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Pricing Interest Rate Derivatives In A Non Parametric Two Factor Term Structure Model
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Book Synopsis Pricing Interest Rate Derivatives in a Non-parametric Two-factor Term-structure Model by : John L. Knight
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.
Book Synopsis Pricing Interest Rate Derivatives in a Non-Parametric Two-Factor Term-Structure Model by : John Knight
Download or read book Pricing Interest Rate Derivatives in a Non-Parametric Two-Factor Term-Structure Model written by John Knight and published by . This book was released on 2000 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diffusion functions in term-structure models are measures of uncertainty about future price movements and are directly related to the risk associated with holding financial securities. Correct specification of diffusion functions is crucial in pricing options and other derivative securities. In contrast to the standard parametric two-factor models, we propose a non-parametric two-factor term-structure model that imposes no restrictions on the functional forms of the diffusion functions. Hence, this model allows for maximum flexibility when fitting diffusion functions into data. A non-parametric procedure is developed for estimating the diffusion functions, based on the discretely sampled observations. The convergence properties and the asymptotic distributions of the proposed non-parametric estimators of the diffusion functions with multivariate dimensions are also obtained. Based on U.S. data, the non-parametric prices of the bonds and bond options are computed and compared with those calculated under an alternative parametric model. The empirical results show that the non-parametric model generates significantly different prices for the derivative securities.
Book Synopsis A Comparison of Fixed Income Valuation Models by : Michael Jacobs
Download or read book A Comparison of Fixed Income Valuation Models written by Michael Jacobs and published by . This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study compares continuous-time stochastic interest rate and stochastic volatility models of interest rate derivatives, examining these models across several dimensions: different classes of models, factor structures, and pricing algorithms. We consider a broader universe of pricing models, using improved econometric and numerical methodologies. We establish several criteria for model quality that are motivated by financial theory as well as practice: realism of the assumed stochastic process for the term structure, consistency with no-arbitrage or financial market equilibrium, consistency with financial practice, parsimony, as well as computational efficiency. A model which scores well along these grounds will also exhibit superior pricing performance with regard to traded interest rate options. This helps resolve the controversies over the stochastic process for yield curve dynamics, the models that best manage and measure interest rate risk, and theories of the term structure that are supported by empirical results. We perform econometric experiments at three levels: the short rate, bond prices, as well as interest rate derivatives. We extend CKLS (1992) to a broader class of single factor spot rate models and international interest rates. We find that a single-factor general parametric model (1FGPM) of the term structure, with non-linearity in the drift function, better captures the time series dynamics of US 30 Day T-Bill rates. The 1FGPM not only forecasts interest rate changes out-of-sample better relative to other parametric models, but also relative to the non-parametric model of Jiang (1998). Finally, our results vary greatly across international markets. Building upon the work of Longstaff and Schwartz (1992), we perform a statistical analysis of the U.S. default-free term structure over the period 4:1964 to 10:1997. We utilize a constant correlation multivariate GARCH principal components analysis (CCM-PCA), and identify at least three factors associated with traditional measures of risk in the fixed income literature (level, slope, and curvature) that capture 98% of the variation in the default-free term structure. We perform tests of various term structure models on US Treasury bonds, comparing a two factor Cox-Ingersoll-Ross (2FCIR) model with a multi-layer perceptron neural network approach (MLP-ANN), in pricing and hedging discount bonds. We find that while the MLP-ANN can better fit bond prices in-sample, the 2F-CIR model is superior in hedging against unanticipated changes in the short rate and its volatility. Furthermore, we find the 2FCIR model to perform favorably in comparison to the CCM-PCA, MLP-ANN, as well as the 1FGPM in forecasting bond yield changes. Finally, we compare various interest rate bond option pricing models, in their ability to price interest rate derivatives and manage and interest rate risk. We compare three approaches to pricing interest rate derivatives: spot rate (e.g., CIR), forward-rate (i.e., HJM), and non-parametric models (e.g., multivariate kernel estimation.) This is extended to a broader factor structure. While the best model in terms of mean square error (MSE) is the non parametric (MNWK) model, the 3 factor jump diffusion (3FGJD) model performs best among parametric models. In hedging analysis, while these preferred models still outperform within each grouping, the non parametric model is no longer the best performing model, while the 2FCIR is the best model in hedging options in terms of MSE.
