Download or read book Distribution of Short term Interest Rate in One factor Models written by Ah Hin Pooi and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 2001 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Examination of the Static and Dynamic Performance of Interest Rate Option Pricing Models In the Dollar Cap-Floor Markets Anurag Gupta Marti G. Subrahmanyam Abstract 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. In addition, the models are evaluated based on the stability of their parameters, the presence of systematic biases, and their numerical complexity and computational efficiency. 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.
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.
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.
Download or read book Understanding And Managing Interest Rate Risks written by Ren-raw Chen and published by World Scientific. This book was released on 1996-10-04 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a systematic summary of modern term structure theories and how interest rate contingent claims are priced under such theories. This is the first book on such an attempt. The book reviews important term structure models and chooses one model to consistantly demonstrate contingent claim pricing. Well-known models are included and their relationships are thoroughly discussed. The book also provides a complete process of model implementation from parameter estimation to hedging. Examples are provided throughout.
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.
Download or read book Estimating One factor Models of Short term Interest Rate written by D. Mc Manus and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Non Existence of a One Factor Interest Rate Model for Volatility Averaged Generalized Fong Vasicek Term Structures written by Beata Stehlikova and published by . This book was released on 2009 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this paper is to study the generalized Fong - Vasicek two-factor interest rate model with stochastic volatility. In this model the dispersion of the stochastic short rate (square of volatility) is assumed to be stochastic as well and it follows a non-negative process with volatility proportional to the square root of dispersion. The drift of the stochastic process for the dispersion is assumed to be in a rather general form including, in particular, linear function having one root (yielding the original Fong - Vasicek model or a cubic like function having three roots (yielding a generalized Fong - Vasicek model for description of the volatility clustering). We consider averaged bond prices with respect to the limiting distribution of stochastic dispersion. The averaged bond prices depend on time and current level of the short rate like it is the case in many popular one-factor interest rate model including in particular the Vasicek and Cox - Ingersoll-Ross model. However, as a main result of this paper we show that there is no such one-factor model yielding the same bond prices as the averaged values described above.
Download or read book Interest Rate Models written by Andrew J. G. Cairns and published by Princeton University Press. This book was released on 2018-06-05 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of financial mathematics has developed tremendously over the past thirty years, and the underlying models that have taken shape in interest rate markets and bond markets, being much richer in structure than equity-derivative models, are particularly fascinating and complex. This book introduces the tools required for the arbitrage-free modelling of the dynamics of these markets. Andrew Cairns addresses not only seminal works but also modern developments. Refreshingly broad in scope, covering numerical methods, credit risk, and descriptive models, and with an approachable sequence of opening chapters, Interest Rate Models will make readers--be they graduate students, academics, or practitioners--confident enough to develop their own interest rate models or to price nonstandard derivatives using existing models. The mathematical chapters begin with the simple binomial model that introduces many core ideas. But the main chapters work their way systematically through all of the main developments in continuous-time interest rate modelling. The book describes fully the broad range of approaches to interest rate modelling: short-rate models, no-arbitrage models, the Heath-Jarrow-Morton framework, multifactor models, forward measures, positive-interest models, and market models. Later chapters cover some related topics, including numerical methods, credit risk, and model calibration. Significantly, the book develops the martingale approach to bond pricing in detail, concentrating on risk-neutral pricing, before later exploring recent advances in interest rate modelling where different pricing measures are important.
Download or read book Interest Rate Models Theory and Practice written by Damiano Brigo and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2nd edition of this successful book has several new features. The calibration discussion of the basic LIBOR market model has been enriched considerably, with an analysis of the impact of the swaptions interpolation technique and of the exogenous instantaneous correlation on the calibration outputs. A discussion of historical estimation of the instantaneous correlation matrix and of rank reduction has been added, and a LIBOR-model consistent swaption-volatility interpolation technique has been introduced. The old sections devoted to the smile issue in the LIBOR market model have been enlarged into a new chapter. New sections on local-volatility dynamics, and on stochastic volatility models have been added, with a thorough treatment of the recently developed uncertain-volatility approach. Examples of calibrations to real market data are now considered. The fast-growing interest for hybrid products has led to a new chapter. A special focus here is devoted to the pricing of inflation-linked derivatives. The three final new chapters of this second edition are devoted to credit. Since Credit Derivatives are increasingly fundamental, and since in the reduced-form modeling framework much of the technique involved is analogous to interest-rate modeling, Credit Derivatives -- mostly Credit Default Swaps (CDS), CDS Options and Constant Maturity CDS - are discussed, building on the basic short rate-models and market models introduced earlier for the default-free market. Counterparty risk in interest rate payoff valuation is also considered, motivated by the recent Basel II framework developments.
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.
Download or read book Pricing Interest Rate Derivatives in a Non parametric Two factor Term structure Model written by John L. Knight and published by . This book was released on 1999 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proposes a non-parametric two-factor term-structure model that imposes no restrictions on the functional forms of the diffusion functions.
Download or read book Estimating Parameters of Short Term Real Interest Rate Models written by Mr.Vadim Khramov and published by International Monetary Fund. This book was released on 2013-10-17 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper sheds light on a narrow but crucial question in finance: What should be the parameters of a model of the short-term real interest rate? Although models for the nominal interest rate are well studied and estimated, dynamics of the real interest rate are rarely explored. Simple ad hoc processes for the short-term real interest rate are usually assumed as building blocks for more sophisticated models. In this paper, parameters of the real interest rate model are estimated in the broad class of single-factor interest rate diffusion processes on U.S. monthly data. It is shown that the elasticity of interest rate volatility—the relationship between the volatility of changes in the interest rate and its level—plays a crucial role in explaining real interest rate dynamics. The empirical estimates of the elasticity of the real interest rate volatility are found to be about 0.5, much lower than that of the nominal interest rate. These estimates show that the square root process, as in the Cox-Ingersoll-Ross model, provides a good characterization of the short-term real interest rate process.
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.
Download or read book Interest Rate Option Models written by Riccardo Rebonato and published by . This book was released on 1996-09-12 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible, first-rate overview of interest rate dependent options for traders and institutional investors Until now market professionals seeking to exploit the profit potential of interest rate dependent options were forced to hunt through esoteric journals for a crumb or two of practical knowledge about their use. This accessible book narrows the information gap. Written in easy-to-follow, non-technical language, it logically reviews all the most commonly used interest rate option models, showing how each one can be applied and implemented for specific market applications. DR. RICARDO REBONATO (London, England) is head of Research, Debt Capital Markets at Barclays de Zoete Wedd Ltd.
Download or read book Interest Rate Models an Infinite Dimensional Stochastic Analysis Perspective written by René Carmona and published by Springer Science & Business Media. This book was released on 2007-05-22 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the mathematical issues that arise in modeling the interest rate term structure by casting the interest-rate models as stochastic evolution equations in infinite dimensions. The text includes a crash course on interest rates, a self-contained introduction to infinite dimensional stochastic analysis, and recent results in interest rate theory. From the reviews: "A wonderful book. The authors present some cutting-edge math." --WWW.RISKBOOK.COM
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.
