A Principal-Component-Based Affine Term Structure Model PDF Download
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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: 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: Ivan Saroka
Publisher:
ISBN:
Category :
Languages : en
Pages : 50
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Book Description
We present an affine multifactor Gaussian term structure model, where we let factors be principal components of yields. Taking forward the affine-yield idea presented in Duffie and Kan (1996) we derive general expressions for the coefficients of a multidimensional affine Gaussian stochastic process given an exogenous matrix of loadings of selected yields on the state variables.
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: Irene Sekyere Asare
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
The term structure of interest rates is relevant to economists as it reflects the information available to the market about the time value of money in the future. Affine term structure models such as short rate models have been used in interest rate modelling over the past years to determine the mechanisms driving the term structure. Machine learning approaches are explored in this thesis and compared to the traditional econometric approach, specifically the Vasicek model. Multifactor Vasicek models are considered as the one factor model is found not adequate to characterize the term structure of interest rates. Since the short rates are not observable the Kalman filter approach is used in estimating the parameters of the Vasicek model. This thesis utilizes the Canadian zero-coupon bond price data in the implementation of both methods and it is observed from both methods that increasing the number of factors to three increases the ability to capture the curvature of the yield curve. The first factor is identified to be responsible for the level of the yield curve, the second factor the slope and third factor the curvature of the yield curve. This is consistent with results obtained from previous work on term structure models. The results from this work indicates that the machine learning technique, specifically the first three principal components of the Principal Component Analysis (PCA), outperforms the Vasicek model in fitting the yield curve.
Author: Riccardo Rebonato
Publisher: Cambridge University Press
ISBN: 1316732959
Category : Business & Economics
Languages : en
Pages : 781
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Book Description
In this book, well-known expert Riccardo Rebonato provides the theoretical foundations (no-arbitrage, convexity, expectations, risk premia) needed for the affine modeling of the government bond markets. He presents and critically discusses the wealth of empirical findings that have appeared in the literature of the last decade, and introduces the 'structural' models that are used by central banks, institutional investors, sovereign wealth funds, academics, and advanced practitioners to model the yield curve, to answer policy questions, to estimate the magnitude of the risk premium, to gauge market expectations, and to assess investment opportunities. Rebonato weaves precise theory with up-to-date empirical evidence to build, with the minimum mathematical sophistication required for the task, a critical understanding of what drives the government bond market.
Author: Pietro Veronesi
Publisher: John Wiley & Sons
ISBN: 1118709195
Category : Business & Economics
Languages : en
Pages : 630
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Book Description
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.
Author: Cheng Few Lee
Publisher: World Scientific
ISBN: 9811202400
Category : Business & Economics
Languages : en
Pages : 5053
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Book Description
This four-volume handbook covers important concepts and tools used in the fields of financial econometrics, mathematics, statistics, and machine learning. Econometric methods have been applied in asset pricing, corporate finance, international finance, options and futures, risk management, and in stress testing for financial institutions. This handbook discusses a variety of econometric methods, including single equation multiple regression, simultaneous equation regression, and panel data analysis, among others. It also covers statistical distributions, such as the binomial and log normal distributions, in light of their applications to portfolio theory and asset management in addition to their use in research regarding options and futures contracts.In both theory and methodology, we need to rely upon mathematics, which includes linear algebra, geometry, differential equations, Stochastic differential equation (Ito calculus), optimization, constrained optimization, and others. These forms of mathematics have been used to derive capital market line, security market line (capital asset pricing model), option pricing model, portfolio analysis, and others.In recent times, an increased importance has been given to computer technology in financial research. Different computer languages and programming techniques are important tools for empirical research in finance. Hence, simulation, machine learning, big data, and financial payments are explored in this handbook.Led by Distinguished Professor Cheng Few Lee from Rutgers University, this multi-volume work integrates theoretical, methodological, and practical issues based on his years of academic and industry experience.
