On Term Structure Of Yield Rates 4 The Duffie Kan Two Factor Model

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On Term Structure of Yield Rates. 4. The Duffie - Kan Two Factor Model

Author : Gennady Medvedev
Publisher :
ISBN 13 :
Total Pages : 8 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis On Term Structure of Yield Rates. 4. The Duffie - Kan Two Factor Model by : Gennady Medvedev

Download or read book On Term Structure of Yield Rates. 4. The Duffie - Kan Two Factor Model written by Gennady Medvedev and published by . This book was released on 2017 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest rate models in which the short-term rate is a unique state variable are usually considered. These models are attractive that analytical decisions often give the chance to receive and provide concerning the simple computing analysis. However one-factor models have certain lacks. Basic of them consists that all term structure determines by only the unique value of the short-term rate fixed at the initial moment of construction of term structure. And it is represented unreasonable from the economic point of view. To avoid this lack authors suggest to use for modeling of dynamics of the interest rate more than one state variable. At transition from the unique factor to several there should be an improvement of approximation of term structure. In general the price for it is loss of possibility of receiving of analytical decisions, receiving of the equations with partial derivatives with the raised dimension and complication of procedure of receiving of results. In the paper the Duffie-Kan models, describing dynamics of the short-term interest rate in a case when the state of the financial market is characterized not only by level of the interest rate, but also one more other parameter changing in time are investigated. It is considered two cases. In the first in quality of an additional state variable local on time the average value of the short-term interest rate is accepted. In the second case as an additional state variable the instant variance of the interest rate is accepted. Two-factor models are under construction so that they led to affine term structure of yield. The basic attention is given to definition of functions of term structure. As the equations turning out for these functions do not suppose analytical decisions, it is offered to find their approximations. In view of that in real cases the volatility is usually small, the method of small parameter of Poincare is for this purpose used.

On Term Structure of Yield Rates. 5. The Duffie - Kan Two Factor Model (Continuation).

Author : Gennady Medvedev
Publisher :
ISBN 13 :
Total Pages : 9 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis On Term Structure of Yield Rates. 5. The Duffie - Kan Two Factor Model (Continuation). by : Gennady Medvedev

Download or read book On Term Structure of Yield Rates. 5. The Duffie - Kan Two Factor Model (Continuation). written by Gennady Medvedev and published by . This book was released on 2017 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: Models of Daffie-Kan, describing dynamics of a short-term interest rate in a case when the state of the financial market is characterized not only by level of the interest rate, but also one more parameter changing in time are investigated. Two cases are considered. In the first in quality of an additional state variable the local on time average value of a short-term interest rate is taken. In the second case as an additional state variable the instant variance of an interest rate is accepted. Two-factor models are under construction so that they led to affine term structure of yield. The main attention is given to properties of yield curve and a forward curve when dynamics of a short-term interest rate is described by two-factor models of Daffie-Kan. Because functions of term structure for additional variables in a closed form can't be received, the type of curves as a whole (for entire interval of change of time) is analyzed by means of numerical calculations though properties of curves on the ends of an interval become clear analytically. For model «a rate - its local average» it is appeared that limiting properties of long-term yield are defined only by properties of an additional variable - local average of interest rates. For model «a rate - its instant variance» it became clear that this model has economic sense only when the weight factor of instant variance at determination of a short-term yield rate is equal to zero. Comparison of yield curves and forward curves for one-factor model and two-factor models shows that at the accepted parameters these curves considerably differ. As values of weight factors essentially influence behavior of yield curves and forward curves, they should be estimated along with market parameters of the price of risk.

On Term Structure of Yield Rates. 3. The Duffie - Kan One-Factor Model

Author : Gennady Medvedev
Publisher :
ISBN 13 :
Total Pages : 8 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis On Term Structure of Yield Rates. 3. The Duffie - Kan One-Factor Model by : Gennady Medvedev

Download or read book On Term Structure of Yield Rates. 3. The Duffie - Kan One-Factor Model written by Gennady Medvedev and published by . This book was released on 2017 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: The time structure of interest rates plays a key role at the bond pricing. Therefore its properties interest many financial analysts. However in the available literature usually there is a schematic description of these properties. Attempt of the detailed description of all possible forms of time structure for a class of affine models of interest rates as for these models it is possible to write down decisions in the closed form here becomes. As the basic the model of Duffie - Kan (DK) with any bottom border for risk free (spot) interest rate is accepted. Results for widely known models CIR and Vasiček turn out as special cases. For one-factor model of affine yield of Duffie - Kan analytical representations of yield curves and forward curves are found and their properties when the duration measure of risk free rates as a time variable is used are investigated. It is shown that for all variety of parameters exist only four possible kinds of yield curves. For small terms to maturity a bond yield is defined, basically, current level of risk free rates while for very long terms to maturity the yield is defined by a stationary expectation of risk free rates. In this connection it would be possible to expect that influence of current level of risk free rates on yield with time increase will damp. However, it is not so. It has appeared that current level of risk free rates essentially influences on sight of entire yield curve and a forward curve. Let's notice also that yield curve and a forward curve start from one point and at increase in term to maturity converge to the same limit that differs from usually accepted point of view that these curves diverge when the term to maturity increase.

