IDEAS home Printed from https://ideas.repec.org/a/eee/jbfina/v122y2021ics0378426620302557.html
   My bibliography  Save this article

Unspanned stochastic volatility from an empirical and practical perspective

Author

Listed:
  • Backwell, Alex

Abstract

I conduct a simulation study to address concerns raised in the empirical literature on unspanned stochastic volatility (USV, i.e., interest-rate-volatility risk that cannot be hedged with bonds or swaps). Regressions have been the popular method of identifying and measuring USV, and have led to a consensus that is in favour of USV models. Despite plausible challenges to this approach, my simulations show that regressions are able to correctly identify the presence and absence of USV. This relies on a number of methodological considerations which are inconsistent in the literature. Regression results from empirical data, from several modern interest-rate markets, resemble results from data simulated from USV models. I then assess the economic significance of USV. By comparing hedged and unhedged returns of market interest-rate options, I develop quantitative guidelines around how unspanned volatility risk compares to interest-rate risk.

Suggested Citation

  • Backwell, Alex, 2021. "Unspanned stochastic volatility from an empirical and practical perspective," Journal of Banking & Finance, Elsevier, vol. 122(C).
    • Handle: RePEc:eee:jbfina:v:122:y:2021:i:c:s0378426620302557
    DOI: 10.1016/j.jbankfin.2020.105993
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378426620302557
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jbankfin.2020.105993?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Haitao Li & Feng Zhao, 2009. "Nonparametric Estimation of State-Price Densities Implicit in Interest Rate Cap Prices," The Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4335-4376, November.
    5. 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, February.
    6. Driessen, Joost & Klaassen, Pieter & Melenberg, Bertrand, 2003. "The Performance of Multi-Factor Term Structure Models for Pricing and Hedging Caps and Swaptions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(3), pages 635-672, September.
    7. Robert Jarrow & Haitao Li & Feng Zhao, 2007. "Interest Rate Caps “Smile” Too! But Can the LIBOR Market Models Capture the Smile?," Journal of Finance, American Finance Association, vol. 62(1), pages 345-382, February.
    8. Roger Lord & Remmert Koekkoek & Dick Van Dijk, 2010. "A comparison of biased simulation schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 177-194.
    9. Scott Joslin & Marcel Priebsch & Kenneth J. Singleton, 2014. "Risk Premiums in Dynamic Term Structure Models with Unspanned Macro Risks," Journal of Finance, American Finance Association, vol. 69(3), pages 1197-1233, June.
    10. 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.
    11. Torben G. Andersen & Luca Benzoni, 2010. "Do Bonds Span Volatility Risk in the U.S. Treasury Market? A Specification Test for Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 65(2), pages 603-653, April.
    12. Damir Filipović & Martin Larsson & Francesco Statti, 2019. "Unspanned stochastic volatility in the multifactor CIR model," Mathematical Finance, Wiley Blackwell, vol. 29(3), pages 827-836, July.
    13. 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.
    14. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    15. Anders B. Trolle & Eduardo S. Schwartz, 2009. "A General Stochastic Volatility Model for the Pricing of Interest Rate Derivatives," The Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 2007-2057, May.
    16. Gupta, Anurag & Subrahmanyam, Marti G., 2005. "Pricing and hedging interest rate options: Evidence from cap-floor markets," Journal of Banking & Finance, Elsevier, vol. 29(3), pages 701-733, March.
    17. 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, February.
    18. Damir Filipović & Martin Larsson & Anders B. Trolle, 2017. "Linear-Rational Term Structure Models," Journal of Finance, American Finance Association, vol. 72(2), pages 655-704, April.
    19. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. Peter Feldhütter & Christian Heyerdahl-Larsen & Philipp Illeditsch, 2018. "Risk Premia and Volatilities in a Nonlinear Term Structure Model [Quadratic term structure models: theory and evidence]," Review of Finance, European Finance Association, vol. 22(1), pages 337-380.
    3. Joslin, Scott & Konchitchki, Yaniv, 2018. "Interest rate volatility, the yield curve, and the macroeconomy," Journal of Financial Economics, Elsevier, vol. 128(2), pages 344-362.
    4. 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.
    5. Hideyuki Takamizawa, 2015. "Predicting Interest Rate Volatility Using Information on the Yield Curve," International Review of Finance, International Review of Finance Ltd., vol. 15(3), pages 347-386, September.
    6. 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).
    7. Scott Joslin, 2018. "Can Unspanned Stochastic Volatility Models Explain the Cross Section of Bond Volatilities?," Management Science, INFORMS, vol. 64(4), pages 1707-1726, April.
    8. Haitao Li & Feng Zhao, 2009. "Nonparametric Estimation of State-Price Densities Implicit in Interest Rate Cap Prices," The Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4335-4376, November.
    9. Bruno Feunou & Jean-Sébastien Fontaine & Anh Le & Christian Lundblad, 2022. "Tractable Term Structure Models," Management Science, INFORMS, vol. 68(11), pages 8411-8429, November.
    10. Creal, Drew D. & Wu, Jing Cynthia, 2015. "Estimation of affine term structure models with spanned or unspanned stochastic volatility," Journal of Econometrics, Elsevier, vol. 185(1), pages 60-81.
    11. Anders B. Trolle & Eduardo S. Schwartz, 2009. "A General Stochastic Volatility Model for the Pricing of Interest Rate Derivatives," The Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 2007-2057, May.
    12. 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.
    13. 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.
    14. 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.
    15. Kwai S. Leung & Hon Y. Ng & Hoi Y. Wong, 2014. "Stochastic Skew in the Interest Rate Cap Market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(12), pages 1146-1169, December.
    16. Anna Cieslak & Pavol Povala, 2016. "Information in the Term Structure of Yield Curve Volatility," Journal of Finance, American Finance Association, vol. 71(3), pages 1393-1436, June.
    17. Monfort, Alain & Pegoraro, Fulvio & Renne, Jean-Paul & Roussellet, Guillaume, 2017. "Staying at zero with affine processes: An application to term structure modelling," Journal of Econometrics, Elsevier, vol. 201(2), pages 348-366.
    18. 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.
    19. 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.
    20. 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.

    More about this item

    Keywords

    Interest-rate volatility; Unspanned stochastic volatility; Volatility risk; Hedging; Market incompleteness; Term structure models;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jbfina:v:122:y:2021:i:c:s0378426620302557. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jbf .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.