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Yield Curves and Forward Curves for Diffusion Models of Short Rates

Author: Gennady A. Medvedev

Publisher: Springer

Published: 2019-05-18

Total Pages: 230

ISBN-13: 3030155005

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. 3. The Duffie - Kan One-Factor Model

Author: Gennady Medvedev

Publisher:

Published: 2017

Total Pages: 8

ISBN-13:

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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 Curve Modeling and Forecasting

Author: Francis X. Diebold

Publisher: Princeton University Press

Published: 2013-01-15

Total Pages: 223

ISBN-13: 0691146802

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Understanding the dynamic evolution of the yield curve is critical to many financial tasks, including pricing financial assets and their derivatives, managing financial risk, allocating portfolios, structuring fiscal debt, conducting monetary policy, and valuing capital goods. Unfortunately, most yield curve models tend to be theoretically rigorous but empirically disappointing, or empirically successful but theoretically lacking. In this book, Francis Diebold and Glenn Rudebusch propose two extensions of the classic yield curve model of Nelson and Siegel that are both theoretically rigorous and empirically successful. The first extension is the dynamic Nelson-Siegel model (DNS), while the second takes this dynamic version and makes it arbitrage-free (AFNS). Diebold and Rudebusch show how these two models are just slightly different implementations of a single unified approach to dynamic yield curve modeling and forecasting. They emphasize both descriptive and efficient-markets aspects, they pay special attention to the links between the yield curve and macroeconomic fundamentals, and they show why DNS and AFNS are likely to remain of lasting appeal even as alternative arbitrage-free models are developed. Based on the Econometric and Tinbergen Institutes Lectures, Yield Curve Modeling and Forecasting contains essential tools with enhanced utility for academics, central banks, governments, and industry.

Yield Curve Modeling

Author: Y. Stander

Publisher: Springer

Published: 2005-06-23

Total Pages: 202

ISBN-13: 0230513743

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This book will give the reader insight into how to model yield curves in our incomplete and imperfect financial markets. An extensive list of yield curve models are shown and discussed. Using actual market instruments, these models are then applied and the different yield curves are compared. It is assumed that the reader has a basic understanding of the financial instruments available in the market. Various issues that have to be taken into account in practice are discussed, like daycount conventions, business-day rules, the credit quality of the instrument and liquidity to name but a few. It is also shown how yield curves can be used to estimate credit spreads and country risk premiums. Creating a yield curve model has some implications in risk management. Specifically - the model, operational, liquidity and basis risks are discussed.

A Model of Discontinuous Interest Rate Behavior, Yield Curves, and Volatility

Author: Steven L. Heston

Publisher:

Published: 1998

Total Pages:

ISBN-13:

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This paper develops an equilibrium model in which interest rates follow a discontinuous (generalized) gamma process. The gamma process has finite variation, takes an infinite number of quot;smallquot; jumps in every interval, and includes the Wiener process as a limiting case. The gamma interest rate model produces yield curves that closely resemble those of diffusion models. But in contrast to diffusion models, the curvature of the yield curve does not directly depend on the true volatility of the interest rate process, but instead depends on a different risk-neutral volatility. The gamma model appears to fit the distribution of interest rates changes and the jump characteristics of interest rate paths. Empirical tests reject a diffusion model of interest rates in favor of the more general gamma model because daily interest rate innovations are highly leptokurtic.

Analysing and Interpreting the Yield Curve

Author: Moorad Choudhry

Publisher: John Wiley & Sons

Published: 2019-04-15

Total Pages: 390

ISBN-13: 1119141052

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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.

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

Author: Gennady Medvedev

Publisher:

Published: 2017

Total Pages: 9

ISBN-13:

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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 in Two-Factor Vasiček Models

Author: Gennady Medvedev

Publisher:

Published: 2017

Total Pages: 6

ISBN-13:

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The paper studies the properties of curves of yield to maturity and forward rates curves for multifactorial and three concrete two-factor Vasiček models with two state variables:• The short-term rate and its average local-in-time value; • The short-term rate and its exponentially smoothed average value; • The Shiu - Yao model. Their comparison is given and a numerical example based on the analysis of real data is given.

Modelling the Yield Curve

Author: Mr.Mark P. Taylor

Publisher: International Monetary Fund

Published: 1991-12-01

Total Pages: 38

ISBN-13: 145193145X

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We test and estimate a variety of alternative models of the yield curve, using weekly, high-quality U.K. data. We extend the Campbell-Shiller technique to the overlapping data case and apply it to reject the pure expectations hypothesis under rational expectations. We also find that risk measures, in the form of conditional interest rate volatility, are unable to explain the term premium. A simple, market segmentation approach is, however, moderately successful in explaining the term premium.

Term-Structure Models

Author: Damir Filipovic

Publisher: Springer Science & Business Media

Published: 2009-07-28

Total Pages: 259

ISBN-13: 3540680152

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Changing interest rates constitute one of the major risk sources for banks, insurance companies, and other financial institutions. Modeling the term-structure movements of interest rates is a challenging task. This volume gives an introduction to the mathematics of term-structure models in continuous time. It includes practical aspects for fixed-income markets such as day-count conventions, duration of coupon-paying bonds and yield curve construction; arbitrage theory; short-rate models; the Heath-Jarrow-Morton methodology; consistent term-structure parametrizations; affine diffusion processes and option pricing with Fourier transform; LIBOR market models; and credit risk. The focus is on a mathematically straightforward but rigorous development of the theory. Students, researchers and practitioners will find this volume very useful. Each chapter ends with a set of exercises, that provides source for homework and exam questions. Readers are expected to be familiar with elementary Itô calculus, basic probability theory, and real and complex analysis.