Can Interest Rate Volatility be Extracted from the Cross Section of Bond Yields? An Investigation of Unspanned Stochastic Volatility
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.
|Date of creation:||Sep 2004|
|Publication status:||published as Collin-Dufresne, Pierre & Goldstein, Robert S. & Jones, Christopher S., 2009. "Can interest rate volatility be extracted from the cross section of bond yields?," Journal of Financial Economics, Elsevier, vol. 94(1), pages 47-66, October.|
|Contact details of provider:|| Postal: National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.|
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- Pennacchi, George G, 1991. "Identifying the Dynamics of Real Interest Rates and Inflation: Evidence Using Survey Data," Review of Financial Studies, Society for Financial Studies, vol. 4(1), pages 53-86.
- Fama, Eugene F & Bliss, Robert R, 1987. "The Information in Long-Maturity Forward Rates," American Economic Review, American Economic Association, vol. 77(4), pages 680-92, September.
- Aït-Sahalia, Yacine & Kimmel, Robert L., 2010.
"Estimating affine multifactor term structure models using closed-form likelihood expansions,"
Journal of Financial Economics,
Elsevier, vol. 98(1), pages 113-144, October.
- Yacine Aït-Sahalia & Robert Kimmel, 2002. "Estimating Affine Multifactor Term Structure Models Using Closed-Form Likelihood Expansions," NBER Technical Working Papers 0286, National Bureau of Economic Research, Inc.
- Ait-Sahalia, Yacine & Kimmel, Robert L., 2008. "Estimating Affine Multifactor Term Structure Models Using Closed-Form Likelihood Expansions," Working Paper Series 2008-19, Ohio State University, Charles A. Dice Center for Research in Financial Economics.
- Whitney K. Newey & Kenneth D. West, 1986.
"A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix,"
NBER Technical Working Papers
0055, National Bureau of Economic Research, Inc.
- Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May.
- Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
- Duarte, Jefferson., 2003. "Evaluating an Alternative Risk Preference in Affine Term Structure Models," Finance Lab Working Papers flwp_49, Finance Lab, Insper Instituto de Ensino e Pesquisa.
- Duan, Jin-Chuan & Simonato, Jean-Guy, 1999.
"Estimating and Testing Exponential-Affine Term Structure Models by Kalman Filter,"
Review of Quantitative Finance and Accounting,
Springer, vol. 13(2), pages 111-35, September.
- Jin-Chuan Duan & Jean-Guy Simonato, 1995. "Estimating and Testing Exponential Affine Term Structure Models by Kalman Filter," CIRANO Working Papers 95s-44, CIRANO.
- Siem Jan Koopman & Neil Shephard, 2002. "Testing the Assumptions Behind the Use of Importance Sampling," Economics Papers 2002-W17, Economics Group, Nuffield College, University of Oxford.
- Shiller, Robert & Campbell, John, 1991.
"Yield Spreads and Interest Rate Movements: A Bird's Eye View,"
3221490, Harvard University Department of Economics.
- John Y. Campbell & Robert J. Shiller, 1991. "Yield Spreads and Interest Rate Movements: A Bird's Eye View," Review of Economic Studies, Oxford University Press, vol. 58(3), pages 495-514.
- John Y. Campbell & Robert J. Shiller, 1989. "Yield Spreads and Interest Rate Movements: A Bird's Eye View," NBER Working Papers 3153, National Bureau of Economic Research, Inc.
- Torben G. Andersen & Luca Benzoni, 2009.
Working Paper Series
WP-09-04, Federal Reserve Bank of Chicago.
- Richard, Jean-Francois & Zhang, Wei, 1996. "Econometric Modelling of UK House Prices Using Accelerated Importance Sampling," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(4), pages 601-13, November.
- Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, 02.
- Kenneth J. Singleton & Len Umantsev, 2002. "Pricing Coupon-Bond Options And Swaptions In Affine Term Structure Models," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 427-446.
- Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Univariate and multivariate stochastic volatility models: estimation and diagnostics," Journal of Empirical Finance, Elsevier, vol. 10(4), pages 505-531, September.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
- Bollerslev, Tim, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
Journal of Econometrics,
Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Duffie, Darrell & Singleton, Kenneth J, 1997. " An Econometric Model of the Term Structure of Interest-Rate Swap Yields," Journal of Finance, American Finance Association, vol. 52(4), pages 1287-1321, September.
- Sandmann, Gleb & Koopman, Siem Jan, 1998. "Estimation of stochastic volatility models via Monte Carlo maximum likelihood," Journal of Econometrics, Elsevier, vol. 87(2), pages 271-301, September.
- Kenneth D. West & Whitney K. Newey, 1995.
"Automatic Lag Selection in Covariance Matrix Estimation,"
NBER Technical Working Papers
0144, National Bureau of Economic Research, Inc.
- Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," Review of Economic Studies, Oxford University Press, vol. 61(4), pages 631-653.
- Newey, W.K. & West, K.D., 1992. "Automatic Lag Selection in Covariance Matrix Estimation," Working papers 9220, Wisconsin Madison - Social Systems.
- Qiang Dai & Kenneth Singleton, 2003. "Term Structure Dynamics in Theory and Reality," Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 631-678, July.
- Diebold, Francis X & Mariano, Roberto S, 2002.
"Comparing Predictive Accuracy,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 20(1), pages 134-144, January.
- Jin, Yan & Glasserman, Paul, 2001. "Equilibrium Positive Interest Rates: A Unified View," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 187-214.
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