Yield Curves and Forward Curves for Diffusion Models of Short Rates

Author : Gennady A. Medvedev
Publisher : Springer
ISBN 13 : 3030155005
Total Pages : 230 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Yield Curves and Forward Curves for Diffusion Models of Short Rates by : Gennady A. Medvedev

Download or read book Yield Curves and Forward Curves for Diffusion Models of Short Rates written by Gennady A. Medvedev and published by Springer. This book was released on 2019-05-18 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to the study of the term structures of the yields of zero-coupon bonds. The methods it describes differ from those usually found in the literature in that the time variable is not the term to maturity but the interest rate duration, or another convenient non-linear transformation of terms. This makes it possible to consider yield curves not only for a limited interval of term values, but also for the entire positive semiaxis of terms. The main focus is the comparative analysis of yield curves and forward curves and the analytical study of their features. Generalizations of yield term structures are studied where the dimension of the state space of the financial market is increased. In cases where the analytical approach is too cumbersome, or impossible, numerical techniques are used. This book will be of interest to financial analysts, financial market researchers, graduate students and PhD students.

On Term Structure of Yield Rates. 6. The Three Factor Model

Author : Gennady Medvedev
Publisher :
ISBN 13 :
Total Pages : 8 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis On Term Structure of Yield Rates. 6. The Three Factor Model by : Gennady Medvedev

Download or read book On Term Structure of Yield Rates. 6. The Three Factor Model written by Gennady Medvedev and published by . This book was released on 2017 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: Models of Duffie - Kan, d ...

Analysing and Interpreting the Yield Curve

Author : Moorad Choudhry
Publisher : John Wiley & Sons
ISBN 13 : 1119141060
Total Pages : 384 pages
Book Rating : 4.1/5 (191 download)

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Book Synopsis Analysing and Interpreting the Yield Curve by : Moorad Choudhry

Download or read book Analysing and Interpreting the Yield Curve written by Moorad Choudhry and published by John Wiley & Sons. This book was released on 2019-04-15 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understand and interpret the global debt capital markets Now in a completely updated and expanded edition, this is a technical guide to the yield curve, a key indicator of the global capital markets and the understanding and accurate prediction of which is critical to all market participants. Being able to accurately and timely predict the shape and direction of the curve permits practitioners to consistently outperform the market. Analysing and Interpreting the Yield Curve, 2nd Edition describes what the yield curve is, explains what it tells participants, outlines the significance of certain shapes that the curve assumes and, most importantly, demonstrates what factors drive it and how it is modelled and used. Covers the FTP curve, the multi-currency curve, CSA, OIS-Libor and 3-curve models Gets you up to speed on the secured curve Describes application of theoretical versus market curve relative value trading Explains the concept of the risk-free rate Accessible demonstration of curve interpolation best-practice using cubic spline, Nelson-Siegel and Svensson 94 models This advanced text is essential reading for traders, asset managers, bankers and financial analysts, as well as graduate students in banking and finance.

Advanced Financial Modelling

Author : Hansjörg Albrecher
Publisher : Walter de Gruyter
ISBN 13 : 3110213133
Total Pages : 465 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Advanced Financial Modelling by : Hansjörg Albrecher

Download or read book Advanced Financial Modelling written by Hansjörg Albrecher and published by Walter de Gruyter. This book was released on 2009 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation This book is a collection of state-of-the-art surveys on various topics in mathematical finance, with an emphasis on recent modelling and computational approaches. The volume is related to a a ~Special Semester on Stochastics with Emphasis on Financea (TM) that took place from September to December 2008 at the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences in Linz, Austria

Modeling the Term Structure of Interest Rates

Author : Rajna Gibson
Publisher : Now Publishers Inc
ISBN 13 : 1601983727
Total Pages : 171 pages
Book Rating : 4.6/5 (19 download)

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Book Synopsis Modeling the Term Structure of Interest Rates by : Rajna Gibson

Download or read book Modeling the Term Structure of Interest Rates written by Rajna Gibson and published by Now Publishers Inc. This book was released on 2010 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Dynamic Term Structure Modeling

Author : Sanjay K. Nawalkha
Publisher : John Wiley & Sons
ISBN 13 : 0470140062
Total Pages : 722 pages
Book Rating : 4.4/5 (71 download)

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Book Synopsis Dynamic Term Structure Modeling by : Sanjay K. Nawalkha

