On Term Structure Of Yield Rates 5 The Duffie Kan Two Factor Model Continuation

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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.

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. 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. 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 ...

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.

Numerical Solution of Stochastic Differential Equations with Jumps in Finance

Author : Eckhard Platen
Publisher : Springer Science & Business Media
ISBN 13 : 364213694X
Total Pages : 868 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Numerical Solution of Stochastic Differential Equations with Jumps in Finance by : Eckhard Platen

Download or read book Numerical Solution of Stochastic Differential Equations with Jumps in Finance written by Eckhard Platen and published by Springer Science & Business Media. This book was released on 2010-07-23 with total page 868 pages. Available in PDF, EPUB and Kindle. Book excerpt: In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations (1992). The present monograph builds on the above-mentioned work and provides an introduction to stochastic differential equations with jumps, in both theory and application, emphasizing the numerical methods needed to solve such equations. It presents many new results on higher-order methods for scenario and Monte Carlo simulation, including implicit, predictor corrector, extrapolation, Markov chain and variance reduction methods, stressing the importance of their numerical stability. Furthermore, it includes chapters on exact simulation, estimation and filtering. Besides serving as a basic text on quantitative methods, it offers ready access to a large number of potential research problems in an area that is widely applicable and rapidly expanding. Finance is chosen as the area of application because much of the recent research on stochastic numerical methods has been driven by challenges in quantitative finance. Moreover, the volume introduces readers to the modern benchmark approach that provides a general framework for modeling in finance and insurance beyond the standard risk-neutral approach. It requires undergraduate background in mathematical or quantitative methods, is accessible to a broad readership, including those who are only seeking numerical recipes, and includes exercises that help the reader develop a deeper understanding of the underlying mathematics.

Continuous-Time Asset Pricing Theory

Author : Robert A. Jarrow
Publisher : Springer Nature
ISBN 13 : 3030744108
Total Pages : 470 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Continuous-Time Asset Pricing Theory by : Robert A. Jarrow

Download or read book Continuous-Time Asset Pricing Theory written by Robert A. Jarrow and published by Springer Nature. This book was released on 2021-07-30 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asset pricing theory yields deep insights into crucial market phenomena such as stock market bubbles. Now in a newly revised and updated edition, this textbook guides the reader through this theory and its applications to markets. The new edition features new results on state dependent preferences, a characterization of market efficiency and a more general presentation of multiple-factor models using only the assumptions of no arbitrage and no dominance. Taking an innovative approach based on martingales, the book presents advanced techniques of mathematical finance in a business and economics context, covering a range of relevant topics such as derivatives pricing and hedging, systematic risk, portfolio optimization, market efficiency, and equilibrium pricing models. For applications to high dimensional statistics and machine learning, new multi-factor models are given. This new edition integrates suicide trading strategies into the understanding of asset price bubbles, greatly enriching the overall presentation and further strengthening the book’s underlying theme of economic bubbles. Written by a leading expert in risk management, Continuous-Time Asset Pricing Theory is the first textbook on asset pricing theory with a martingale approach. Based on the author’s extensive teaching and research experience on the topic, it is particularly well suited for graduate students in business and economics with a strong mathematical background.

Financial Derivatives Pricing

Author : Robert A. Jarrow
Publisher : World Scientific
ISBN 13 : 9812819223
Total Pages : 609 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis Financial Derivatives Pricing by : Robert A. Jarrow

Download or read book Financial Derivatives Pricing written by Robert A. Jarrow and published by World Scientific. This book was released on 2008 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of original papers by Robert Jarrow that contributed to significant advances in financial economics. Divided into three parts, Part I concerns option pricing theory and its foundations. The papers here deal with the famous Black-Scholes-Merton model, characterizations of the American put option, and the first applications of arbitrage pricing theory to market manipulation and liquidity risk.Part II relates to pricing derivatives under stochastic interest rates. Included is the paper introducing the famous HeathOCoJarrowOCoMorton (HJM) model, together with papers on topics like the characterization of the difference between forward and futures prices, the forward price martingale measure, and applications of the HJM model to foreign currencies and commodities.Part III deals with the pricing of financial derivatives considering both stochastic interest rates and the likelihood of default. Papers cover the reduced form credit risk model, in particular the original Jarrow and Turnbull model, the Markov model for credit rating transitions, counterparty risk, and diversifiable default risk.

A Yield-factor Model of Interest Rates

Author : Darrell Duffie
Publisher :
ISBN 13 :
Total Pages : 36 pages
Book Rating : 4.:/5 (464 download)

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Book Synopsis A Yield-factor Model of Interest Rates by : Darrell Duffie

Download or read book A Yield-factor Model of Interest Rates written by Darrell Duffie and published by . This book was released on 1995 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Handbook of Fixed-Income Securities

Author : Pietro Veronesi
Publisher : John Wiley & Sons
ISBN 13 : 1118709195
Total Pages : 630 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 2016-04-04 with total page 630 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.

