Interest Rate Models Implied Volatility

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Interest Rate Models Theory and Practice

Author : Damiano Brigo
Publisher : Springer Science & Business Media
ISBN 13 : 3662045532
Total Pages : 544 pages
Book Rating : 4.6/5 (62 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 2013-04-17 with total page 544 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.

Interest Rate Models Implied Volatility

Author : Thomas S.Y. Ho
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Interest Rate Models Implied Volatility by : Thomas S.Y. Ho

Download or read book Interest Rate Models Implied Volatility written by Thomas S.Y. Ho and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents a one-factor and a two-factor arbitrage-free interest rate models with parsimonious implied volatility functions. The models are empirically tested on the entire swaption surface in three currencies (US dollar, Euro, and Japanese yen) over a 5-year period. They are shown to be robust in explaining the swaption values, and the implied volatility functions are shown to exhibit a three-factor movement in all three currencies. The results show that the observed swaption prices incorporate the market conditional expectations of the correlations of the key interest rates and the stochastic process of the yield curve, and the interest rate models should be calibrated to such market information to provide accurate relative valuation. Further this paper describes a modeling approach that has important implications on hedging interest rate derivatives dynamically taking the stochastic volatility risks into account.

Interest Rate Models - Theory and Practice

Author : Damiano Brigo
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.

Interest Rate Derivatives Explained: Volume 2

Author : Jörg Kienitz
Publisher : Springer
ISBN 13 : 1137360194
Total Pages : 261 pages
Book Rating : 4.1/5 (373 download)

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Book Synopsis Interest Rate Derivatives Explained: Volume 2 by : Jörg Kienitz

Download or read book Interest Rate Derivatives Explained: Volume 2 written by Jörg Kienitz and published by Springer. This book was released on 2017-11-08 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on Interest Rate Derivatives has three parts. The first part is on financial products and extends the range of products considered in Interest Rate Derivatives Explained I. In particular we consider callable products such as Bermudan swaptions or exotic derivatives. The second part is on volatility modelling. The Heston and the SABR model are reviewed and analyzed in detail. Both models are widely applied in practice. Such models are necessary to account for the volatility skew/smile and form the fundament for pricing and risk management of complex interest rate structures such as Constant Maturity Swap options. Term structure models are introduced in the third part. We consider three main classes namely short rate models, instantaneous forward rate models and market models. For each class we review one representative which is heavily used in practice. We have chosen the Hull-White, the Cheyette and the Libor Market model. For all the models we consider the extensions by a stochastic basis and stochastic volatility component. Finally, we round up the exposition by giving an overview of the numerical methods that are relevant for successfully implementing the models considered in the book.

Stochastic Interest Rates

Author : Daragh McInerney
Publisher : Cambridge University Press
ISBN 13 : 1107002575
Total Pages : 171 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Stochastic Interest Rates by : Daragh McInerney

Download or read book Stochastic Interest Rates written by Daragh McInerney and published by Cambridge University Press. This book was released on 2015-08-13 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for Master's students, this practical text strikes the right balance between mathematical rigour and real-world application.

Semiparametric Modeling of Implied Volatility

Author : Matthias R. Fengler
Publisher : Springer Science & Business Media
ISBN 13 : 3540305912
Total Pages : 232 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Semiparametric Modeling of Implied Volatility by : Matthias R. Fengler

Download or read book Semiparametric Modeling of Implied Volatility written by Matthias R. Fengler and published by Springer Science & Business Media. This book was released on 2005-12-19 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers recent advances in the theory of implied volatility and refined semiparametric estimation strategies and dimension reduction methods for functional surfaces. The first part is devoted to smile-consistent pricing approaches. The second part covers estimation techniques that are natural candidates to meet the challenges in implied volatility surfaces. Empirical investigations, simulations, and pictures illustrate the concepts.

