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Unspanned Stochastic Volatility in Affine Models: Evidence from Eurodollar Futures and Options

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  • Ruslan Bikbov

    (Federal Reserve Board, Washington, DC 20551)

  • Mikhail Chernov

    (London Business School and CEPR, London NW1 4SA, United Kingdom)

Abstract

Unspanned stochastic volatility (USV) refers to the inability of bonds to replicate volatility-sensitive derivative securities. Affine term structure models require special restrictions on the parameters to exhibit USV. We use a joint Eurodollar futures and options data set to estimate affine three-factor models with and without USV restrictions. The unrestricted model captures prices of futures and options well. Option pricing errors are much larger in the USV model. The USV model is rejected in favor of the unrestricted model based on the likelihood ratio and Wald tests. We use the implications of the unrestricted model as a benchmark for understanding the extant evidence that favors USV. Specifically, we replicate extant tests in samples simulated from the unrestricted model. We show that none of the existing findings contradict the model without USV restrictions.

Suggested Citation

  • Ruslan Bikbov & Mikhail Chernov, 2009. "Unspanned Stochastic Volatility in Affine Models: Evidence from Eurodollar Futures and Options," Management Science, INFORMS, vol. 55(8), pages 1292-1305, August.
    • Handle: RePEc:inm:ormnsc:v:55:y:2009:i:8:p:1292-1305
    DOI: 10.1287/mnsc.1090.1020
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    3. Hideyuki Takamizawa, 2018. "A term structure model of interest rates with quadratic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 18(7), pages 1173-1198, July.
    4. Backwell, Alex, 2021. "Unspanned stochastic volatility from an empirical and practical perspective," Journal of Banking & Finance, Elsevier, vol. 122(C).
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    6. Drew D. Creal & Jing Cynthia Wu, 2017. "Monetary Policy Uncertainty And Economic Fluctuations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 58(4), pages 1317-1354, November.
    7. Yuecai Han & Fengtong Zhang, 2024. "Pricing fixed income derivatives under a three-factor CIR model with unspanned stochastic volatility," Review of Derivatives Research, Springer, vol. 27(1), pages 37-53, April.
    8. Bakshi, Gurdip & Crosby, John & Gao, Xiaohui & Hansen, Jorge W., 2023. "Treasury option returns and models with unspanned risks," Journal of Financial Economics, Elsevier, vol. 150(3).
    9. Michael D. Bauer & Glenn D. Rudebusch, 2017. "Resolving the Spanning Puzzle in Macro-Finance Term Structure Models," Review of Finance, European Finance Association, vol. 21(2), pages 511-553.
    10. Michael D Bauer & Aeimit Lakdawala & Philippe Mueller, 2022. "Market-Based Monetary Policy Uncertainty," The Economic Journal, Royal Economic Society, vol. 132(644), pages 1290-1308.
    11. Christensen, Bent Jesper & Kjær, Mads Markvart & Veliyev, Bezirgen, 2023. "The incremental information in the yield curve about future interest rate risk," Journal of Banking & Finance, Elsevier, vol. 155(C).
    12. Mueller, Philippe & Vedolin, Andrea & Yen, Yu-Min, 2012. "Bond variance risk premia," LSE Research Online Documents on Economics 119053, London School of Economics and Political Science, LSE Library.
    13. Sarno, Lucio & Schneider, Paul & Wagner, Christian, 2012. "Properties of foreign exchange risk premiums," Journal of Financial Economics, Elsevier, vol. 105(2), pages 279-310.
    14. Stefano Giglio & Bryan Kelly, 2018. "Excess Volatility: Beyond Discount Rates," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(1), pages 71-127.
    15. Park, Yang-Ho, 2016. "The effects of asymmetric volatility and jumps on the pricing of VIX derivatives," Journal of Econometrics, Elsevier, vol. 192(1), pages 313-328.
    16. 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.
    17. Peter Christoffersen & Christian Dorion & Kris Jacobs & Lotfi Karoui, 2014. "Nonlinear Kalman Filtering in Affine Term Structure Models," Management Science, INFORMS, vol. 60(9), pages 2248-2268, September.
    18. Ho, Hsiao-Wei & Huang, Henry H. & Yildirim, Yildiray, 2014. "Affine model of inflation-indexed derivatives and inflation risk premium," European Journal of Operational Research, Elsevier, vol. 235(1), pages 159-169.
    19. Scott Joslin & Anh Le, 2021. "Interest Rate Volatility and No-Arbitrage Affine Term Structure Models," Management Science, INFORMS, vol. 67(12), pages 7391-7416, December.
    20. Jens H. E. Christensen & Jose A. Lopez & Glenn D. Rudebusch, 2014. "Can Spanned Term Structure Factors Drive Stochastic Yield Volatility?," Working Paper Series 2014-3, Federal Reserve Bank of San Francisco.
    21. Yang-Ho Park, 2015. "The Effects of Asymmetric Volatility and Jumps on the Pricing of VIX Derivatives," Finance and Economics Discussion Series 2015-71, Board of Governors of the Federal Reserve System (U.S.).

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