Download or read book Efficient method of moments estimation of continuous time interest rate models written by Kim Mortensen and published by . This book was released on 2003 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Estimation of Continuous Time Models for Stock Returns and Interest Rates written by A. Ronald Gallant and published by . This book was released on 2008 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: Efficient Method of Moments (EMM) is used to estimate and test continuous time diffusion models for stock returns and interest rates. For stock returns, a four-state, two-factor diffusion with one state observed can account for the dynamics of the daily return on the Samp;P composite index, 1927-1987. This contrasts with results indicating that discrete-time, stochastic volatility models cannot explain these dynamics. For interest rates, a trivariate yield factor model is estimated from weekly, 1962-1995, Treasury rates. The yield factor model is sharply rejected, although extensions permitting convexities in the local variance come closer to fitting the data.

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 Generalized Method of Moments Estimation written by Laszlo Matyas and published by Cambridge University Press. This book was released on 1999-04-13 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: The generalized method of moments (GMM) estimation has emerged as providing a ready to use, flexible tool of application to a large number of econometric and economic models by relying on mild, plausible assumptions. The principal objective of this volume is to offer a complete presentation of the theory of GMM estimation as well as insights into the use of these methods in empirical studies. It is also designed to serve as a unified framework for teaching estimation theory in econometrics. Contributors to the volume include well-known authorities in the field based in North America, the UK/Europe, and Australia. The work is likely to become a standard reference for graduate students and professionals in economics, statistics, financial modeling, and applied mathematics.