Interest Rate Modelling

Author : Jessica James
Publisher : John Wiley & Sons
ISBN 13 :
Total Pages : 680 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Interest Rate Modelling by : Jessica James

Download or read book Interest Rate Modelling written by Jessica James and published by John Wiley & Sons. This book was released on 2000-06-08 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: Back Cover ( this section should include endorsements also) 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. Back Flap Jessica James Jessica James is Head of Research for Bank One's Strategic Risk Management group, based in the UK. Jessica started life as a physicist at Manchester University and completed her D Phil in Theoretical Atomic and Nuclear Physics at Christ Church, Oxford, under Professor Sandars. After a year as a college lecturer at Trinity, Oxford, she began work at the First National Bank of Chicago, now Bank One, where she still works. She is well known as a speaker on the conference circuit, lecturing on a variety of topics such as VaR, capital allocation, credit derivatives and interest rate modelling, and has published articles on various aspects of financial modelling. Nick Webber Nick Webber is a lecturer in Finance at Warwick Business School. Prior to his academic career, Nick had extensive experience in the industrial and commercial world in operational research and computing. After obtaining a PhD in Theoretical Physics from Imperial College he began research into financial options. His main area of research centres on interest rate modelling and computational finance. He has taught practitioner and academic courses for many years, chiefly on options and interest rates. Front Flap Interest Rate Modelling provides a comprehensive resource on all the main aspects of valuing and hedging interest rate products. A series of introductory chapters reviews the theoretical background, pointing out the problems in using naïve valuation and implementation techniques. There follows a full analysis of interest rate models including major categories, such as Affine, HJM and Market models, and in addition, lesser well known types that include Consol, Random field and Jump-augmented Models. Implementation methods are discussed in depth including the latest developments in the use of finite difference, Lattice and Monte Carlo methods and their particular application to the valuation of interest rate derivatives. Containing previously unpublished material, Interest Rate Modelling is a key reference work both for practitioners developing and implementing models for real and for academics teaching and researching in the field.

Interest Rate Derivatives

Author : Ingo Beyna
Publisher : Springer Science & Business Media
ISBN 13 : 3642349250
Total Pages : 220 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Interest Rate Derivatives by : Ingo Beyna

Download or read book Interest Rate Derivatives written by Ingo Beyna and published by Springer Science & Business Media. This book was released on 2013-02-20 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The class of interest rate models introduced by O. Cheyette in 1994 is a subclass of the general HJM framework with a time dependent volatility parameterization. This book addresses the above mentioned class of interest rate models and concentrates on the calibration, valuation and sensitivity analysis in multifactor models. It derives analytical pricing formulas for bonds and caplets and applies several numerical valuation techniques in the class of Cheyette model, i.e. Monte Carlo simulation, characteristic functions and PDE valuation based on sparse grids. Finally it focuses on the sensitivity analysis of Cheyette models and derives Model- and Market Greeks. To the best of our knowledge, this sensitivity analysis of interest rate derivatives in the class of Cheyette models is unique in the literature. Up to now the valuation of interest rate derivatives using PDEs has been restricted to 3 dimensions only, since the computational effort was too great. The author picks up the sparse grid technique, adjusts it slightly and can solve high-dimensional PDEs (four dimensions plus time) accurately in reasonable time. Many topics investigated in this book are new areas of research and make a significant contribution to the scientific community of financial engineers. They also represent a valuable development for practitioners.

Modern Pricing of Interest-Rate Derivatives

Author : Riccardo Rebonato
Publisher : Princeton University Press
ISBN 13 : 1400829321
Total Pages : 486 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Modern Pricing of Interest-Rate Derivatives by : Riccardo Rebonato

Download or read book Modern Pricing of Interest-Rate Derivatives written by Riccardo Rebonato and published by Princeton University Press. This book was released on 2012-01-16 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, interest-rate modeling has developed rapidly in terms of both practice and theory. The academic and practitioners' communities, however, have not always communicated as productively as would have been desirable. As a result, their research programs have often developed with little constructive interference. In this book, Riccardo Rebonato draws on his academic and professional experience, straddling both sides of the divide to bring together and build on what theory and trading have to offer. Rebonato begins by presenting the conceptual foundations for the application of the LIBOR market model to the pricing of interest-rate derivatives. Next he treats in great detail the calibration of this model to market prices, asking how possible and advisable it is to enforce a simultaneous fitting to several market observables. He does so with an eye not only to mathematical feasibility but also to financial justification, while devoting special scrutiny to the implications of market incompleteness. Much of the book concerns an original extension of the LIBOR market model, devised to account for implied volatility smiles. This is done by introducing a stochastic-volatility, displaced-diffusion version of the model. The emphasis again is on the financial justification and on the computational feasibility of the proposed solution to the smile problem. This book is must reading for quantitative researchers in financial houses, sophisticated practitioners in the derivatives area, and students of finance.