Download or read book Dynamic Term Structure Modeling written by Sanjay K. Nawalkha and published by John Wiley & Sons. This book was released on 2007-05-23 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

On Term Structure of Yield Rates. 7. Another Temporal Variable for Maturities

Author : Gennady Medvedev
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis On Term Structure of Yield Rates. 7. Another Temporal Variable for Maturities by : Gennady Medvedev

Download or read book On Term Structure of Yield Rates. 7. Another Temporal Variable for Maturities written by Gennady Medvedev and published by . This book was released on 2017 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: In paper it is offered to consider a time variable that describes term to maturity of zero-coupon bonds as result of nonlinear transformation of the temporary terms that are independent on parameters of interest rate dynamics model, allowing to map the time numerical axis into an interval of unit length. This way has advantages before application as a measure of time of a duration of a short-term interest rate because at the duration application the time variable depends on parameters of considered models that complicates a comparison of yields for the same real terms to maturity. It is shown that resulting yield functions possess practically the same properties as a yield to maturity curve and a forward curve, except for (in certain cases) properties connected with the second derivative. At the same time they it is more convenient because allow to analyze visually the yields on all time axis. Use of such approach is illustrated in the analysis of properties of the yield curve and the forward curve for one-factor model of Duffie - Kan, Fong - Vasicek two-factor model and three-factor models of interest rates: Fong - Vasicek expanded model, Chen model and the BDFS model. In paper the mathematical models of dynamics of the state variables for all these cases (six various models) are formulated, the equations for functions of term structure are deduced and (when it is possible) their analytical solutions are found. As the main part of the equations can be solved only by calculations, numerical calculations for all six models are carried out and comparisons of yield functions characterizing their term structure are carried out. Calculations were carried out for a set of the parameters based on estimates, published by D. Ahn and B. Gao, fitting one-factor Duffie - Kan model for the description of dynamics of process of an annualized one-month U.S. Treasury bill rate for the supervision period from January, 1960 to February, 1991. Calculations showed that the increase of model dimension implies the decrease of yield rate.

Term-Structure Models

Author : Damir Filipovic
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.

Quantitative Analysis In Financial Markets: Collected Papers Of The New York University Mathematical Finance Seminar (Vol Iii)

Author : Marco Avellaneda
Publisher : World Scientific
ISBN 13 : 9814490598
Total Pages : 363 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Quantitative Analysis In Financial Markets: Collected Papers Of The New York University Mathematical Finance Seminar (Vol Iii) by : Marco Avellaneda

Download or read book Quantitative Analysis In Financial Markets: Collected Papers Of The New York University Mathematical Finance Seminar (Vol Iii) written by Marco Avellaneda and published by World Scientific. This book was released on 2002-01-18 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book contains lectures presented at the Courant Institute's Mathematical Finance Seminar. The audience consisted of academics from New York University and other universities, as well as practitioners from investment banks, hedge funds and asset-management firms.

Interest Rate Modeling for Risk Management: Market Price of Interest Rate Risk (Second Edition)

Author : Takashi Yasuoka
Publisher : Bentham Science Publishers
ISBN 13 : 1681086891
Total Pages : 325 pages
Book Rating : 4.6/5 (81 download)

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Book Synopsis Interest Rate Modeling for Risk Management: Market Price of Interest Rate Risk (Second Edition) by : Takashi Yasuoka

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.

Seminar on Stochastic Analysis, Random Fields and Applications III

Author : Robert C. Dalang
Publisher : Birkhäuser
ISBN 13 : 3034882092
Total Pages : 310 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Seminar on Stochastic Analysis, Random Fields and Applications III by : Robert C. Dalang

Download or read book Seminar on Stochastic Analysis, Random Fields and Applications III written by Robert C. Dalang and published by Birkhäuser. This book was released on 2012-12-06 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 20 refereed research or review papers presented at the five-day Third Seminar on Stochastic Analysis, Random Fields and Applications which took place at the Centro Stefano Franscini (Monte Verità) in Ascona, Switzerland, from September 20 to 24, 1999. The seminar focused on three topics: fundamental aspects of stochastic analysis, physical modeling, and applications to financial engineering. The third topic was the subject of a mini-symposium on stochastic methods in financial models.