Book Synopsis Interest Rate Derivatives Explained: Volume 2 by : Jörg Kienitz
Download or read book Interest Rate Derivatives Explained: Volume 2 written by Jörg Kienitz and published by Springer. This book was released on 2017-11-08 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on Interest Rate Derivatives has three parts. The first part is on financial products and extends the range of products considered in Interest Rate Derivatives Explained I. In particular we consider callable products such as Bermudan swaptions or exotic derivatives. The second part is on volatility modelling. The Heston and the SABR model are reviewed and analyzed in detail. Both models are widely applied in practice. Such models are necessary to account for the volatility skew/smile and form the fundament for pricing and risk management of complex interest rate structures such as Constant Maturity Swap options. Term structure models are introduced in the third part. We consider three main classes namely short rate models, instantaneous forward rate models and market models. For each class we review one representative which is heavily used in practice. We have chosen the Hull-White, the Cheyette and the Libor Market model. For all the models we consider the extensions by a stochastic basis and stochastic volatility component. Finally, we round up the exposition by giving an overview of the numerical methods that are relevant for successfully implementing the models considered in the book.
Book Synopsis Nonparametric Pricing of Interest Rate Derivative Securities by : Yacine Ait-Sahalia
Download or read book Nonparametric Pricing of Interest Rate Derivative Securities written by Yacine Ait-Sahalia and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper derives a nonparametric estimation procedure for continuous-time models and provides the asymptotic distribution of the estimator. Since the pricing of derivative securities depends crucially on the form of the instantaneous volatility of the underlying asset, the diffusion function of the spot interest rate is unrestricted and estimated nonparametrically. The diffusion function is identified by requiring that the distribution of the process match that of the data. Even though only discrete data are used, the estimation procedure does not rely on replacing the continuous-time process by some discrete approximation. The continuous-time process followed by the short term interest rate is estimated. Nonparametric prices are computed for bonds, yielding the term structure of interest rates, and bond options.
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
Book Synopsis Handbook of Quantitative Finance and Risk Management by : Cheng-Few Lee
Download or read book Handbook of Quantitative Finance and Risk Management written by Cheng-Few Lee and published by Springer Science & Business Media. This book was released on 2010-06-14 with total page 1700 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantitative finance is a combination of economics, accounting, statistics, econometrics, mathematics, stochastic process, and computer science and technology. Increasingly, the tools of financial analysis are being applied to assess, monitor, and mitigate risk, especially in the context of globalization, market volatility, and economic crisis. This two-volume handbook, comprised of over 100 chapters, is the most comprehensive resource in the field to date, integrating the most current theory, methodology, policy, and practical applications. Showcasing contributions from an international array of experts, the Handbook of Quantitative Finance and Risk Management is unparalleled in the breadth and depth of its coverage. Volume 1 presents an overview of quantitative finance and risk management research, covering the essential theories, policies, and empirical methodologies used in the field. Chapters provide in-depth discussion of portfolio theory and investment analysis. Volume 2 covers options and option pricing theory and risk management. Volume 3 presents a wide variety of models and analytical tools. Throughout, the handbook offers illustrative case examples, worked equations, and extensive references; additional features include chapter abstracts, keywords, and author and subject indices. From "arbitrage" to "yield spreads," the Handbook of Quantitative Finance and Risk Management will serve as an essential resource for academics, educators, students, policymakers, and practitioners.
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 Pricing Interest-Rate Derivatives by : Markus Bouziane
Download or read book Pricing Interest-Rate Derivatives written by Markus Bouziane and published by Springer Science & Business Media. This book was released on 2008-03-18 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author derives an efficient and accurate pricing tool for interest-rate derivatives within a Fourier-transform based pricing approach, which is generally applicable to exponential-affine jump-diffusion models.
Book Synopsis A New Approach to the Valuation of Interest Rate Derivatives by : Padideh Jalali
Download or read book A New Approach to the Valuation of Interest Rate Derivatives written by Padideh Jalali and published by . This book was released on 1999 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a complete, arbitrage-free securities market, the value of a discount bond is modeled in terms of the pricing kernel and the transition density function of the spot interest rate process. The prices of discount bonds are taken from the current term structure of interest rates, and the transition density function is estimated from historical term structure data, using both parametric and nonparametric techniques. The pricing kernel and associated prices of Arrow-Debreu securities are then determined. The resulting Arrow-Debreu prices have two merits: they are consistent with the current term structure of interest rates, and therefore arbitrage-free, and, in addition, they embody the observed historical behavior of the term structure.