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

Download or read book Infinitesimal Operator Based Methods for Continuous time Finance Models written by Zhaogang Song and published by . This book was released on 2011 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuous time Markov processes, including diffusion, jump-diffusion and Levy jump-diffusion models, have become an essential tool of modern finance over the past three decades. Nowadays, they are widely used in modeling dynamics of, for instance, interest rates, stock prices, exchange rates and option prices. However, data are always recorded at discrete points in time, e.g., monthly, weekly, and daily, although these models are formulated in continuous time. This feature makes most econometric inferential procedures developed for discrete time econometrics unsuitable for continuous time models and complicates the econometric analysis considerably. For example, estimators obtained by applying discrete time econometric methods to the discretized version of continuous time models are not consistent for a fixed sampling interval. More seriously, although the maximum likelihood method is a very appealing econometric procedure due to its nice properties like efficiency, the transition density and hence likelihood function of most continuous time Markov models have no analytic expressions. This poses a serious impediment for the implementation of likelihood procedures. Many approaches have been proposed to deal with this problem but they either incur substantive computation burdens especially for multivariate cases or involve complicated approximation formulas with limited applicability. Consequently, there is a strong need for convenient econometric methodologies designed for continuous time mod- els given discrete sampled data. Unlike the transition density, the infinitesimal operator, as an important mathematical tool in probability theory, enjoys the nice property of being a closed-form expression of drift, diffusion and jump terms of the process. As a result, no approximated formulas or simulation based implementations are needed. Furthermore, it is equivalent to the transition density in characterizing the complete dynamics of the processes. Based on this convenient infinitesimal operator, this dissertation proposes a sequence of econometric procedures for continuous time Markov models with applications to affine jump diffusion (AJD) term structure models of interest rates. It is divided into four chapters. In the first chapter, "Infinitesimal Operator Based Estimation for Continuous Time Markov Processes", I propose an estimation method based on the infinitesimal operator for general multivariate continuous-time Markov processes, which cover diffusion, jump-diffusion and Levy-driven jump models as special cases. A conditional moment restriction is first obtained via the infinitesimal operator based identification of the process. Then an empirical likelihood type estimator is constructed by a kernel smoothing approach. Unlike the transition density which is rarely available in closed-form, the infinitesimal operator has an analytic form for all continuous time Markov models. As a result, different from the maximum likelihood estimator (MLE) which involves either numerical or simulated transition densities, the proposed estimator can be conveniently implemented by plugging in parametric components of the models. Furthermore, I prove that the proposed estimator attains the semi-parametric efficiency bound for conditional moment restrictions models of Markov processes and hence is asymptotically efficient. Simulation studies show that the proposed estimator has good finite sample performances comparable to the MLE. In the empirical application, I estimate Levy jump diffusion models for daily Euro/Dollar (2000-2010) and Yen/Dollar (1990-2000) rates. Results show that Levy jumps are important components in exchange rate dynamics and Poissontype jump diffusion models cannot capture them. In the second chapter, "Expectation Puzzles, Time Varying Conditional Volatility, and Jumps in Affine Term Structure Models", I study how jumps in interest rates, which are well documented in the literature, affect the term structure dynamics of the LIBOR-Swap curve in a multivariate AJD model. The motivation is that affine diffusion (AD) term structure models, as the major framework for interest rate dynamics, face two empirical challenges: first, they ignore well-documented jumps in interest rates as the state variables follow affine diffusions; second, they fail to capture simultaneously time variations in risk premiums implied by the violations of the "expectation hypothesis" and time variations in volatilities which are critical for pricing fixed-income derivatives. In this paper, I develop a multivariate AJD term structure model that overcomes these two challenges. Using LIBOR-Swap yields from 1990 to 2008, I estimate three-factor AJD models with infinitesimal operator methods and examine the contributions of jumps to term structure dynamics. I find that jumps are state dependent and negative. The risk premium is positive for jump size risk and negative for jump time risk, while the total jump risk premium is positive. Jump risk premiums lead to flexible time-varying market prices of risks without restricting time variations in conditional volatilities. As a result, two models in the three-factor AJD class capture time variations in both the risk premium and conditional volatility of LIBOR-Swap yields simultaneously. In the third chapter (part of this chapter has been published as Song (2011) in Journal of Econometrics, 162-2, 189-212.), "A Martingale Approach for Testing Diffusion Models Based on Infinitesimal Operator", I develop an omnibus specification test for diffusion models based on the infinitesimal operator instead of the transition density extensively used in literature. The infinitesimal operator based identification of the diffusion process is equivalent to a "martingale hypothesis" for the processes obtained by a transformation of the original diffusion model. My test procedure is then constructed by checking the "martingale hypothesis" via a multivariate generalized spectral derivative based approach which delivers an N(0,1) asymptotical null distribution for the test statistic. The infinitesimal operator of the diffusion process enjoys the nice property of being a closed-form function of drift and diffusion terms. Consequently, my test procedure covers both univariate and multivariate diffusion models in a unified framework and is particularly convenient for the multivariate case. Moreover, different transformed martingale processes contain separate information about the drift and diffusion specifications and about their interactions. This motivates me to propose a separate inferential test procedure to explore the sources of rejection when a parametric form is rejected. Simulation studies show that the proposed tests have reasonable size and excellent power performances. An empirical application of my test procedure using Eurodollar interest rates finds that most popular short-rate models are rejected and the drift mis-specification plays an important role in such rejections. In the fourth chapter, "Estimating Semi-Parametric Diffusion Models with Unrestricted Volatility via Infinitesimal Operator", two generalized method of moments estimators are proposed for the drift parameters in both univariate and multivariate semi-parametric diffusion models with unrestricted volatility based on the infinitesimal operator. The first estimator is obtained by integrating out the diffusion function via the quadratic variation (co-variation), which is estimated by the realized volatility (covariance) in a first step using high frequency data. The second is constructed based on the separate identification condition and is actually applicable for a general instantaneous conditional mean model in continuous time, which covers the stochastic volatility and jump diffusion models as special cases. Simulation studies show that they possess fairly good finite sample performances.

Download or read book Stochastic Volatility written by Neil Shephard and published by Oxford University Press, USA. This book was released on 2005 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic volatility is the main concept used in the fields of financial economics and mathematical finance to deal with time-varying volatility in financial markets. This work brings together some of the main papers that have influenced this field, andshows that the development of this subject has been highly multidisciplinary.