Essays on the Volatility of the Term Structure of Interest Rates

Author : Miguel A. Ferreira
Publisher :
ISBN 13 :
Total Pages : 204 pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis Essays on the Volatility of the Term Structure of Interest Rates by : Miguel A. Ferreira

Download or read book Essays on the Volatility of the Term Structure of Interest Rates written by Miguel A. Ferreira and published by . This book was released on 2000 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Elementary Introduction to Stochastic Interest Rate Modeling

Author : Nicolas Privault
Publisher : World Scientific
ISBN 13 : 9814390860
Total Pages : 243 pages
Book Rating : 4.8/5 (143 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 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.

Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives

Author : Jean-Pierre Fouque
Publisher : Cambridge University Press
ISBN 13 : 113950245X
Total Pages : 456 pages
Book Rating : 4.1/5 (395 download)

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Book Synopsis Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives by : Jean-Pierre Fouque

Download or read book Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives written by Jean-Pierre Fouque and published by Cambridge University Press. This book was released on 2011-09-29 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building upon the ideas introduced in their previous book, Derivatives in Financial Markets with Stochastic Volatility, the authors study the pricing and hedging of financial derivatives under stochastic volatility in equity, interest-rate, and credit markets. They present and analyze multiscale stochastic volatility models and asymptotic approximations. These can be used in equity markets, for instance, to link the prices of path-dependent exotic instruments to market implied volatilities. The methods are also used for interest rate and credit derivatives. Other applications considered include variance-reduction techniques, portfolio optimization, forward-looking estimation of CAPM 'beta', and the Heston model and generalizations of it. 'Off-the-shelf' formulas and calibration tools are provided to ease the transition for practitioners who adopt this new method. The attention to detail and explicit presentation make this also an excellent text for a graduate course in financial and applied mathematics.

Heath, Jarrow and Morton Implied Volatility Functions and Conditional Heteroskedasticity Models

Author : Kaushik I. Amin
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Heath, Jarrow and Morton Implied Volatility Functions and Conditional Heteroskedasticity Models by : Kaushik I. Amin

Download or read book Heath, Jarrow and Morton Implied Volatility Functions and Conditional Heteroskedasticity Models written by Kaushik I. Amin and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We evaluate various popular models of interest rate volatility and the Heath-Jarrow-Morton (HJM) approach to value interest rate derivatives by studying the information content and the forecast ability of HJM implied volatility in the Eurodollar futures options market. Implied volatility corresponding to the Ho-Lee, Courtadon, Cox-Ingersoll-Ross, Vasicek, and a linear proportional volatility model are examined within the HJM framework. The exercise compares these implied volatilities to a number of historical volatility benchmarks based on the GARCH model, the Glosten-Jagannathan-Runkle model, and several hybrid models combining the Cox-Ingersoll-Ross and Courtadon spot rate models and the GARCH and GJR approaches to model interest rate volatility. Our results show that there is a strong interaction effect between return shocks and the level of the interest rates in the volatility dynamics that none of the existing HJM volatility models and none of the GARCH type models can fully capture. Specifically, the impact of a shock to interest rate volatility is higher under a high interest rate than a low interest rate. The importance of implied volatility from the Ho-Lee, Courtadon, and Cox-Ingersoll-Ross models is significantly reduced after a term capturing the interaction effect is added to the volatility specification. The importance of implied volatility from the linear proportional and the Vasicek models is reduced but they can still explain a reasonably large portion of the time-variation in volatility.