Empirical Dynamic Asset Pricing

Author : Kenneth J. Singleton
Publisher : Princeton University Press
ISBN 13 : 1400829232
Total Pages : 497 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Empirical Dynamic Asset Pricing by : Kenneth J. Singleton

Download or read book Empirical Dynamic Asset Pricing written by Kenneth J. Singleton and published by Princeton University Press. This book was released on 2009-12-13 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by one of the leading experts in the field, this book focuses on the interplay between model specification, data collection, and econometric testing of dynamic asset pricing models. The first several chapters provide an in-depth treatment of the econometric methods used in analyzing financial time-series models. The remainder explores the goodness-of-fit of preference-based and no-arbitrage models of equity returns and the term structure of interest rates; equity and fixed-income derivatives prices; and the prices of defaultable securities. Singleton addresses the restrictions on the joint distributions of asset returns and other economic variables implied by dynamic asset pricing models, as well as the interplay between model formulation and the choice of econometric estimation strategy. For each pricing problem, he provides a comprehensive overview of the empirical evidence on goodness-of-fit, with tables and graphs that facilitate critical assessment of the current state of the relevant literatures. As an added feature, Singleton includes throughout the book interesting tidbits of new research. These range from empirical results (not reported elsewhere, or updated from Singleton's previous papers) to new observations about model specification and new econometric methods for testing models. Clear and comprehensive, the book will appeal to researchers at financial institutions as well as advanced students of economics and finance, mathematics, and science.

Handbook of Fixed-Income Securities

Author : Pietro Veronesi
Publisher : John Wiley & Sons
ISBN 13 : 1118709187
Total Pages : 632 pages
Book Rating : 4.1/5 (187 download)

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Book Synopsis Handbook of Fixed-Income Securities by : Pietro Veronesi

Download or read book Handbook of Fixed-Income Securities written by Pietro Veronesi and published by John Wiley & Sons. This book was released on 2016-03-23 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive guide to the current theories and methodologies intrinsic to fixed-income securities Written by well-known experts from a cross section of academia and finance, Handbook of Fixed-Income Securities features a compilation of the most up-to-date fixed-income securities techniques and methods. The book presents crucial topics of fixed income in an accessible and logical format. Emphasizing empirical research and real-life applications, the book explores a wide range of topics from the risk and return of fixed-income investments, to the impact of monetary policy on interest rates, to the post-crisis new regulatory landscape. Well organized to cover critical topics in fixed income, Handbook of Fixed-Income Securities is divided into eight main sections that feature: • An introduction to fixed-income markets such as Treasury bonds, inflation-protected securities, money markets, mortgage-backed securities, and the basic analytics that characterize them • Monetary policy and fixed-income markets, which highlight the recent empirical evidence on the central banks’ influence on interest rates, including the recent quantitative easing experiments • Interest rate risk measurement and management with a special focus on the most recent techniques and methodologies for asset-liability management under regulatory constraints • The predictability of bond returns with a critical discussion of the empirical evidence on time-varying bond risk premia, both in the United States and abroad, and their sources, such as liquidity and volatility • Advanced topics, with a focus on the most recent research on term structure models and econometrics, the dynamics of bond illiquidity, and the puzzling dynamics of stocks and bonds • Derivatives markets, including a detailed discussion of the new regulatory landscape after the financial crisis and an introduction to no-arbitrage derivatives pricing • Further topics on derivatives pricing that cover modern valuation techniques, such as Monte Carlo simulations, volatility surfaces, and no-arbitrage pricing with regulatory constraints • Corporate and sovereign bonds with a detailed discussion of the tools required to analyze default risk, the relevant empirical evidence, and a special focus on the recent sovereign crises A complete reference for practitioners in the fields of finance, business, applied statistics, econometrics, and engineering, Handbook of Fixed-Income Securities is also a useful supplementary textbook for graduate and MBA-level courses on fixed-income securities, risk management, volatility, bonds, derivatives, and financial markets. Pietro Veronesi, PhD, is Roman Family Professor of Finance at the University of Chicago Booth School of Business, where he teaches Masters and PhD-level courses in fixed income, risk management, and asset pricing. Published in leading academic journals and honored by numerous awards, his research focuses on stock and bond valuation, return predictability, bubbles and crashes, and the relation between asset prices and government policies.

Modelling Stock Market Volatility

Author : Peter H. Rossi
Publisher : Elsevier
ISBN 13 : 0080511872
Total Pages : 505 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Modelling Stock Market Volatility by : Peter H. Rossi

Download or read book Modelling Stock Market Volatility written by Peter H. Rossi and published by Elsevier. This book was released on 1996-11-19 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: This essay collection focuses on the relationship between continuous time models and Autoregressive Conditionally Heteroskedastic (ARCH) models and applications. For the first time, Modelling Stock Market Volatility provides new insights about the links between these two models and new work on practical estimation methods for continuous time models. Featuring the pioneering scholarship of Daniel Nelson, the text presents research about the discrete time model, continuous time limits and optimal filtering of ARCH models, and the specification and estimation of continuous time processes. This work will lead to a rapid growth in their empirical application as they are increasingly subjected to routine specification testing. Provides for the first time new insights on the links between continuous time and ARCH models Collects seminal scholarship by some of the most renowned researchers in finance and econometrics Captures complex arguments underlying the approximation and proper statistical modelling of continuous time volatility dynamics