Do Bonds Span Volatility Risk in the U.S. Treasury Market? A Specification Test for Affine Term Structure Models

61 Pages Posted: 15 Mar 2006 Last revised: 25 Jun 2008

See all articles by Torben G. Andersen

Torben G. Andersen

Northwestern University - Kellogg School of Management; National Bureau of Economic Research (NBER); Aarhus University - CREATES

Luca Benzoni

Federal Reserve Bank of Chicago - Research Department

Multiple version iconThere are 2 versions of this paper

Date Written: May 23, 2008

Abstract

We investigate whether bonds span the volatility risk in the U.S. Treasury market, as predicted by most `affine' term structure models. To this end, we construct powerful and model-free empirical measures of the quadratic yield variation for a cross-section of fixed-maturity zero-coupon bonds (`realized yield volatility') through the use of high-frequency data. We find that the yield curve fails to span yield volatility, as the systematic volatility factors are largely unrelated to the cross-section of yields. We conclude that a broad class of affine diffusive, Gaussian-quadratic and affine jump-diffusive models is incapable of accommodating the observed yield volatility dynamics. An important implication is that the bond markets per se are incomplete and yield volatility risk cannot be hedged by taking positions solely in the Treasury bond market. We also advocate using the empirical realized yield volatility measures more broadly as a basis for specification testing and (parametric) model selection within the term structure literature.

Keywords: Interest Rate Volatility, Hedging, Volatility Risk, Unspanned Stochastic Volatility, Affine Models, Term Structure Models

JEL Classification: E43, G12

Suggested Citation

Andersen, Torben G. and Benzoni, Luca, Do Bonds Span Volatility Risk in the U.S. Treasury Market? A Specification Test for Affine Term Structure Models (May 23, 2008). AFA 2007 Chicago Meetings Paper; FRB of Chicago Working Paper No. 2006-15. Available at SSRN: https://ssrn.com/abstract=853105 or http://dx.doi.org/10.2139/ssrn.853105

Torben G. Andersen

Northwestern University - Kellogg School of Management ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Aarhus University - CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Luca Benzoni (Contact Author)

Federal Reserve Bank of Chicago - Research Department ( email )

230 South LaSalle Street
Chicago, IL 60604
United States
312-322-8499 (Phone)

HOME PAGE: http://lbenzoni.frbchi.googlepages.com/

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