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On A General Class Of One Factor Models For The Term Structure Of Interest Rates
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Book Synopsis On a General Class of One-Factor Models for the Term Structure of Interest Rates by : Wolfgang M. Schmidt
Download or read book On a General Class of One-Factor Models for the Term Structure of Interest Rates written by Wolfgang M. Schmidt and published by . This book was released on 1997 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a general one-factor model for the term structure of interest rates which is based upon a model for the short rate. The dynamics of the short rate is described by an appropriate function of a time changed Wiener process. The model allows for perfect fitting of given term structure of interest rates and volatilities, as well as for mean reversion. Moreover, every type of distribution of the short rate can be achieved, in particular, the distribution can be concentrated on an interval. The model includes several popular models such as the generalized Vasicek (or Hull- White) model, the Black-Derman-Toy, Black-Karasinski model, and others. There is a unified numerical approach to the general model based on a simple lattice approximation which, in particular, can be chosen as a binomial or N-nomial lattice with branching probabilities 1/N.
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.
Book Synopsis Estimating One-factor Models of Short-term Interest Rates by : Desmond John Mc Manus
Download or read book Estimating One-factor Models of Short-term Interest Rates written by Desmond John Mc Manus and published by . This book was released on 1999 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: Considers a wide range of several continuous-time one-factor models for short-term interest rates that are nested into one general model.
Book Synopsis One-factor models of the term structure of interest rates by :
Download or read book One-factor models of the term structure of interest rates written by and published by . This book was released on 2004 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis Essays on the Term Structure of Interest Rates by : Wei Shi
Download or read book Essays on the Term Structure of Interest Rates written by Wei Shi and published by . This book was released on 1995 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis On the Estimation of Term Structure Models and An Application to the United States by : International Monetary Fund
Download or read book On the Estimation of Term Structure Models and An Application to the United States written by International Monetary Fund and published by International Monetary Fund. This book was released on 2010-11-01 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper discusses the estimation of models of the term structure of interest rates. After reviewing the term structure models, specifically the Nelson-Siegel Model and Affine Term- Structure Model, this paper estimates the terms structure of Treasury bond yields for the United States with pre-crisis data. This paper uses a software developed by Fund staff for this purpose. This software makes it possible to estimate the term structure using at least nine models, while opening up the possibility of generating simulated paths of the term structure.
Book Synopsis A Two-Factor Model of the German Term Structure of Interest Rates by : Nuno Cassola
Download or read book A Two-Factor Model of the German Term Structure of Interest Rates written by Nuno Cassola and published by . This book was released on 2004 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we show that a two-factor constant volatility model provides an adequate description of the dynamics and shape of the German term structure of interest rates from 1972 up to 1998. The model also provides reasonable estimates of the volatility and term premium curves. Following the conjecture that the two factors driving the German term structure of interest rates represent the ex-ante real interest rate and the expected inflation rate, the identification of one factor with expected inflation is discussed. Our estimates are obtained using a Kalman filter and a maximum likelihood procedure including in the measurement equation both the yields and their volatilities.
Book Synopsis Building and Using Dynamic Interest Rate Models by : Ken O. Kortanek
Download or read book Building and Using Dynamic Interest Rate Models written by Ken O. Kortanek and published by John Wiley & Sons. This book was released on 2001-11-28 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a new approach to interest rate and modeling term structure by using models based on optimization of dynamical systems, rather than the traditional stochastic differential equation models. The authors use dynamic models to estimate the term structure of interest rates and show the reader how to build their own numerical simulations. It includes software that will enable readers to simulate the various models covered in the book.
Book Synopsis An Examination of the Static and Dynamic Performance of Interest Rate Option Pricing Models in the Dollar Cap-Floor Markets by : Anurag Gupta
Download or read book An Examination of the Static and Dynamic Performance of Interest Rate Option Pricing Models in the Dollar Cap-Floor Markets written by Anurag Gupta and published by . This book was released on 2008 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper examines the static and dynamic accuracy of interest rate option pricing models in the U.S. dollar interest rate cap and floor markets. We evaluate alternative one-factor and two-factor term structure models of the spot and the forward interest rates on the basis of their out-of-sample predictive ability in terms of pricing and hedging performance. The one-factor models analyzed consist of two spot-rate specifications (Hull and White (1990) and Black-Karasinski (1991), five forward rate specifications (within the general Heath, Jarrow and Morton (1990b) class), and one LIBOR market model (Brace, Gatarek and Musiela (1997) [BGM]). For two-factor models, two alternative forward rate specifications are implemented within the HJM framework. We conduct tests on daily data from March-December 1998, consisting of actual cap and floor prices across both strike rates and maturities. Results show that fitting the skew of the underlying interest rate distribution provides accurate pricing results within a one-factor framework. However, for hedging performance, introducing a second stochastic factor is more important than fitting the skew of the underlying distribution. Overall, the one-factor lognormal model for short term interest rates outperforms other competing models in pricing tests, while two-factor models perform significantly better than one-factor models in hedging tests. Modeling the second factor allows a better representation of the dynamic evolution of the term structure by incorporating expected twists in the yield curve. Thus, the interest rate dynamics embedded in two-factor models appears to be closer to the one driving the actual economic environment, leading to more accurate hedges. This constitutes evidence against claims in the literature that correctly specified and calibrated one-factor models could replace multi-factor models for consistent pricing and hedging of interest rate contingent claims.
