Affine Term Structure Models, Volatility and the Segmentation Hypothesis

53 Pages Posted: 2 Aug 2006

See all articles by Kris Jacobs

Kris Jacobs

University of Houston - C.T. Bauer College of Business

Lotfi Karoui

Goldman, Sachs & Co

Date Written: July 31, 2006

Abstract

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.

Keywords: term structure model, affine, conditional volatility, segmentation hypothesis, time series, cross section, EGARCH

JEL Classification: G12

Suggested Citation

Jacobs, Kris and Karoui, Lotfi, Affine Term Structure Models, Volatility and the Segmentation Hypothesis (July 31, 2006). Available at SSRN: https://ssrn.com/abstract=921744 or http://dx.doi.org/10.2139/ssrn.921744

Kris Jacobs (Contact Author)

University of Houston - C.T. Bauer College of Business ( email )

Houston, TX 77204-6021
United States

Lotfi Karoui

Goldman, Sachs & Co ( email )

1 New York Plaza
New York, NY 10004
United States

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