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

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Author Info
Pierre Collin-Dufresne (Carnegie Mellon University,)
Robert S. Goldstein (Washington University, St. Louis)
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. Copyright The American Finance Association 2002.

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Article provided by American Finance Association in its journal The Journal of Finance.

Volume (Year): 57 (2002)
Issue (Month): 4 (08)
Pages: 1685-1730
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Handle: RePEc:bla:jfinan:v:57:y:2002:i:4:p:1685-1730

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  1. Christiansen, Charlotte & Lund, Jesper, 2002. "Revisiting the shape of the yield curve: the effect of interest rate volatility," Finance Working Papers 02-3, University of Aarhus, Aarhus School of Business, Department of Business Studies. [Downloadable!]
  2. Don H. Kim, 2009. "Challenges in macro-finance modeling," Review, Federal Reserve Bank of St. Louis, issue Sep, pages 519-544. [Downloadable!]
  3. 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. [Downloadable!]
  4. Anders B. Trolle & Eduardo S. Schwartz, 2006. "A General Stochastic Volatility Model for the Pricing and Forecasting of Interest Rate Derivatives," NBER Working Papers 12337, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  5. Jensen, Malene Shin & Svenstrup, Mikkel, 2002. "Efficient Control Variates and Strategies for Bermudan Swaptions in a Libor Market Model," Finance Working Papers 02-23, University of Aarhus, Aarhus School of Business, Department of Business Studies. [Downloadable!]
  6. Torben G. Andersen & Luca Benzoni, 2007. "Do Bonds Span Volatility Risk in the U.S. Treasury Market? A Specification Test for Affine Term Structure Models," CREATES Research Papers 2007-25, School of Economics and Management, University of Aarhus. [Downloadable!]
    Other versions:
  7. Svenstrup, Mikkel, 2003. "On the Suboptimality of Single-Factor Exercise Strategies for Bermudan Swaptions," Finance Working Papers 02-24, University of Aarhus, Aarhus School of Business, Department of Business Studies. [Downloadable!]
  8. Don Kim, 2008. "Challenges in macro-finance modeling," Finance and Economics Discussion Series 2008-06, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  9. Stefania D'Amico & Don H. Kim & Min Wei, 2008. "Tips from TIPS: the informational content of Treasury Inflation-Protected Security prices," Finance and Economics Discussion Series 2008-30, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  10. Georg Mosburger & Paul Schneider, 2005. "Modelling International Bond Markets with Affine Term Structure Models," Finance 0509003, EconWPA. [Downloadable!]
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