Affine Term Structure Models Volatility And The Segmentation Hypothesis
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| Author | : Kris Jacobs |
| Publisher | : |
| Total Pages | : 53 |
| Release | : 2007 |
| Genre | : |
| ISBN | : |
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 | : Huarong Tang |
| Publisher | : |
| Total Pages | : 51 |
| Release | : 2005 |
| Genre | : |
| ISBN | : |
| Author | : Qiang Dai |
| Publisher | : |
| Total Pages | : 51 |
| Release | : 1997 |
| Genre | : Geometry, Affine |
| ISBN | : |
This paper characterizes, interprets, and tests the over-identifying restrictions imposed in affine models of the term" structure. Letting r(t) = ë Y(t), where Y is an unobserved vector affine process, our analysis proceeds in three steps. First, we show that affine models can be categorized according to the different over-identifying restrictions they impose on (i) ë, and (ii) the parameters of the diffusion matrices. Second, this formulation is shown to be equivalent to a model in which there is a terraced drift structure with one of the state variables being the stochastic long-run mean of r. This equivalence allows direct comparisons of the substantive restrictions on the dynamics of interest rates imposed in CIR-style models and models in which the state variables are the stochastic long-run mean and volatility of r. Third, we compute simulated method of moments estimates of a three-factor affine term structure model, and test the over-identifying restrictions on the joint distribution of long- and short-term interest rates implied by extant affine models of r. We find allowing for correlated factors is key to simultaneously describing the short and long ends of the yield curve. This finding is interpreted in terms of the properties of the risk factors underlying term structure movements
| Author | : Eva Ferreira |
| Publisher | : |
| Total Pages | : |
| Release | : 2010 |
| Genre | : |
| ISBN | : |
This article proposes a new approach to testing for the hypothesis of a single priced risk factor driving the term structure of interest rates. The method does not rely on any parametric specification of the state variable dynamics or the market price of risk. It simply exploits the constraint imposed by the no-arbitrage condition on instantaneous expected bond returns. In order to achieve our goal, we develop a Kolmogorov-Smirnov test and apply it to data on Treasury bills and bonds for both the United States and Spain. We find that the single risk factor hypothesis cannot be rejected for either dataset.
| Author | : Pierre Collin-Dufresne |
| Publisher | : |
| Total Pages | : 62 |
| Release | : 2011 |
| Genre | : |
| ISBN | : |
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 | : Sanjay K. Nawalkha |
| Publisher | : John Wiley & Sons |
| Total Pages | : 722 |
| Release | : 2007-05-23 |
| Genre | : Business & Economics |
| ISBN | : 0470140062 |
Praise for Dynamic Term Structure Modeling "This book offers the most comprehensive coverage of term-structure models I have seen so far, encompassing equilibrium and no-arbitrage models in a new framework, along with the major solution techniques using trees, PDE methods, Fourier methods, and approximations. It is an essential reference for academics and practitioners alike." --Sanjiv Ranjan Das Professor of Finance, Santa Clara University, California, coeditor, Journal of Derivatives "Bravo! This is an exhaustive analysis of the yield curve dynamics. It is clear, pedagogically impressive, well presented, and to the point." --Nassim Nicholas Taleb author, Dynamic Hedging and The Black Swan "Nawalkha, Beliaeva, and Soto have put together a comprehensive, up-to-date textbook on modern dynamic term structure modeling. It is both accessible and rigorous and should be of tremendous interest to anyone who wants to learn about state-of-the-art fixed income modeling. It provides many numerical examples that will be valuable to readers interested in the practical implementations of these models." --Pierre Collin-Dufresne Associate Professor of Finance, UC Berkeley "The book provides a comprehensive description of the continuous time interest rate models. It serves an important part of the trilogy, useful for financial engineers to grasp the theoretical underpinnings and the practical implementation." --Thomas S. Y. Ho, PHD President, Thomas Ho Company, Ltd, coauthor, The Oxford Guide to Financial Modeling
| Author | : Kris Jacobs |
| Publisher | : |
| Total Pages | : 55 |
| Release | : 2008 |
| Genre | : |
| ISBN | : |
