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Modeling And Simulating Interest Rates Via Time Dependent Mean Reversion
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Book Synopsis Modeling and Simulating Interest Rates Via Time-dependent Mean Reversion by : Andrew Jason Dweck
Download or read book Modeling and Simulating Interest Rates Via Time-dependent Mean Reversion written by Andrew Jason Dweck and published by . This book was released on 2014 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this thesis is to compare the effectiveness of several interest rate models in fitting the true value of interest rates. Up until 1990, the universally accepted models were the equilibrium models, namely the Rendleman{Bartter model, the Vasicek model, and the Cox{Ingersoll{Ross (CIR) model. While these models were probably considered relatively accurate around the time of their discovery, they do not provide a good fit to the initial term structure of interest rates, making them substandard for use by traders in pricing interest rate options. The fourth model we consider is the Hull{White one-factor model, which does provide this fit. After calibrating, simulating, and comparing these four models, we findnd that the Hull{White model gives the best fit to our data sets.
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 Interest Rate Derivatives by : Ingo Beyna
Download or read book Interest Rate Derivatives written by Ingo Beyna and published by Springer Science & Business Media. This book was released on 2013-02-20 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The class of interest rate models introduced by O. Cheyette in 1994 is a subclass of the general HJM framework with a time dependent volatility parameterization. This book addresses the above mentioned class of interest rate models and concentrates on the calibration, valuation and sensitivity analysis in multifactor models. It derives analytical pricing formulas for bonds and caplets and applies several numerical valuation techniques in the class of Cheyette model, i.e. Monte Carlo simulation, characteristic functions and PDE valuation based on sparse grids. Finally it focuses on the sensitivity analysis of Cheyette models and derives Model- and Market Greeks. To the best of our knowledge, this sensitivity analysis of interest rate derivatives in the class of Cheyette models is unique in the literature. Up to now the valuation of interest rate derivatives using PDEs has been restricted to 3 dimensions only, since the computational effort was too great. The author picks up the sparse grid technique, adjusts it slightly and can solve high-dimensional PDEs (four dimensions plus time) accurately in reasonable time. Many topics investigated in this book are new areas of research and make a significant contribution to the scientific community of financial engineers. They also represent a valuable development for practitioners.
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 Efficient and Exact Simulation of the Gaussian Affine Interest Rate Models (with Application to the Hull White Model and G2++ Model). by : Vladimir Ostrovski
Download or read book Efficient and Exact Simulation of the Gaussian Affine Interest Rate Models (with Application to the Hull White Model and G2++ Model). written by Vladimir Ostrovski and published by . This book was released on 2018 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Gaussian affine interest rate models are widely used in the financial industry for pricing, hedging and also risk management purposes. We consider the multifactor models with time dependent parameters. Usually the models are simulated using some appropriate discretization schema because the joint distribution of the stochastic and discounting factors is not known. We derive the exact joint conditional distribution of the stochastic and discounting factors. Additionally we show how an efficient and exact Monte Carlo simulation of the Hull White and G2++ interest rates models could be performed.
Book Synopsis Interest Rate, Term Structure, and Valuation Modeling by : Frank J. Fabozzi
Download or read book Interest Rate, Term Structure, and Valuation Modeling written by Frank J. Fabozzi and published by John Wiley & Sons. This book was released on 2002-11-29 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ultimate guide contains an excellent blend of theory and practice This comprehensive guide covers various aspects of model building for fixed income securities and derivatives. Filled with expert advice, valuable insights, and advanced modeling techniques, Interest Rate, Term Structure, and Valuation Modeling is a book that all institutional investors, portfolio managers, and risk professionals should have. John Wiley & Sons, Inc. is proud to be the publisher of the esteemed Frank J. Fabozzi Series. Comprising nearly 100 titles-which include numerous bestsellers—The Frank J. Fabozzi Series is a key resource for finance professionals and academics, strategists and students, and investors. The series is overseen by its eponymous editor, whose expert instruction and presentation of new ideas have been at the forefront of financial publishing for over twenty years. His successful career has provided him with the knowledge, insight, and advice that has led to this comprehensive series. Frank J. Fabozzi, PhD, CFA, CPA, is Editor of the Journal of Portfolio Management, which is read by thousands of institutional investors, as well as editor or author of over 100 books on finance for the professional and academic markets. Currently, Dr. Fabozzi is an adjunct Professor of Finance at Yale University's School of Management and on the board of directors of the Guardian Life family of funds and the Black Rock complex of funds.
Book Synopsis Interest Rate Modeling for Risk Management: Market Price of Interest Rate Risk (Second Edition) by : Takashi Yasuoka
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.
Book Synopsis An Overview of the Vasicek Short Rate Model by : Nicholas Burgess
Download or read book An Overview of the Vasicek Short Rate Model written by Nicholas Burgess and published by . This book was released on 2017 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Vasicek model (1977) is one of the earliest stochastic models of the term structure of interest rates. This model, though it has it's shortcomings, has many advantages, such as analytical tractability and mean reversion features, and may be viewed as a short rate model template.Several short rate models have their foundations rooted in the Vasicek model. The classical Hull-White model (1990a), for example, is an extension of the Vasicek model with time dependent parameters.In the work that follows we derive the short rate implied by the Vasicek model using the integrating factor method and provide an overview of this method and it's shorthand. Secondly we consider the model dynamics and finally we apply the model to zero-coupon bond pricing and provide a detailed derivation. Finally in reviewing the Vasicek model we outline it's disadvantages, consider other short rate models and look at the Hull-White extension to this model. The aim of the paper is to provide an overview of the Vasicek model and an introduction into short rate modelling.
