Time-series and Cross-section Information in Affine Term Structure Models PDF Download
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Author: Frank de Jong
Publisher:
ISBN:
Category : Interest rates
Languages : en
Pages : 56
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Book Description
Author: Frank de Jong
Publisher:
ISBN:
Category : Interest rates
Languages : en
Pages : 56
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Book Description
Author: Franciscus Cornelis Johannes Maria Jong
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Pierre Collin-Dufresne
Publisher:
ISBN:
Category :
Languages : en
Pages : 62
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Book Description
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.
Author: Januj Juneja
Publisher:
ISBN:
Category :
Languages : en
Pages : 274
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Book Description
The first essay empirically evaluates recently developed techniques that have been proposed to improve the estimation of affine term structure models. The evaluation presented here is performed on two dimensions. On the first dimension, I find that invariant transformations and rotations can be used to reduce the number of free parameters needed to estimate the model and subsequently, improve the empirical performance of affine term structure models. The second dimension of this evaluation surrounds the comparison between estimating an affine term structure model using the model-free method and the inversion method. Using daily LIBOR rate and swap rate quotes from June 1996 to July 2008 to extract a panel of 3,034 time-series observations and 14 cross sections, this paper shows that, a term structure model that is estimated using the model-free method does not perform significantly better in fitting yields, at any horizon, than the more traditional methods available in the literature. The second essay attempts explores implications of using principal components analysis in the estimation of affine term structure models. Early work employing principal component analysis focused on portfolio formation and trading strategies. Recent work, however, has moved the usage of principal components analysis into more formal applications such as the direct involvement of principal component based factors within an affine term structure model. It is this usage of principal components analysis in formal model settings that warrants a study of potential econometric implications of its application to term structure modeling. Serial correlation in interest rate data, for example, has been documented by several authors. The majority of the literature has focused on strong persistence in state variables as giving rise to this phenomena. In this paper, I take yields as given, and hence document the effects of whitening on the model-implied state-dependent factors, subsequently estimated by the principal component based model-free method. These results imply that the process of pre-whitening the data does play a critical role in model estimation. Results are robust to Monte Carlo Simulations. Empirical results are obtained from using daily LIBOR rate and swap rate quotes from June 1996 to July 2008 to extract a panel of zero-coupon yields consisting of 3,034 time-series observations and 14 cross sections. The third essay examines the extent to which the prevalence of estimation risk in numerical integration creates bias, inefficiencies, and inaccurate results in the widely used class of affine term structure models. In its most general form, this class of models relies on the solution to a system of non-linear Ricatti equations to back out the state-factor coefficients. Only in certain cases does this class of models admit explicit, and thus analytically tractable, solutions for the state factor coefficients. Generally, and for more economically plausible scenarios, explicit closed form solutions do not exist and the application of Runge-Kutta methods must be employed to obtain numerical estimates of the coefficients for the state variables. Using a panel of 3,034 yields and 14 cross-sections, this paper examines what perils, if any, exist in this trade off of analytical tractability against economic flexibility. Robustness checks via Monte Carlo Simulations are provided. In specific, while the usage of analytical methods needs less computational time, numerical methods can be used to estimate a broader set of economic scenarios. Regardless of the data generating process, the generalized Gaussian process seems to dominate the Vasicek model in terms of bias and efficiency. However, when the data are generated from a Vasicek model, the Vasicek model performs better than the generalized Gaussian process for fitting the yield curve. These results impart new and important information about the trade off that exists between using analytical methods and numerical methods for estimate affine term structure models.
Author: Riccardo Rebonato
Publisher:
ISBN:
Category :
Languages : en
Pages : 42
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Book Description
We present an essentially affine model with pricipal components as state variables. We show that, once no-arbitrage is imposed, this choice of state variables imposes some unexpected constraints on the reversionspeed matrix, whose N2 elements can be uniquely specified by its N eigenvalues. The requirement that some of its elements should be negative gives rise to a potentially complex dynamics, whose implications we discuss at length. We show how the free parameters of the model can be determined by combining cross-sectional information on bond prices with time-series information about excess returns and by enforcing a 'smoothness' requirement. The calibration in the P and Q measures does not require heavy numerical search, and can be carried out almost fully with elementary matrix operations. Once calibrated, the model recovers exactly the (discrete) yield cuirve shape, the yield covariance matrix, its eigenvalues and eigenvectors. The ability to recover yield volatilities well makes it useful for the estimation of convexity and term premia. The model also recovers well quantities to which it has not been calibrated, and offers an estimation of the term premia for yields of different maturities which we discuss in the last section.