Book Synopsis Efficient Methods for Valuing Interest Rate Derivatives by : Antoon Pelsser
Download or read book Efficient Methods for Valuing Interest Rate Derivatives written by Antoon Pelsser and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the models that can be used for valuing and managing interest rate derivatives. Split into two parts, the first discusses and compares the traditional models, such as spot- and forward-rate models, while the second concentrates on the more recently developed Market models. Unlike most of his competitors, the author's focus is not only on the mathematics: Antoon Pelsser draws on his experience in industry to explore a host of practical issues.
Book Synopsis A Two Factor No-Arbitrage Model of the Term Structure of Interest Rates by : T.S. Ho
Download or read book A Two Factor No-Arbitrage Model of the Term Structure of Interest Rates written by T.S. Ho and published by . This book was released on 2008 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive a no-arbitrage model of the term structure in which any two futures rates act as factors. The term structure shifts and tilts as the factor rates vary. The cross-sectional properties of the model derive from the solution of a two-dimensional ARMA process for the short rate which exhibits mean reversion and a lagged memory parameter. We show that the correlation of the factor rates is restricted by the no-arbitrage conditions of the model. Hence in a multiple-factor model it is not valid to independently choose both the mean reversion, volatility and correlation parameters. The term-structure model, derived here, can be used to value options on bonds and swaps or to generate term structure scenarios for the risk management of portfolios of interest-rate derivatives.
Book Synopsis Interest Rate Dynamics, Derivatives Pricing, and Risk Management by : Lin Chen
Download or read book Interest Rate Dynamics, Derivatives Pricing, and Risk Management written by Lin Chen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are two types of tenn structure models in the literature: the equilibrium models and the no-arbitrage models. And there are, correspondingly, two types of interest rate derivatives pricing fonnulas based on each type of model of the tenn structure. The no-arbitrage models are characterized by the work of Ho and Lee (1986), Heath, Jarrow, and Morton (1992), Hull and White (1990 and 1993), and Black, Dennan and Toy (1990). Ho and Lee (1986) invent the no-arbitrage approach to the tenn structure modeling in the sense that the model tenn structure can fit the initial (observed) tenn structure of interest rates. There are a number of disadvantages with their model. First, the model describes the whole volatility structure by a sin gle parameter, implying a number of unrealistic features. Furthennore, the model does not incorporate mean reversion. Black-Dennan-Toy (1990) develop a model along tbe lines of Ho and Lee. They eliminate some of the problems of Ho and Lee (1986) but create a new one: for a certain specification of the volatility function, the short rate can be mean-fteeting rather than mean-reverting. Heath, Jarrow and Morton (1992) (HJM) construct a family of continuous models of the term struc ture consistent with the initial tenn structure data.
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 A Non-parametric Approach to Model the Term Structure of Interest Rates by : Viviana Fernández M.
Download or read book A Non-parametric Approach to Model the Term Structure of Interest Rates written by Viviana Fernández M. and published by . This book was released on 2001 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Computational Finance by : Jin-Chuan Duan
Download or read book Handbook of Computational Finance written by Jin-Chuan Duan and published by Springer Science & Business Media. This book was released on 2011-10-25 with total page 791 pages. Available in PDF, EPUB and Kindle. Book excerpt: Any financial asset that is openly traded has a market price. Except for extreme market conditions, market price may be more or less than a “fair” value. Fair value is likely to be some complicated function of the current intrinsic value of tangible or intangible assets underlying the claim and our assessment of the characteristics of the underlying assets with respect to the expected rate of growth, future dividends, volatility, and other relevant market factors. Some of these factors that affect the price can be measured at the time of a transaction with reasonably high accuracy. Most factors, however, relate to expectations about the future and to subjective issues, such as current management, corporate policies and market environment, that could affect the future financial performance of the underlying assets. Models are thus needed to describe the stochastic factors and environment, and their implementations inevitably require computational finance tools.
Book Synopsis Nonparametric Pricing of Interest Rate Derivative Securities by : Yacine Aït-Sahalia
Download or read book Nonparametric Pricing of Interest Rate Derivative Securities written by Yacine Aït-Sahalia and published by . This book was released on 1995 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a nonparametric estimation procedure for continuous- time stochastic models. Because prices of derivative securities depend crucially on the form of the instantaneous volatility of the underlying process, we leave the volatility function unrestricted and estimate it nonparametrically. Only discrete data are used but the estimation procedure still does not rely on replacing the continuous- time model by some discrete approximation. Instead the drift and volatility functions are forced to match the densities of the process. We estimate the stochastic differential equation followed by the short term interest rate and compute nonparametric prices for bonds and bond options.
