TY - JOUR

T1 - Can interest rate volatility be extracted from the cross section of bond yields?

AU - Collin-Dufresne, Pierre

AU - Goldstein, Robert S.

AU - Jones, Christopher S.

PY - 2009/10

Y1 - 2009/10

N2 - Most affine models of the term structure with stochastic volatility predict that the variance of the short rate should play a 'dual role' in that it should also equal a linear combination of yields. However, we find that estimation of a standard affine three-factor model results in a variance state variable that, while instrumental in explaining the shape of the yield curve, is essentially unrelated to GARCH estimates of the quadratic variation of the spot rate process or to implied variances from options. We then investigate four-factor affine models. Of the models tested, only the model that exhibits 'unspanned stochastic volatility' (USV) generates both realistic short rate volatility estimates and a good cross-sectional fit. Our findings suggest that short rate volatility cannot be extracted from the cross-section of bond prices. In particular, short rate volatility and convexity are only weakly correlated.

AB - Most affine models of the term structure with stochastic volatility predict that the variance of the short rate should play a 'dual role' in that it should also equal a linear combination of yields. However, we find that estimation of a standard affine three-factor model results in a variance state variable that, while instrumental in explaining the shape of the yield curve, is essentially unrelated to GARCH estimates of the quadratic variation of the spot rate process or to implied variances from options. We then investigate four-factor affine models. Of the models tested, only the model that exhibits 'unspanned stochastic volatility' (USV) generates both realistic short rate volatility estimates and a good cross-sectional fit. Our findings suggest that short rate volatility cannot be extracted from the cross-section of bond prices. In particular, short rate volatility and convexity are only weakly correlated.

KW - Affine models

KW - Stochastic volatility

KW - Term structure of interest rates

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U2 - 10.1016/j.jfineco.2008.06.007

DO - 10.1016/j.jfineco.2008.06.007

M3 - Article

AN - SCOPUS:70049109228

SN - 0304-405X

VL - 94

SP - 47

EP - 66

JO - Journal of Financial Economics

JF - Journal of Financial Economics

IS - 1

ER -