Author: Wolfgang Lemke
Publisher: Springer Science & Business Media
ISBN: 3540283447
Category : Business & Economics
Languages : en
Pages : 224
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Book Description
This book has been prepared during my work as a research assistant at the Institute for Statistics and Econometrics of the Economics Department at the University of Bielefeld, Germany. It was accepted as a Ph.D. thesis titled "Term Structure Modeling and Estimation in a State Space Framework" at the Department of Economics of the University of Bielefeld in November 2004. It is a pleasure for me to thank all those people who have been helpful in one way or another during the completion of this work. First of all, I would like to express my gratitude to my advisor Professor Joachim Frohn, not only for his guidance and advice throughout the com pletion of my thesis but also for letting me have four very enjoyable years teaching and researching at the Institute for Statistics and Econometrics. I am also grateful to my second advisor Professor Willi Semmler. The project I worked on in one of his seminars in 1999 can really be seen as a starting point for my research on state space models. I thank Professor Thomas Braun for joining the committee for my oral examination.
Author: Eric Zivot
Publisher: Springer Science & Business Media
ISBN: 9780387955490
Category : Business & Economics
Languages : en
Pages : 648
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Book Description
The field of financial econometrics has exploded since the early 1990s. 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. It shows 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.
Author: Kris Jacobs
Publisher:
ISBN:
Category :
Languages : en
Pages : 53
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Book Description
Several papers have questioned the ability of multifactor affine models to extract interest rate volatility from the cross-section of bond prices. These studies find that the conditional volatility implied by these models is very poorly or even negatively correlated with model-free volatility. We provide an in-depth investigation of the conditional volatility of monthly Treasury yields implied by three-factor affine models. We investigate different specifications of the price of risk and different specifications of volatility. For long maturities, the correlation between model-implied and EGARCH volatility estimates is approximately 82% for yield differences and 92% for yield levels. For short-maturity yields, the correlation varies between 58% and 71% for yield differences and between 62% and 76% for yield levels. The differences at short maturities are largely accounted for by the number of factors affecting volatility. A model-free measure of the level factor is highly correlated with EGARCH volatility as well as model-implied volatilities, which explains most of our findings. We conclude that multifactor affine models are much better at extracting time-series volatility from the cross-section of yields than argued in the literature. However, existing models have difficulty capturing volatility dynamics at the short end of the maturity spectrum, perhaps indicating some form of segmentation between long-maturity and short-maturity bonds. These results are robust to the choice of sample period, interpolation method and estimation method.
Author: Ting Ting Huang
Publisher: Cambridge Scholars Publishing
ISBN: 1443815829
Category : Business & Economics
Languages : en
Pages : 89
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Book Description
This paper is the first that completely studies dynamical and cross-sectional structures of bonds, typically used as risk-free assets in mathematical finance, on the independence of the common factors with the empirical copula. During the last decade, financial models based empirically on common factors have acquired increasing popularity in risk management and asset pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for non-specialists to understand, and the mathematical tools required for applications can be intimidating. Although many of the copula models used in finance are theoretical, the nature of financial data suggests the empirical copula is more appropriate for forecasting and accurately describing returns, volatility and interdependence.
Author: Adrian R. Bell
Publisher: Edward Elgar Publishing
ISBN: 0857936093
Category : Business & Economics
Languages : en
Pages : 494
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Book Description
This impressive Handbook presents the quantitative techniques that are commonly employed in empirical finance research together with real-world, state-of-the-art research examples. Written by international experts in their field, the unique approach describes a question or issue in finance and then demonstrates the methodologies that may be used to solve it. All of the techniques described are used to address real problems rather than being presented for their own sake, and the areas of application have been carefully selected so that a broad range of methodological approaches can be covered. The Handbook is aimed primarily at doctoral researchers and academics who are engaged in conducting original empirical research in finance. In addition, the book will be useful to researchers in the financial markets and also advanced Masters-level students who are writing dissertations.
