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Identification and Estimation of 'Maximal' Affine Term Structure Models

Identification and Estimation of 'Maximal' Affine Term Structure Models
Author: Pierre Collin-Dufresne
Publisher:
Total Pages: 62
Release: 2011
Genre:
ISBN:

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We propose a canonical representation for affine term structure models where the state vector is comprised of the first few Taylor-series components of the yield curve and their quadratic (co-)variations. With this representation: (i) the state variables have simple physical interpretations such as level, slope and curvature, (ii) their dynamics remain affine and tractable, (iii) the model is by construction 'maximal' (i.e., it is the most general model that is econometrically identifiable), and (iv) model-insensitive estimates of the state vector process implied from the term structure are readily available. (Furthermore, this representation may be useful for identifying the state variables in a squared-Gaussian framework where typically there is no one-to-one mapping between observable yields and latent state variables). We find that the 'unrestricted' A1(3) model of Dai and Singleton (2000) estimated by 'inverting' the yield curve for the state variables generates volatility estimates that are negatively correlated with the time series of volatility estimated using a standard GARCH approach. This occurs because the 'unrestricted' A1(3) model imposes the restriction that the volatility state variable is simultaneously a linear combination of yields (i.e., it impacts the cross-section of yields), and the quadratic variation of the spot rate process (i.e., it impacts the time-series of yields). We then investigate the A1(3) model which exhibits 'unspanned stochastic volatility' (USV). This model predicts that the cross section of bond prices is independent of the volatility state variable, and hence breaks the tension between the time-series and cross-sectional features of the term structure inherent in the unrestricted model. We find that explicitly imposing the USV constraint on affine models significantly improves the volatility estimates, while maintaining a good fit cross-sectionally.


Identification of Maximal Affine Term Structure Models

Identification of Maximal Affine Term Structure Models
Author: Pierre Collin-Dufresne
Publisher:
Total Pages: 53
Release: 2011
Genre:
ISBN:

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Building on the approach of Duffie and Kan (1996) who use finite maturity yields as the state vector, we propose a new representation of affine models in which the state vector is composed of infinitesimal maturity yields and their quadratic covariations. Because these variables possess unambiguous economic interpretations, they generate a representation that is globally identifiable. Further, this representation is more flexible than the maximal model of Dai and Singleton (2000) in that there are more identifiable parameters. We implement this new representation for two different three-factor models. The fact that our state vector can be estimated model-independently from yield curve data presents advantages for the estimation and interpretation of multi-factor models.


Identification and estimation of Gaussian affine term structure models

Identification and estimation of Gaussian affine term structure models
Author: James D. Hamilton
Publisher:
Total Pages: 60
Release: 2012
Genre: Economics
ISBN:

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This paper develops new results for identification and estimation of Gaussian affine term structure models. We establish that three popular canonical representations are unidentified, and demonstrate how unidentified regions can complicate numerical optimization. A separate contribution of the paper is the proposal of minimum-chi-square estimation as an alternative to MLE. We show that, although it is asymptotically equivalent to MLE, it can be much easier to compute. In some cases, MCSE allows researchers to recognize with certainty whether a given estimate represents a global maximum of the likelihood function and makes feasible the computation of small-sample standard errors.


Estimation of Affine Term Structure Models with Spanned Or Unspanned Stochastic Volatility

Estimation of Affine Term Structure Models with Spanned Or Unspanned Stochastic Volatility
Author: Drew D. Creal
Publisher:
Total Pages: 0
Release: 2014
Genre: Economics
ISBN:

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We develop new procedures for maximum likelihood estimation of affine term structure models with spanned or unspanned stochastic volatility. Our approach uses linear regression to reduce the dimension of the numerical optimization problem yet it produces the same estimator as maximizing the likelihood. It improves the numerical behavior of estimation by eliminating parameters from the objective function that cause problems for conventional methods. We find that spanned models capture the cross-section of yields well but not volatility while unspanned models fit volatility at the expense of fitting the cross-section.


Simulated Likelihood Estimation of Affine Term Structure Models from Panel Data

Simulated Likelihood Estimation of Affine Term Structure Models from Panel Data
Author: Michael W. Brandt
Publisher:
Total Pages: 36
Release: 2006
Genre:
ISBN:

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We show how to estimate affine term structure models from a panel of noisy bond yields using simulated maximum likelihood based on importance sampling. We approximate the likelihood function of the state-space representation of the model by correcting the likelihood function of a Gaussian first-order approximation for the non-normalities introduced by the affine factor dynamics. Depending on the accuracy of the correction, which is computed through simulations, the quality of the estimator ranges from quasi-maximum likelihood (no correction) to exact maximum likelihood as the simulation size grows.


