Can Interest Rate Volatility Be Extracted from the Cross Section of Bond Yields? an Investigation of Unspanned Stochastic Volatility

76 Pages Posted: 1 Jun 2006

See all articles by Pierre Collin-Dufresne

Pierre Collin-Dufresne

Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute; National Bureau of Economic Research (NBER)

Robert S. Goldstein

University of Minnesota - Twin Cities - Carlson School of Management; National Bureau of Economic Research (NBER)

Christopher S. Jones

University of Southern California - Marshall School of Business - Finance and Business Economics Department

Date Written: September 2004

Abstract

Most affine models of the term structure with stochastic volatility (SV) predict that the variance of the short rate is simultaneously a linear combination of yields and the quadratic variation of the spot rate. However, we find empirically that the A1(3) SV model generates a time series for the variance state variable that is strongly negatively correlated with a GARCH estimate of the quadratic variation of the spot rate process. We then investigate affine models that exhibit "unspanned stochastic volatility (USV)." Of the models tested, only the A1(4) USV model is found to generate both realistic volatility estimates and a good cross-sectional fit. Our findings suggests that interest rate volatility cannot be extracted from the cross-section of bond prices. Separately, we propose an alternative to the canonical representation of affine models introduced by Dai and Singleton (2001). This representation has several advantages, including: (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 econometrically identifiable, (iv) model-insensitive estimates of the state vector process implied from the term structure are readily available, and (v) it isolates those parameters which are not identifiable from bond prices alone if the model is specified to exhibit USV.

Suggested Citation

Collin-Dufresne, Pierre and Goldstein, Robert S. and Jones, Christopher S., Can Interest Rate Volatility Be Extracted from the Cross Section of Bond Yields? an Investigation of Unspanned Stochastic Volatility (September 2004). NBER Working Paper No. w10756. Available at SSRN: https://ssrn.com/abstract=590768

Pierre Collin-Dufresne (Contact Author)

Ecole Polytechnique Fédérale de Lausanne ( email )

Quartier UNIL-Dorigny, Bâtiment Extranef, # 211
40, Bd du Pont-d'Arve
CH-1015 Lausanne, CH-6900
Switzerland

Swiss Finance Institute

c/o University of Geneva
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Switzerland

National Bureau of Economic Research (NBER)

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Cambridge, MA 02138
United States

Robert S. Goldstein

University of Minnesota - Twin Cities - Carlson School of Management ( email )

19th Avenue South
Minneapolis, MN 55455
United States
612-624-8581 (Phone)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Christopher S. Jones

University of Southern California - Marshall School of Business - Finance and Business Economics Department ( email )

Marshall School of Business
Los Angeles, CA 90089
United States

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