Download or read book Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models written by Matt Pritsker and published by . This book was released on 1997 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Palgrave Handbook of Econometrics written by Terence C. Mills and published by Springer. This book was released on 2009-06-25 with total page 1406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following theseminal Palgrave Handbook of Econometrics: Volume I , this second volume brings together the finestacademicsworking in econometrics today andexploresapplied econometrics, containing contributions onsubjects includinggrowth/development econometrics and applied econometrics and computing.

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:

Download or read book Generalized Method of Moments written by Alastair R. Hall and published by Oxford University Press. This book was released on 2005 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Method of Moments (GMM) has become one of the main statistical tools for the analysis of economic and financial data. This book is the first to provide an intuitive introduction to the method combined with a unified treatment of GMM statistical theory and a survey of recentimportant developments in the field. Providing a comprehensive treatment of GMM estimation and inference, it is designed as a resource for both the theory and practice of GMM: it discusses and proves formally all the main statistical results, and illustrates all inference techniques using empiricalexamples in macroeconomics and finance.Building from the instrumental variables estimator in static linear models, it presents the asymptotic statistical theory of GMM in nonlinear dynamic models. Within this framework it covers classical results on estimation and inference techniques, such as the overidentifying restrictions test andtests of structural stability, and reviews the finite sample performance of these inference methods. And it discusses in detail recent developments on covariance matrix estimation, the impact of model misspecification, moment selection, the use of the bootstrap, and weak instrumentasymptotics.

Download or read book Generalized Method of Moments Estimation of Heath Jarrow Morton Models of Interest rate Contingent Claims written by Peter Albert Abken and published by . This book was released on 1994 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Efficient Method of Moments Estimation of the Longstaff and Schwartz Interest Rate Model written by M. Berg Jensen and published by . This book was released on 2000 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Modelling Stock Market Volatility written by Peter H. Rossi and published by Elsevier. This book was released on 1996-11-19 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: This essay collection focuses on the relationship between continuous time models and Autoregressive Conditionally Heteroskedastic (ARCH) models and applications. For the first time, Modelling Stock Market Volatility provides new insights about the links between these two models and new work on practical estimation methods for continuous time models. Featuring the pioneering scholarship of Daniel Nelson, the text presents research about the discrete time model, continuous time limits and optimal filtering of ARCH models, and the specification and estimation of continuous time processes. This work will lead to a rapid growth in their empirical application as they are increasingly subjected to routine specification testing. Provides for the first time new insights on the links between continuous time and ARCH models Collects seminal scholarship by some of the most renowned researchers in finance and econometrics Captures complex arguments underlying the approximation and proper statistical modelling of continuous time volatility dynamics

Download or read book Financial Econometrics written by Christian Gourieroux and published by Princeton University Press. This book was released on 2022-12-13 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial econometrics is a great success story in economics. Econometrics uses data and statistical inference methods, together with structural and descriptive modeling, to address rigorous economic problems. Its development within the world of finance is quite recent and has been paralleled by a fast expansion of financial markets and an increasing variety and complexity of financial products. This has fueled the demand for people with advanced econometrics skills. For professionals and advanced graduate students pursuing greater expertise in econometric modeling, this is a superb guide to the field's frontier. With the goal of providing information that is absolutely up-to-date—essential in today's rapidly evolving financial environment—Gourieroux and Jasiak focus on methods related to foregoing research and those modeling techniques that seem relevant to future advances. They present a balanced synthesis of financial theory and statistical methodology. Recognizing that any model is necessarily a simplified image of reality and that econometric methods must be adapted and applied on a case-by-case basis, the authors employ a wide variety of data sampled at frequencies ranging from intraday to monthly. These data comprise time series representing both the European and North American markets for stocks, bonds, and foreign currencies. Practitioners are encouraged to keep a critical eye and are armed with graphical diagnostics to eradicate misspecification errors. This authoritative, state-of-the-art reference text is ideal for upper-level graduate students, researchers, and professionals seeking to update their skills and gain greater facility in using econometric models. All will benefit from the emphasis on practical aspects of financial modeling and statistical inference. Doctoral candidates will appreciate the inclusion of detailed mathematical derivations of the deeper results as well as the more advanced problems concerning high-frequency data and risk control. By establishing a link between practical questions and the answers provided by financial and statistical theory, the book also addresses the needs of applied researchers employed by financial institutions.