Estimating Parameters of Short-Term Real Interest Rate Models

Author : Mr.Vadim Khramov
Publisher : International Monetary Fund
ISBN 13 : 1475591225
Total Pages : 27 pages
Book Rating : 4.4/5 (755 download)

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Book Synopsis Estimating Parameters of Short-Term Real Interest Rate Models by : Mr.Vadim Khramov

Download or read book Estimating Parameters of Short-Term Real Interest Rate Models written by Mr.Vadim Khramov and published by International Monetary Fund. This book was released on 2013-10-17 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper sheds light on a narrow but crucial question in finance: What should be the parameters of a model of the short-term real interest rate? Although models for the nominal interest rate are well studied and estimated, dynamics of the real interest rate are rarely explored. Simple ad hoc processes for the short-term real interest rate are usually assumed as building blocks for more sophisticated models. In this paper, parameters of the real interest rate model are estimated in the broad class of single-factor interest rate diffusion processes on U.S. monthly data. It is shown that the elasticity of interest rate volatility—the relationship between the volatility of changes in the interest rate and its level—plays a crucial role in explaining real interest rate dynamics. The empirical estimates of the elasticity of the real interest rate volatility are found to be about 0.5, much lower than that of the nominal interest rate. These estimates show that the square root process, as in the Cox-Ingersoll-Ross model, provides a good characterization of the short-term real interest rate process.

Market Practice In Financial Modelling

Author : Chia Chiang Tan
Publisher : World Scientific Publishing Company
ISBN 13 : 9814434582
Total Pages : 439 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Market Practice In Financial Modelling by : Chia Chiang Tan

Download or read book Market Practice In Financial Modelling written by Chia Chiang Tan and published by World Scientific Publishing Company. This book was released on 2012-07-11 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written to bridge the gap between foundational quantitative finance and market practice, this book goes beyond the basics covered in most textbooks by presenting content concerning actual industry norms, thus resulting in a clearer picture of the field for the readers. These include, for instance, the practitioner's perspective of how local versus stochastic volatility affects forward smile, or the implications of mean reversion on forward volatility.Key considerations for modelling in rates, equities and foreign exchange are presented from the perspective of common themes across various assets, as well as their individual characteristics.The discussion on models emphasizes the key aspects that are relevant to the pricing of different types of financial derivatives, so that the reader can observe how an appropriate choice of models is essential in reflecting the risk profile and hedging considerations for different products.With the knowledge gleaned from this book, readers will attain a more comprehensive understanding of market practice in derivatives modelling.

Term Structure of Interest Rates, Yield Curve Residuals, and the Consistent Pricing of Interest Rate Derivatives

Author : Massoud Heidari
Publisher :
ISBN 13 :
Total Pages : 44 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Term Structure of Interest Rates, Yield Curve Residuals, and the Consistent Pricing of Interest Rate Derivatives by : Massoud Heidari

Download or read book Term Structure of Interest Rates, Yield Curve Residuals, and the Consistent Pricing of Interest Rate Derivatives written by Massoud Heidari and published by . This book was released on 2005 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamic term structure models price interest rate options based on the model-implied fair values of the yield curve, ignoring any pricing residuals on the yield curve that are either from model approximations or market imperfections. In contrast, option pricing in practice often takes the market observed yield curve as given and focuses exclusively on the specification of the volatility structure of forward rates. Thus, if any errors exist on the observed yield curve, they will be carried over permanently. In this paper, we propose an m+n model structure that bridges the gap between the two approaches and consistently prices both interest rates and interest rate options. The first m factors capture the systematic movement of the yield curve, whereas the latter n factors capture the impacts of the yield curve residuals on option pricing. We estimate a 3+3 Gaussian affine example using eight years of data on U.S. dollar LIBOR, swap rates, and interest rate caps. The model performs well in pricing both interest rates and interest rate caps. Furthermore, estimation shows that small residuals on the yield curve can have large impacts on pricing interest rate caps. Under the estimated model, the three yield curve factors explain over 99 percent of the variation on the yield curve, but account for less than 50 percent of the variation on cap implied volatilities. Incorporating the three residual factors improves the explained variance on cap implied volatility to over 99 percent.

Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective

Author : René Carmona
Publisher : Springer Science & Business Media
ISBN 13 : 3540270671
Total Pages : 236 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective by : René Carmona

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