Several papers have questioned the ability of multifactor affine models to extract interest rate volatility from the cross-section of yields. These studies find that model-implied conditional volatility is very poorly or even negatively correlated with model-free volatility. We study the ability of three-factor models to extract conditional volatility using interest rate swap yields for 1991-2005 and a sample of Treasury yields for 1970-2003. For the extended Treasury sample, the correlation between model-implied and EGARCH volatility is between 60% and 75%. For swaps,the correlation is rather low or negative. Results for swaps are also more model-dependent and less robust. For Treasuries, a model-free measure of the level factor is highly correlated with EGARCH volatility as well as model-implied volatilities. For swaps, the level factor is not as highly correlated with conditional volatility. We find that these differences in model performance are primarily due to the timing of the swap sample, and not to institutional differences between swap and Treasury markets. Our results are confirmed using metrics other than correlation. They are also robust to the choice of estimation method, interpolation method and volatility measure, and hold for yield ifferences as well as yield levels. We conclude that the ability of multifactor affine models to extract conditional volatility depends on the sample period, but that overall these models perform better than has been argued in the literature.
| Author | : Drew Creal |
| Publisher | : |
| Total Pages | : 61 |
| Release | : 2017 |
| Genre | : |
| ISBN | : |
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.
| Author | : Ruslan Bikbov |
| Publisher | : |
| Total Pages | : 65 |
| Release | : 2004 |
| Genre | : |
| ISBN | : |
We evaluate the ability of several affine models to explain the term structure of the interest rates and option prices. Since the key distinguishing characteristic of the affine models is the specification of conditional volatility of the factors, we explore models which have critical differences in this respect: Gaussian (constant volatility), stochastic volatility, and unspanned stochastic volatility models. We estimate the models based on the Eurodollar futures and options data. We find that both Gaussian and stochastic volatility models, despite the differences in the specifications, do a great job matching the conditional mean and volatility of the term structure. When these models are estimated using options data, their properties change, and they are more successful in pricing options and matching higher moments of the term structure distribution. The unspanned stochastic volatility (USV) model fails to resolve the tension between the futures and options fits. Unresolved tension in the fits points to additional factors or, even more likely, jumps, as ways to improve the performance of the models. Our results indicate that Gaussian and stochastic volatility models cannot be distinguished based on the yield curve dynamics alone. Options data are helpful in identifying the differences. In particular, Gaussian models cannot explain the relationship between implied volatilities and the term structure observed in the data.
| Author | : Cheikh Mbaye |
| Publisher | : |
| Total Pages | : 55 |
| Release | : 2019 |
| Genre | : |
| ISBN | : |
We address the so-called calibration problem which consists of fitting in a tractable way a given model to a specified term structure like, e.g., yield, prepayment or default probability curves. Time-homogeneous jump-diffusions like Vasicek or Cox-Ingersoll-Ross (possibly coupled with compound Poisson jumps, JCIR), are tractable processes but have limited flexibility; they fail to replicate actual market curves. The deterministic shift extension of the latter (Hull-White or JCIR++) is a simple but yet efficient solution that is widely used by both academics and practitioners. However, the shift approach is often not appropriate when positivity is required, which is a common constraint when dealing with credit spreads or default intensities. In this paper, we tackle this problem by adopting a time change approach. On the top of providing an elegant solution to the calibration problem under positivity constraint, our model features additional interesting properties in terms of implied volatilities. It is compared to the shift extension on various credit risk applications such as credit default swap, credit default swaption and credit valuation adjustment under wrong-way risk. The time change approach is able to generate much larger volatility and covariance effects under the positivity constraint. Our model offers an appealing alternative to the shift in such cases.