Book Synopsis An Empirical Comparison of the Short Term Interest Rate Models by : Mona Ben Salah
Download or read book An Empirical Comparison of the Short Term Interest Rate Models written by Mona Ben Salah and published by . This book was released on 2014 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article attempts to identify the best model of the short term interest rates that can predict its stochastic process over time.We studied eight different models of interest rates in the short term. The choice of these models was the aim of analyzing the relevance of certain specifications of the stochastic process of the short term interest rates, the effect of mean reversion and the sensitivity of the volatility to the level of interest rate.The yield on three months treasury bills is used as a proxy for the short term interest rates. The parameters of the different stochastic process are estimated using the generalized method of moments. The results show that the effect of mean reversion is not statistically significant and that volatility is highly sensitive to the level of interest rates.To further study the performance prediction of the intertemporal behavior of the short term interest rate of the various models; we simulated their stochastic process for different periods.The results show that none of the studied models reproduce the actual path of the short term interest rates. The problem lies in the parametric specification of the mean and volatility of the diffusion process.
Book Synopsis Discrete-Time Continuous-State Interest Rate Models by :
Download or read book Discrete-Time Continuous-State Interest Rate Models written by and published by DIANE Publishing. This book was released on with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Discrete-time Continuous-state Interest Rate Models by : Michael A. Sullivan
Download or read book Discrete-time Continuous-state Interest Rate Models written by Michael A. Sullivan and published by . This book was released on 2000 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Integrated Model for the Term and Volatility Structures of Interest Rates by : Ren-Raw Chen
Download or read book An Integrated Model for the Term and Volatility Structures of Interest Rates written by Ren-Raw Chen and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we present a model for the term structure of interest rates, which integrates the existing multifactor and time dependent approaches of term structure models. This integrated model uses the time series data so that it has macroeconomic implications such as interest rate volatility and mean reversion. It also uses the cross sectional data so that it fits the yield curve and the volatility curve. In contrast to other multifactor time dependent models, this model is easy to implement. It has closed form solutions for discount bonds as well as their European claims. For American claims, the lattice model can be constructed as easily as a fixed parameter model. The fitting of the volatility curve and the fitting of the yield curve are separable in the model. The capability of combining both time series and cross sectional information in a computationally tractable framework is the main contribution of this model.
Book Synopsis Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective by : René Carmona
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
Book Synopsis Interest Rate Modelling by : S. Svoboda
Download or read book Interest Rate Modelling written by S. Svoboda and published by Springer. This book was released on 2003-12-18 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Growth in the derivatives market has brought with it a greater volume and range of interest rate dependent products. These products have become increasingly innovative and complex to price, requiring sophisticated market models that capture the full dynamics of the yield curve. A study of the evolution of interest rate modelling theory places these models in the correct mathematical context, allowing appreciation of their key assumptions, concepts and implications. The book guides the practitioner through the derivation and implementation of a variety of models that account for the characteristics and irregularities of observed term structures.
Book Synopsis Monte Carlo Simulation and Finance by : Don L. McLeish
Download or read book Monte Carlo Simulation and Finance written by Don L. McLeish and published by John Wiley & Sons. This book was released on 2011-09-13 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods have been used for decades in physics, engineering, statistics, and other fields. Monte Carlo Simulation and Finance explains the nuts and bolts of this essential technique used to value derivatives and other securities. Author and educator Don McLeish examines this fundamental process, and discusses important issues, including specialized problems in finance that Monte Carlo and Quasi-Monte Carlo methods can help solve and the different ways Monte Carlo methods can be improved upon. This state-of-the-art book on Monte Carlo simulation methods is ideal for finance professionals and students. Order your copy today.
Book Synopsis An Elementary Introduction to Stochastic Interest Rate Modeling by : Nicolas Privault
Download or read book An Elementary Introduction to Stochastic Interest Rate Modeling written by Nicolas Privault and published by World Scientific. This book was released on 2012 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest rate modeling and the pricing of related derivatives remain subjects of increasing importance in financial mathematics and risk management. This book provides an accessible introduction to these topics by a step-by-step presentation of concepts with a focus on explicit calculations. Each chapter is accompanied with exercises and their complete solutions, making the book suitable for advanced undergraduate and graduate level students. This second edition retains the main features of the first edition while incorporating a complete revision of the text as well as additional exercises with their solutions, and a new introductory chapter on credit risk. The stochastic interest rate models considered range from standard short rate to forward rate models, with a treatment of the pricing of related derivatives such as caps and swaptions under forward measures. Some more advanced topics including the BGM model and an approach to its calibration are also covered.
Book Synopsis A One-Factor Lognormal Markovian Interest Rate Model by : Anlong Li
Download or read book A One-Factor Lognormal Markovian Interest Rate Model written by Anlong Li and published by . This book was released on 2006 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents a parsimonious Markovian interest rate model where the logarithm of the interest rate process is a scaled and shifted Ornstein-Uhlenbeck process. The model has many desirable properties such as lognormal distributed rates, mean reversion, and time-varying parameters. The corresponding discrete (lattice) approximation reduces to the discretization of the Ornstein-Uhlenbeck process, as we demonstrate by a simple and efficient trinomial lattice. In calibrating the model to the initial yield curve (or, equivalently, the term structure of zero-coupon bonds), we need only solve a linear equation instead of a nonlinear one as in current practice. This saves a considerable amount of computation time, especially in calibrating the model to interest rate options where calibrating to the yield curve is repeated many times over. The paper also discusses the merits of Monte-Carlo simulation of paths from the calibrated lattice.