Download or read book Econometric Modelling with Time Series written by Vance Martin and published by Cambridge University Press. This book was released on 2013 with total page 925 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Maximum likelihood estimation is a general method for estimating the parameters of econometric models from observed data. The principle of maximum likelihood plays a central role in the exposition of this book, since a number of estimators used in econometrics can be derived within this framework. Examples include ordinary least squares, generalized least squares and full-information maximum likelihood. In deriving the maximum likelihood estimator, a key concept is the joint probability density function (pdf) of the observed random variables, yt. Maximum likelihood estimation requires that the following conditions are satisfied. (1) The form of the joint pdf of yt is known. (2) The specification of the moments of the joint pdf are known. (3) The joint pdf can be evaluated for all values of the parameters, 9. Parts ONE and TWO of this book deal with models in which all these conditions are satisfied. Part THREE investigates models in which these conditions are not satisfied and considers four important cases. First, if the distribution of yt is misspecified, resulting in both conditions 1 and 2 being violated, estimation is by quasi-maximum likelihood (Chapter 9). Second, if condition 1 is not satisfied, a generalized method of moments estimator (Chapter 10) is required. Third, if condition 2 is not satisfied, estimation relies on nonparametric methods (Chapter 11). Fourth, if condition 3 is violated, simulation-based estimation methods are used (Chapter 12). 1.2 Motivating Examples To highlight the role of probability distributions in maximum likelihood estimation, this section emphasizes the link between observed sample data and 4 The Maximum Likelihood Principle the probability distribution from which they are drawn"-- publisher.

Download or read book Modeling Financial Time Series with S PLUS written by Eric Zivot and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of financial econometrics has exploded over the last decade This book represents an integration of theory, methods, and examples using the S-PLUS statistical modeling language and the S+FinMetrics module to facilitate the practice of financial econometrics. This is the first book to show the power of S-PLUS for the analysis of time series data. It is written for researchers and practitioners in the finance industry, academic researchers in economics and finance, and advanced MBA and graduate students in economics and finance. Readers are assumed to have a basic knowledge of S-PLUS and a solid grounding in basic statistics and time series concepts. This Second Edition is updated to cover S+FinMetrics 2.0 and includes new chapters on copulas, nonlinear regime switching models, continuous-time financial models, generalized method of moments, semi-nonparametric conditional density models, and the efficient method of moments. Eric Zivot is an associate professor and Gary Waterman Distinguished Scholar in the Economics Department, and adjunct associate professor of finance in the Business School at the University of Washington. He regularly teaches courses on econometric theory, financial econometrics and time series econometrics, and is the recipient of the Henry T. Buechel Award for Outstanding Teaching. He is an associate editor of Studies in Nonlinear Dynamics and Econometrics. He has published papers in the leading econometrics journals, including Econometrica, Econometric Theory, the Journal of Business and Economic Statistics, Journal of Econometrics, and the Review of Economics and Statistics. Jiahui Wang is an employee of Ronin Capital LLC. He received a Ph.D. in Economics from the University of Washington in 1997. He has published in leading econometrics journals such as Econometrica and Journal of Business and Economic Statistics, and is the Principal Investigator of National Science Foundation SBIR grants. In 2002 Dr. Wang was selected as one of the "2000 Outstanding Scholars of the 21st Century" by International Biographical Centre.