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Author : Jiti Gao
Publisher :
ISBN 13 :
Total Pages : 25 pages
Book Rating : 4.:/5 (897 download)
Download or read book Nonparametric Estimation and Comparisons in Stochastic Short-term Interest Rate Models written by Jiti Gao and published by . This book was released on 2003 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Mona Ben Salah
Publisher :
ISBN 13 :
Total Pages : 12 pages
Book Rating : 4.:/5 (13 download)
Download or read book 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 12 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 nine different models of the short term interest rates. The choice of these models was the aim of analyzing the relevance of certain specifications of the the short term interest rate stochastic process, the effect of mean reversion and the sensitivity of the volatility to the level of interest rate.The yield on US 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 To further study the accurate parametric specification of the interest rate stochastic process we use a nonparametric estimation of the drift and the diffusion functions. The results prove that both should be nonlinear.
Author : Manuel Arapis
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (129 download)
Download or read book Empirical Comparisons in Short-Term Interest Rate Models Using Nonparametric Methods written by Manuel Arapis and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This study applies the nonparametric estimation procedure to the diffusion process modeling the dynamics of short-term interest rates. This approach allows us to operate in continuous time, estimating the continuous-time model, despite the use of discrete data. Three methods are proposed. We apply these methods to two important financial data. After selecting an appropriate bandwidth for each dataset, empirical comparisons indicate that the specification of the drift has a considerable impact on the pricing of derivatives through its effect on the diffusion function. In addition, a novel nonparametric test has been proposed for specification of linearity in the drift. Our simulation directs us to reject the null hypothesis of linearity at the 5% significance level for the two financial datasets.
Author : Teresa Corzo
Publisher :
ISBN 13 :
Total Pages : 43 pages
Book Rating : 4.:/5 (129 download)
Download or read book Nonparametric Estimation of Convergence of Interest Rates written by Teresa Corzo and published by . This book was released on 2002 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present and estimate, using nonparametric regression techniques, a model of short term interest rate dynamics and use the estimation to value bonds. We study the case of two European countries - Spain and Italy - that belong to EMU, and compare the resulting bond prices of a one factor model with that of a two factor, the second factor being a stochastic mean. The pricing errors for both models are 34% smaller than those reported on the parametric literature. Furthermore, the two factor model, which takes into account the convergence with Europe of the domestic economies, obtains better results than the one factor model. Our findings give strong support to the importance of a correct specification of the volatility of interest rates.
Author : Mr.Vadim Khramov
Publisher : International Monetary Fund
ISBN 13 : 1475591225
Total Pages : 27 pages
Book Rating : 4.4/5 (755 download)
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.
Author : René Carmona
Publisher : Springer Science & Business Media
ISBN 13 : 3540270671
Total Pages : 236 pages
Book Rating : 4.5/5 (42 download)
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
Author : Nicolas Privault
Publisher : World Scientific
ISBN 13 : 9814390860
Total Pages : 243 pages
Book Rating : 4.8/5 (143 download)
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.
Author : Yacine Aït-Sahalia
Publisher :
ISBN 13 :
Total Pages : 39 pages
Book Rating : 4.:/5 (339 download)
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.
Author : Chris Downing
Publisher :
ISBN 13 :
Total Pages : 60 pages
Book Rating : 4.E/5 ( download)
Download or read book Nonparametric Estimation of Multifactor Continuous Time Interest Rate Models written by Chris Downing and published by . This book was released on 1999 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yacine Ait-Sahalia
Publisher :
ISBN 13 :
Total Pages : 45 pages
Book Rating : 4.:/5 (129 download)
Download or read book Nonparametric Pricing of Interest Rate Derivative Securities written by Yacine Ait-Sahalia and published by . This book was released on 2010 with total page 45 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.
Author : Nicolas Privault
Publisher : World Scientific
ISBN 13 : 9814401641
Total Pages : 243 pages
Book Rating : 4.8/5 (144 download)
Download or read book Elementary Introduction To Stochastic Interest Rate Modeling, An (2nd Edition) written by Nicolas Privault and published by World Scientific. This book was released on 2012-05-04 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.