Handbook of Financial Econometrics

Handbook of Financial Econometrics
Author: Yacine Ait-Sahalia
Publisher: Elsevier
Total Pages: 385
Release: 2009-10-21
Genre: Business & Economics
ISBN: 0444535497

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Applied financial econometrics subjects are featured in this second volume, with papers that survey important research even as they make unique empirical contributions to the literature. These subjects are familiar: portfolio choice, trading volume, the risk-return tradeoff, option pricing, bond yields, and the management, supervision, and measurement of extreme and infrequent risks. Yet their treatments are exceptional, drawing on current data and evidence to reflect recent events and scholarship. A landmark in its coverage, this volume should propel financial econometric research for years. Presents a broad survey of current research Contributors are leading econometricians Offers a clarity of method and explanation unavailable in other financial econometrics collections


Third International Conference on Credit Analysis and Risk Management

Third International Conference on Credit Analysis and Risk Management
Author: Joseph Callaghan
Publisher: Cambridge Scholars Publishing
Total Pages: 315
Release: 2015-09-04
Genre: Business & Economics
ISBN: 1443882151

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Held at Oakland University, School of Business Administration, Department of Accounting and Finance. This book provides a summary of state-of-the-art methods and research in the analysis of credit. As such, it offers very useful insights into this vital area of finance, which has too often been under-researched and little-taught in academia. Including an overview of processes that are utilized for estimating the probability of default and the loss given default for a wide array of debts, the book will also be useful in evaluating individual loans and bonds, as well as managing entire portfolios of such assets. Each chapter is written by authors who presented and discussed their contemporary research and knowledge at the Third International Conference on Credit Analysis and Risk Management, held on August 21–22, 2014 at the Department of Accounting and Finance, School of Business administration, Oakland University. This collection of writings by these experts in the field is uniquely designed to enhance the understanding of credit analysis in a fashion that permits a broad perspective on the science and art of credit analysis.


Long Memory Affine Term Structure Models

Long Memory Affine Term Structure Models
Author: Adam Golinski
Publisher:
Total Pages: 61
Release: 2017
Genre:
ISBN:

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We develop a Gaussian discrete time essentially affine term structure model with long memory state variables. This feature reconciles the strong persistence observed in nominal yields and inflation with the theoretical implications of affine models, especially for long maturities. We characterise in closed-form the dynamic and cross-sectional implications of long memory for our model. We explain how long memory can naturally arise within the term structure of interest rates, providing a theoretical underpinning for our model. Despite the infinite-dimensional structure that long memory implies, we show how to cast the model in state space and estimate it by maximum likelihood. An empirical application of our model is presented.


Handbook of Fixed-Income Securities

Handbook of Fixed-Income Securities
Author: Pietro Veronesi
Publisher: John Wiley & Sons
Total Pages: 630
Release: 2016-04-04
Genre: Business & Economics
ISBN: 1118709195

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A comprehensive guide to the current theories and methodologies intrinsic to fixed-income securities Written by well-known experts from a cross section of academia and finance, Handbook of Fixed-Income Securities features a compilation of the most up-to-date fixed-income securities techniques and methods. The book presents crucial topics of fixed income in an accessible and logical format. Emphasizing empirical research and real-life applications, the book explores a wide range of topics from the risk and return of fixed-income investments, to the impact of monetary policy on interest rates, to the post-crisis new regulatory landscape. Well organized to cover critical topics in fixed income, Handbook of Fixed-Income Securities is divided into eight main sections that feature: • An introduction to fixed-income markets such as Treasury bonds, inflation-protected securities, money markets, mortgage-backed securities, and the basic analytics that characterize them • Monetary policy and fixed-income markets, which highlight the recent empirical evidence on the central banks’ influence on interest rates, including the recent quantitative easing experiments • Interest rate risk measurement and management with a special focus on the most recent techniques and methodologies for asset-liability management under regulatory constraints • The predictability of bond returns with a critical discussion of the empirical evidence on time-varying bond risk premia, both in the United States and abroad, and their sources, such as liquidity and volatility • Advanced topics, with a focus on the most recent research on term structure models and econometrics, the dynamics of bond illiquidity, and the puzzling dynamics of stocks and bonds • Derivatives markets, including a detailed discussion of the new regulatory landscape after the financial crisis and an introduction to no-arbitrage derivatives pricing • Further topics on derivatives pricing that cover modern valuation techniques, such as Monte Carlo simulations, volatility surfaces, and no-arbitrage pricing with regulatory constraints • Corporate and sovereign bonds with a detailed discussion of the tools required to analyze default risk, the relevant empirical evidence, and a special focus on the recent sovereign crises A complete reference for practitioners in the fields of finance, business, applied statistics, econometrics, and engineering, Handbook of Fixed-Income Securities is also a useful supplementary textbook for graduate and MBA-level courses on fixed-income securities, risk management, volatility, bonds, derivatives, and financial markets. Pietro Veronesi, PhD, is Roman Family Professor of Finance at the University of Chicago Booth School of Business, where he teaches Masters and PhD-level courses in fixed income, risk management, and asset pricing. Published in leading academic journals and honored by numerous awards, his research focuses on stock and bond valuation, return predictability, bubbles and crashes, and the relation between asset prices and government policies.