Conditional Volatility in Affine Term Structure Models PDF Download
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Author: Kris Jacobs
Publisher:
ISBN:
Category :
Languages : en
Pages : 55
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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 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: Kris Jacobs
Publisher:
ISBN:
Category :
Languages : en
Pages : 55
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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 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: 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: Frank de Jong
Publisher:
ISBN:
Category : Interest rates
Languages : en
Pages : 56
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Book Description
Author: Ruslan Bikbov
Publisher:
ISBN:
Category :
Languages : en
Pages : 65
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Book Description
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: Anne Lundgaard Hansen
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
It is well-known that interest rates are extremely persistent, yet they are best modeled and understood as stationary processes. These properties are contradictory in the workhorse Gaussian affine term structure model in which persistent data often result in unit roots that imply non-stationarity. We resolve this puzzle by proposing a term structure model with volatilityinduced stationarity. Our model employs a leveldependent conditional volatility that maintains stationarity despite the presence of unit roots in the characteristic polynomial corresponding to the conditional mean. The model is consistent with key characteristics of U.S. Treasury data and obtains term premia that are economically plausible and consistent with survey data. Compared to the Gaussian affine term structure model, we improve out-of-sample forecasting of the yield curve.
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: Rajna Gibson
Publisher: Now Publishers Inc
ISBN: 1601983727
Category : Business & Economics
Languages : en
Pages : 171
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Book Description
Modeling the Term Structure of Interest Rates provides a comprehensive review of the continuous-time modeling techniques of the term structure applicable to value and hedge default-free bonds and other interest rate derivatives.
Author: Drew Creal
Publisher:
ISBN:
Category :
Languages : en
Pages : 61
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Book Description
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: Drew D. Creal
Publisher:
ISBN:
Category :
Languages : en
Pages : 67
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Book Description
Author: Drew D. Creal
Publisher:
ISBN:
Category : Economics
Languages : en
Pages : 0
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Book Description
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.