Author : Yacine Ait-Sahalia
Publisher : Elsevier
ISBN 13 : 0080929842
Total Pages : 809 pages
Book Rating : 4.0/5 (89 download)
Download or read book Handbook of Financial Econometrics written by Yacine Ait-Sahalia and published by Elsevier. This book was released on 2009-10-19 with total page 809 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of original articles—8 years in the making—shines a bright light on recent advances in financial econometrics. From a survey of mathematical and statistical tools for understanding nonlinear Markov processes to an exploration of the time-series evolution of the risk-return tradeoff for stock market investment, noted scholars Yacine Aït-Sahalia and Lars Peter Hansen benchmark the current state of knowledge while contributors build a framework for its growth. Whether in the presence of statistical uncertainty or the proven advantages and limitations of value at risk models, readers will discover that they can set few constraints on the value of this long-awaited volume. Presents a broad survey of current research—from local characterizations of the Markov process dynamics to financial market trading activity Contributors include Nobel Laureate Robert Engle and leading econometricians Offers a clarity of method and explanation unavailable in other financial econometrics collections
Author : Nicolas Privault
Publisher : World Scientific Publishing Company
ISBN 13 : 9813107308
Total Pages : 191 pages
Book Rating : 4.8/5 (131 download)
Download or read book An Elementary Introduction To Stochastic Interest Rate Modeling written by Nicolas Privault and published by World Scientific Publishing Company. This book was released on 2008-10-13 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is written as an accessible introduction to interest rate modeling and related derivatives, which have become increasingly important subjects of interest in financial mathematics. The models considered range from standard short rate to forward rate models and include more advanced topics such as the BGM model and an approach to its calibration. An elementary treatment of the pricing of caps and swaptions under forward measures is also provided, with a focus on explicit calculations and a step-by-step introduction of concepts. Each chapter is accompanied with exercises and their complete solutions, making this book suitable for advanced undergraduate or beginning graduate-level students.
Author : Desmond John Mc Manus
Publisher :
ISBN 13 :
Total Pages : 50 pages
Book Rating : 4.3/5 ( download)
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.
Author : Nicolas Privault
Publisher : World Scientific
ISBN 13 : 9811226628
Total Pages : 373 pages
Book Rating : 4.8/5 (112 download)
Download or read book Stochastic Interest Rate Modeling With Fixed Income Derivative Pricing (Third Edition) written by Nicolas Privault and published by World Scientific. This book was released on 2021-09-02 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the mathematics of stochastic interest rate modeling and the pricing of related derivatives, based on a step-by-step presentation of concepts with a focus on explicit calculations. The types of interest rates considered range from short rates to forward rates such as LIBOR and swap rates, which are presented in the HJM and BGM frameworks. The pricing and hedging of interest rate and fixed income derivatives such as bond options, caps, and swaptions, are treated using forward measure techniques. An introduction to default bond pricing and an outlook on model calibration are also included as additional topics.This third edition represents a significant update on the second edition published by World Scientific in 2012. Most chapters have been reorganized and largely rewritten with additional details and supplementary solved exercises. New graphs and simulations based on market data have been included, together with the corresponding R codes.This new edition also contains 75 exercises and 4 problems with detailed solutions, making it suitable for advanced undergraduate and graduate level students.
Author : Stefano M. Iacus
Publisher : Springer Science & Business Media
ISBN 13 : 0387758399
Total Pages : 298 pages
Book Rating : 4.3/5 (877 download)
Download or read book Simulation and Inference for Stochastic Differential Equations written by Stefano M. Iacus and published by Springer Science & Business Media. This book was released on 2009-04-27 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers a highly relevant and timely topic that is of wide interest, especially in finance, engineering and computational biology. The introductory material on simulation and stochastic differential equation is very accessible and will prove popular with many readers. While there are several recent texts available that cover stochastic differential equations, the concentration here on inference makes this book stand out. No other direct competitors are known to date. With an emphasis on the practical implementation of the simulation and estimation methods presented, the text will be useful to practitioners and students with minimal mathematical background. What’s more, because of the many R programs, the information here is appropriate for many mathematically well educated practitioners, too.
Author : Mona Ben Salah
Publisher :
ISBN 13 :
Total Pages : 11 pages
Book Rating : 4.:/5 (13 download)
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.
