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Spanned stochastic volatility in bond markets: a reexamination of the relative pricing between bonds and bond options

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  • Don H Kim
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    Abstract

    This paper reexamines the issue of unspanned stochastic volatility (USV) in bond markets and the puzzle of poor relative pricing between bonds and bond options. I make a distinction between the "weak USV" and the "strong USV" scenarios, and analyze the evidence for each of them. I argue that the poor bonds/options relative pricing in the extant literature is not necessarily evidence for the strong USV scenario, and show that a maximally flexible 2-factor quadratic-Gaussian model (a non-USV model) estimated without bond options data can capture much of the movement in bond option prices. Dropping the positive-definiteness requirement for nominal interest rates and adopting "regularized" estimations turn out to be important for obtaining sensible results.

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    Bibliographic Info

    Paper provided by Bank for International Settlements in its series BIS Working Papers with number 239.

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    Length: 40 pages
    Date of creation: Dec 2007
    Date of revision:
    Handle: RePEc:bis:biswps:239

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    Related research

    Keywords: term structure of interest rates; unspanned stochastic volatility; relative pricing; interest rate derivatives;

    References

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    1. David Backus & Jonathan H. Wright, 2007. "Cracking the conundrum," Finance and Economics Discussion Series 2007-46, Board of Governors of the Federal Reserve System (U.S.).
    2. Ravi Jagannathan & Andrew Kaplin & Steve Guoqiang Sun, 2001. "An Evaluation of Multi-Factor CIR Models Using LIBOR, Swap Rates, and Cap and Swaption Prices," NBER Working Papers 8682, National Bureau of Economic Research, Inc.
    3. Charles M. Jones & Owen Lamont & Robin L. Lumsdaine, . "Macroeconomic News and Bond Market Volatility," CRSP working papers 333, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
    4. Backus, David & Foresi, Silverio & Mozumdar, Abon & Wu, Liuren, 2001. "Predictable changes in yields and forward rates," Journal of Financial Economics, Elsevier, vol. 59(3), pages 281-311, March.
    5. Markus Leippold & Liuren Wu, 2002. "Asset Pricing Under The Quadratic Class," Finance 0207015, EconWPA.
    6. Michael J. Fleming & Eli M. Remolona, 1997. "What moves the bond market?," Economic Policy Review, Federal Reserve Bank of New York, issue Dec, pages 31-50.
    7. Nicholas Economides, 2007. "Nonbanks in the Payments System: Vertical Integration Issues," Working Papers 07-06, NET Institute.
    8. Caio Almeida & Jeremy J. Graveline & Scott Joslin, 2005. "Do Options Contain Information About Excess Bond Returns?," IBMEC RJ Economics Discussion Papers 2005-04, Economics Research Group, IBMEC Business School - Rio de Janeiro.
    9. Don H. Kim & Athanasios Orphanides, 2005. "Term structure estimation with survey data on interest rate forecasts," Finance and Economics Discussion Series 2005-48, Board of Governors of the Federal Reserve System (U.S.).
    10. 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, 08.
    11. David H. Cutler & James M. Poterba & Lawrence H. Summers, 1988. "What Moves Stock Prices?," Working papers 487, Massachusetts Institute of Technology (MIT), Department of Economics.
    12. Markus Leippold & Liuren Wu, 2002. "Design and Estimation of Quadratic Term Structure Models," Finance 0207014, EconWPA.
    13. Torben G. Andersen & Luca Benzoni, 2006. "Do bonds span volatility risk in the U.S. Treasury market? a specification test for affine term structure models," Working Paper Series WP-06-15, Federal Reserve Bank of Chicago.
    14. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 243-288, March.
    15. Haitao Li & Feng Zhao, 2006. "Unspanned Stochastic Volatility: Evidence from Hedging Interest Rate Derivatives," Journal of Finance, American Finance Association, vol. 61(1), pages 341-378, 02.
    16. Black, Fischer, 1995. " Interest Rates as Options," Journal of Finance, American Finance Association, vol. 50(5), pages 1371-76, December.
    17. Rong Fan & Anurag Gupta & Peter Ritchken, 2003. "Hedging in the Possible Presence of Unspanned Stochastic Volatility: Evidence from Swaption Markets," Journal of Finance, American Finance Association, vol. 58(5), pages 2219-2248, October.
    18. 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.
    19. 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.
    20. Don H Kim & Athanasios Orphanides, 2007. "The bond market term premium: what is it, and how can we measure it?," BIS Quarterly Review, Bank for International Settlements, June.
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    Citations

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    Cited by:
    1. Stefania D'Amico & Don H Kim & Min Wei, 2008. "Tips from TIPS: the informational content of Treasury Inflation-Protected Security prices," BIS Working Papers 248, Bank for International Settlements.
    2. Andreasen, Martin & Meldrum, Andrew, 2013. "Likelihood inference in non-linear term structure models: the importance of the lower bound," Bank of England working papers 481, Bank of England.
    3. Almeida, Caio & Graveline, Jeremy J. & Joslin, Scott, 2011. "Do interest rate options contain information about excess returns?," Journal of Econometrics, Elsevier, vol. 164(1), pages 35-44, September.

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