many core ideas. But the main chapters work their way systematically through all of the main developments in continuous-time interest rate modelling. The book describes fully the broad range of approaches to interest rate modelling: short-rate models, no-arbitrage models, the Heath-Jarrow-Morton framework, multifactor models, forward measures, positive-interest models, and market models. Later chapters cover some related topics, including numerical methods, credit risk, and model calibration. Significantly, the book develops the martingale approach to bond pricing in detail, concentrating on risk-neutral pricing, before later exploring recent advances in interest rate modelling where different pricing measures are important.
Author : Lixin Wu
Publisher : CRC Press
ISBN 13 : 1351227408
Total Pages : 325 pages
Book Rating : 4.3/5 (512 download)
Download or read book Interest Rate Modeling written by Lixin Wu and published by CRC Press. This book was released on 2019-03-04 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Containing many results that are new, or which exist only in recent research articles, Interest Rate Modeling: Theory and Practice, 2nd Edition 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. Features Presents a complete cycle of model construction and applications, showing readers how to build and use models Provides a systematic treatment of intriguing industrial issues, such as volatility and correlation adjustments Contains exercise sets and a number of examples, with many based on real market data Includes comments on cutting-edge research, such as volatility-smile, positive interest-rate models, and convexity adjustment New to the 2nd edition: volatility smile modeling; a new paradigm for inflation derivatives modeling; an extended market model for credit derivatives; a dual-curved model for the post-crisis interest-rate derivatives markets; and an elegant framework for the xVA.
Author : Damiano Brigo
Publisher : Springer
ISBN 13 : 3540417729
Total Pages : 564 pages
Book Rating : 4.5/5 (44 download)
Download or read book Interest Rate Models - Theory and Practice written by Damiano Brigo and published by Springer. This book was released on 2001-08-09 with total page 564 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.
