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Do Bonds Span the Fixed Income Markets? Theory and Evidence for Unspanned Stochastic Volatility

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  • Pierre Collin‐Dufresne
  • Robert S. Goldstein

Abstract

Most term structure models assume bond markets are complete, that is, that all fixed income derivatives can be perfectly replicated using solely bonds. How ever, we find that, in practice, swap rates have limited explanatory power for returns on at‐the‐money straddles—portfolios mainly exposed to volatility risk. We term this empirical feature unspanned stochastic volatility (USV). While USV can be captured within an HJM framework, we demonstrate that bivariate models cannot exhibit USV. We determine necessary and sufficient conditions for trivariate Markov affine systems to exhibit USV. For such USV models, bonds alone may not be sufficient to identify all parameters. Rather, derivatives are needed.

Suggested Citation

  • Pierre Collin‐Dufresne & Robert S. Goldstein, 2002. "Do Bonds Span the Fixed Income Markets? Theory and Evidence for Unspanned Stochastic Volatility," Journal of Finance, American Finance Association, vol. 57(4), pages 1685-1730, August.
    • Handle: RePEc:bla:jfinan:v:57:y:2002:i:4:p:1685-1730
    DOI: 10.1111/1540-6261.00475
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