Author: Biancen Xie
Publisher:
ISBN:
Category : Electronic dissertations
Languages : en
Pages : 111
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Book Description
In my dissertation, I focus on theoretical affine term structure models and the development of Bayesian econometric methods to estimate them.In the first Chapter, we address the question of which unspanned macroeconomic factors are the best in the class of macro-finance Gaussian affine term structure models. To answer this question, we extend Joslin, Priebsch, and Singleton (2014) in two dimensions. First, following Ang and Piazzesi (2003) and Chib and Ergashev (2009), three latent factors, instead of the first three principal components of the yield curve, are used to represent the level, slope and curvature of the yield curve. Second we postulate a grand affine model that includes all the macro-variables in contention. Specific models are then derived from this grand model by letting each of the macro-variables play the role of a relevant macro factor (i.e. by affecting the time-varying market price of factor risks), or the role of an irrelevant macro factor (having no effect on the market price of factor risks). The Bayesian marginal likelihoods of the resulting models are computed by an efficient Markov chain Monte Carlo algorithm and the method of Chib (1995) and Chib and Jeliazkov (2001). Given eight common macro factors, our comparison of 28=256 affine models shows that the most relevant macro factors for the U.S. yield curve are the federal funds rate, industrial production, total capacity utilization, and housing sales. We also show that the best supported model substantially improves out-of-sample yield curve forecasting and the understanding of term-premium.The second Chapter considers the question of which unspanned macro factors can improve prediction in arbitrage-free affine term structure models and convert return forecasts into economic gains. To achieve this, we develop a Bayesian framework for incorporating different combinations of macro variables within an affine term structure framework. Then each specific model within the framework is evaluated statistically and economically. For the statistical evaluation, we examine its out-of-sample yield density forecasting. The economic value of each model is compared in terms of the bond portfolio choice of a Bayesian risk- averse investor. We consider two main kinds of macro factors: representative macro factors in Chib et al. (2019) and principal component macro factors in Ludvigson and Ng (2009b). Our empirical results show that regardless of macro dataset we use(either Chib et al. (2019) or Ludvigson and Ng (2009b)), macro factor in real economic activity, financial sector and price index will help generate notable gains in out-of-sample forecast. Such gains in predictive accuracy translate into higher portfolio returns after accounting for estimation error and model uncertainty. In contrast, incorporating redundant macro variables into the affine term structure models can even decrease utility and prediction accuracy for investors. In addition, given the data sample we consider in the Chapter, we also find that principle component factors can perform relatively better than representative macro factors in terms of certainty equivalence return (CER).The third Chapter compares the posterior sampling performance of No-U-Turn sam- pler(NUTS) algorithm and tailored randomized-blocking Metropolis-Hastings (TaRB-MH) for macro-finance affine Term structure models. We conduct empirical experiments on 3 affine term structure models with the U.S. yield curve data. For each experiment, we examine the sampling efficiency of model parameters, factors, term premium, predictive yields,etc. Our emprical results indicate that the TaRB-MH substantially outperforms the NUTS methodin terms of the convergence and efficiency in posterior sampling. Furthermore, we show that NUTS' inefficiency in simulating the affine term structure models will be robust given different initial values for the algorithm.
Author: Alexei V. Egorov
Publisher:
ISBN:
Category :
Languages : en
Pages : 39
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Book Description
Modeling the joint term structure of interest rates in the United States and the European Union, the two largest economies in the world, is extremely important in international finance. In this paper, we provide both theoretical and empirical analysis of multi-factor joint affine term structure models for dollar and euro interest rates. In particular, we provide a systematic classification of multi-factor joint affine term structure models similar to that of Dai and Singleton (2000). A principal component analysis of daily dollar and euro interest rates reveals four factors in the data. We estimate four-factor joint affine term structure models using the approximate maximum likelihood method of Ait-Sahalia (2002, 2007) and compare the in-sample and out-of-sample performances of these models using some of the latest nonparametric methods. We find that a new four-factor model with two common and two local factors captures the joint term structure dynamics in the U.S. and the E.U. reasonably well.
Author: Damir Filipovic
Publisher: Springer Science & Business Media
ISBN: 3540680152
Category : Mathematics
Languages : en
Pages : 259
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Book Description
Changing interest rates constitute one of the major risk sources for banks, insurance companies, and other financial institutions. Modeling the term-structure movements of interest rates is a challenging task. This volume gives an introduction to the mathematics of term-structure models in continuous time. It includes practical aspects for fixed-income markets such as day-count conventions, duration of coupon-paying bonds and yield curve construction; arbitrage theory; short-rate models; the Heath-Jarrow-Morton methodology; consistent term-structure parametrizations; affine diffusion processes and option pricing with Fourier transform; LIBOR market models; and credit risk. The focus is on a mathematically straightforward but rigorous development of the theory. Students, researchers and practitioners will find this volume very useful. Each chapter ends with a set of exercises, that provides source for homework and exam questions. Readers are expected to be familiar with elementary Itô calculus, basic probability theory, and real and complex analysis.