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.
Book Synopsis Analyzing the Term Structure of Interest Rates with Macroeconomic Factor Models by : Arne Halberstadt
Download or read book Analyzing the Term Structure of Interest Rates with Macroeconomic Factor Models written by Arne Halberstadt and published by . This book was released on 2013 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Term Structure Models with Unspanned Factors and Unspanned Stochastic Volatility by : Alex Backwell
Download or read book Term Structure Models with Unspanned Factors and Unspanned Stochastic Volatility written by Alex Backwell and published by . This book was released on 2018 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: Certain models of the term structure of interest rates exhibit unspanned stochastic volatility (USV). A model has this property if it involves a source of stochastic variation -- called an unspanned factor -- that does not affect the model's interest rates directly, but does affect the extent to which future interests are liable to change (that is, interest-rate volatility). This thesis is concerned with these models, from a variety of perspectives.Firstly, the theoretical foundation of the USV property is addressed. Formal definitions of unspanned factors and USV are developed, generalising ones tentatively proposed in the literature. Several results from these definitions and the accompanying framework are derived. Particularly, the ability to hedge general claims (i.e., the completeness or lack thereof) of these models is examined in detail. Examples are given to illustrate the features of the proposed framework and the necessity of the generalised definitions.Secondly, the empirical issue of whether USV models are necessary to plausibly represent ob- served interest-rate markets is interrogated. An empirical derivative-hedging approach is adopted, the results of which are contextualised by also treating data simulated from models with USV and non-USV versions. It is shown that hedging effectiveness is relatively robust to the presence of USV, which resolves the apparent conflict between the two studies that have taken a hedging approach to this question. Despite the cross-sectional hedging effects being surprisingly minor, further regression results show that USV models are needed to model the time series of market interest rates.Finally, the thesis addresses a certain class of models that exhibit USV: those with one spanned factor (driving interest-rate variation) and one unspanned, volatility-related factor. Being the simplest non-trivial USV models, these bivariate USV models are fundamental, and -- like one- factor models in general settings -- are helpful in introducing and comparing higher-factor models when simple ones are insufficient. These models are shown to exist (contradicting a claim in the literature); to share a particular affine form for their bond pricing functions; and to necessarily exhibit a short-term interest rate with dynamics of a certain type. A specific bivariate USV model is then proposed, which is analysed and compared to others in the literature.
Book Synopsis The Performance of One-versus Two-factor Models of the Term Structure of Interest Rates by : Tom Vinaimont
Download or read book The Performance of One-versus Two-factor Models of the Term Structure of Interest Rates written by Tom Vinaimont and published by . This book was released on 2003 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Implementation of a One-Factor Markov-Functional Interest Rate Model by : Baptiste Truchot
Download or read book Implementation of a One-Factor Markov-Functional Interest Rate Model written by Baptiste Truchot and published by . This book was released on 2016 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interest rate market has been expanding immensely for thirty years, both in term of volumes and diversity of traded contracts. The growing complexity of derivatives has implied a need for sophisticated models in order to price and hedge these products. Three main approaches can be distinguished in interest rates modeling. Short-rate models model the dynamics of the term structure of interest rates by specifying the dynamics of a single rate (the spot rate or the instantaneous spot rate) from which the whole term structure at any point in time can be calculated. The prices of derivatives in these models are quite involved functions of the underlying process which is being modeled. This fact makes these models difficult to calibrate. However the short rate process is easy to follow and hence implementation is straightforward.Unlike short rate models the class of Market Models is formulated in terms of market rates which are directly related to tradable assets. Thus they exhibit better calibration properties than short rate models. However they are high dimensional by construction and tedious to implement.In 1999, Hunt, Kennedy and Pelsser introduced the class of Markov-Functional Models (MFM) aiming at developing models which could match as many market prices as Market Models while maintaining the efficiency of short rate models in calculating derivative prices.After a general overview of the two dominant paradigms in section III, this report will focus on the class of Markov-functional models. Section IV presents the general framework. Then several issues related to the implementation of a one-factor MFM model are analyzed in section V. Finally we will display in section VI some numerical results of the simulations of this one-factor model.
Book Synopsis The Term Structure of Interest Rates as a Random Field by : Robert S. Goldstein
Download or read book The Term Structure of Interest Rates as a Random Field written by Robert S. Goldstein and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Note: This abstract was revised by the author since June 1997.Forward rate dynamics are modeled as a random field. In contrast to multi-factor models, random field models offer a parsimonious description of term structure dynamics, while eliminating the self-inconsistent practice of recalibration. The form of the drift of the instantaneous forward rate process necessary to preclude arbitrage under the risk neutral measure is obtained. Forward measures are characterized, and used to price a bond option when the forward volatility structure depends upon the square root of the current spot rate. In addition, it is demonstrated that random field models offer a parsimonious method to account for parameter uncertainty, inherently predicting that the best hedging instrument for a given asset is one of similar maturity. Finally, a random field is shown to be supported within a general equilibrium framework, allowing the risk-neutral measure and risk premia to be identified.
