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

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  • Pierre Collin-Dufresne
  • Christopher S. Jones
  • Robert S. Goldstein

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

  • Pierre Collin-Dufresne & Christopher S. Jones & Robert S. Goldstein, 2004. "Can Interest Rate Volatility be Extracted from the Cross Section of Bond Yields? An Investigation of Unspanned Stochastic Volatility," NBER Working Papers 10756, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:10756
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    References listed on IDEAS

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    Cited by:

    1. Shu Wu, 2007. "Interest Rate Risk and the Forward Premium Anomaly in Foreign Exchange Markets," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(2-3), pages 423-442, March.
    2. Ahmet Can Ýnci, 2007. "Currency and yield Co-integration between a developed and an emerging Country: The Case of Turkey," Bogazici Journal, Review of Social, Economic and Administrative Studies, Bogazici University, Department of Economics, vol. 21(1+2), pages 1-20.
    3. Torben G. Andersen & Luca Benzoni, 2010. "Do Bonds Span Volatility Risk in the U.S. Treasury Market? A Specification Test for Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 65(2), pages 603-653, April.
    4. Don H Kim, 2007. "Spanned stochastic volatility in bond markets: a reexamination of the relative pricing between bonds and bond options," BIS Working Papers 239, Bank for International Settlements.
    5. Balázs Romhányi, 2005. "A learning hypothesis of the term structure of interest rates," Macroeconomics 0503001, EconWPA.

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    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics

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