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.

Mortgage Valuation Models

Author : Andrew S. Davidson
Publisher : Oxford University Press, USA
ISBN 13 : 0199998167
Total Pages : 465 pages
Book Rating : 4.1/5 (999 download)

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Book Synopsis Mortgage Valuation Models by : Andrew S. Davidson

Download or read book Mortgage Valuation Models written by Andrew S. Davidson and published by Oxford University Press, USA. This book was released on 2014 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: Valuation of mortgage-backed securities requires blending empirical analysis of borrower behavior and mathematical modeling of interest rates and home prices, with recognition of various prices of risk and uncertainty. This book offers a detailed description of the sophisticated theories and advanced methods used for the real-world valuation of MBS.

Encyclopedia of Actuarial Science

Author : Jef L. Teugels
Publisher :
ISBN 13 :
Total Pages : 642 pages
Book Rating : 4.0/5 ( download)

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Book Synopsis Encyclopedia of Actuarial Science by : Jef L. Teugels

Download or read book Encyclopedia of Actuarial Science written by Jef L. Teugels and published by . This book was released on 2004 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The Encyclopedia of Actuarial Science presents a timely and comprehensive body of knowledge designed to serve as an essential reference for the actuarial profession and all related business and financial activities, as well as researchers and students in actuarial science and related areas. Drawing on the experience of leading international editors and authors from industry and academic research the encyclopedia provides an authoritative exposition of both quantitative methods and practical aspects of actuarial science and insurance. The cross-disciplinary nature of the work is reflected not only in its coverage of key concepts from business, economics, risk, probability theory and statistics but also by the inclusion of supporting topics such as demography, genetics, operations research and informatics. Visit the encyclopedia's website where you can gain access to further resources and freely available sample articles: www.wileyeurope.com/eoas." -- Publisher.

Numerical Simulation of the Term Structure of Interest Rates Using a Random Field

Author : Stuart McDonald
Publisher :
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Numerical Simulation of the Term Structure of Interest Rates Using a Random Field by : Stuart McDonald

Download or read book Numerical Simulation of the Term Structure of Interest Rates Using a Random Field written by Stuart McDonald and published by . This book was released on 2002 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Quantitative Fund Management

Author : M.A.H. Dempster
Publisher : CRC Press
ISBN 13 : 1420081926
Total Pages : 488 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Quantitative Fund Management by : M.A.H. Dempster

Download or read book Quantitative Fund Management written by M.A.H. Dempster and published by CRC Press. This book was released on 2008-12-22 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: The First Collection That Covers This Field at the Dynamic Strategic and One-Period Tactical Levels. Addressing the imbalance between research and practice, Quantitative Fund Management presents leading-edge theory and methods, along with their application in practical problems encountered in the fund management industry. A Current Snapshot of State-of-the-Art Applications of Dynamic Stochastic Optimization Techniques to Long-Term Financial Planning - The first part of the book initially looks at how the quantitative techniques of the equity industry are shifting from basic Markowitz mean-variance portfolio optimization to risk management and trading applications. This section also explores novel aspects of lifetime individual consumption investment problems, fixed-mix portfolio rebalancing allocation strategies, debt management for funding mortgages and national debt, and guaranteed return fund construction. Up-to-Date Overview of Tactical Financial Planning and Risk Management - The second section covers nontrivial computational approaches to tactical fund management. This part focuses on portfolio construction and risk management at the individual security or fund manager level over the period up to the next portfolio rebalance. It discusses non-Gaussian returns, new risk-return tradeoffs, and the robustness of benchmarks and portfolio decisions. The Future Use of Quantitative Techniques in Fund Management - With contributions from well-known academics and practitioners, this volume will undoubtedly foster the recognition and wider acceptance of stochastic optimization techniques in financial practice.

Comparing Models for Forecasting the Yield Curve

Author : Marco S. Matsumura
Publisher :
ISBN 13 :
Total Pages : 40 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Comparing Models for Forecasting the Yield Curve by : Marco S. Matsumura

Download or read book Comparing Models for Forecasting the Yield Curve written by Marco S. Matsumura and published by . This book was released on 2006 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Yield Curves and Forward Curves for Diffusion Models of Short Rates

Author : Gennady A. Medvedev
Publisher : Springer
ISBN 13 : 9783030155025
Total Pages : 230 pages
Book Rating : 4.1/5 (55 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 2020-08-14 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.