IDEAS home Printed from https://ideas.repec.org/a/gam/jjrfmx/v13y2020i11p287-d447859.html
   My bibliography  Save this article

A Hausman Test for Partially Linear Models with an Application to Implied Volatility Surface

Author

Listed:
  • Yixiao Jiang

    (Department of Economics, Christopher Newport University, Newport News, VA 23606, USA)

Abstract

This paper develops a test that helps assess whether the term structure of option implied volatility is constant across different levels of moneyness. The test is based on the Hausman principle of comparing two estimators, one that is efficient but not robust to the deviation being tested, and one that is robust but not as efficient. Distribution of the proposed test statistic is investigated in a general semiparametric setting via the multivariate Delta method. Using recent S&P 500 index traded options data from September 2009 to December 2018, we find that a partially linear model permitting a flexible “volatility smile” and an additive quadratic time effect is a statistically adequate depiction of the implied volatility data for most years. The constancy of implied volatility term structure, in turn, implies that option traders shall feel confident and execute volatility-based strategies using at-the-money options for its high liquidity.

Suggested Citation

  • Yixiao Jiang, 2020. "A Hausman Test for Partially Linear Models with an Application to Implied Volatility Surface," JRFM, MDPI, vol. 13(11), pages 1-12, November.
    • Handle: RePEc:gam:jjrfmx:v:13:y:2020:i:11:p:287-:d:447859
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1911-8074/13/11/287/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1911-8074/13/11/287/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    2. Wang, Wenju & Wang, Qiao, 2019. "Consistent specification test for partially linear models with the k-nearest-neighbor method," Economics Letters, Elsevier, vol. 177(C), pages 89-93.
    3. Daniel J. Henderson & Christopher F. Parmeter, 2015. "Single-Step Estimation of a Partially Linear Model," Working Papers 2015-01, University of Miami, Department of Economics.
    4. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    5. Ahn, Dong-Hyun & Dittmar, Robert F. & Gallant, A. Ronald & Gao, Bin, 2003. "Purebred or hybrid?: Reproducing the volatility in term structure dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 147-180.
    6. Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-890, July.
    7. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," The Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 243-288, March.
    8. Soku Byoun & Chuck C. Y. Kwok & Hun Y. Park, 2003. "Expectations Hypothesis of the Term Structure of Implied Volatility: Evidence from Foreign Currency and Stock Index Options," Journal of Financial Econometrics, Oxford University Press, vol. 1(1), pages 126-151.
    9. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    10. Philippe Jorion, 1988. "On Jump Processes in the Foreign Exchange and Stock Markets," The Review of Financial Studies, Society for Financial Studies, vol. 1(4), pages 427-445.
    11. Li, Q. & Wang, Suojin, 1998. "A simple consistent bootstrap test for a parametric regression function," Journal of Econometrics, Elsevier, vol. 87(1), pages 145-165, August.
    12. Jin E. Zhang & Jinghong Shu & Menachem Brenner, 2010. "The new market for volatility trading," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 30(9), pages 809-833, September.
    13. Whang, Yoon-Jae & Andrews, Donald W. K., 1993. "Tests of specification for parametric and semiparametric models," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 277-318.
    14. Egloff, Daniel & Leippold, Markus & Wu, Liuren, 2010. "The Term Structure of Variance Swap Rates and Optimal Variance Swap Investments," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(5), pages 1279-1310, October.
    15. Eric Renault & Nizar Touzi, 1996. "Option Hedging And Implied Volatilities In A Stochastic Volatility Model1," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 279-302, July.
    16. Campa, Jose Manuel & Chang, P H Kevin, 1995. "Testing the Expectations Hypothesis on the Term Structure of Volatilities in Foreign Exchange Options," Journal of Finance, American Finance Association, vol. 50(2), pages 529-547, June.
    17. Klein, Roger & Shen, Chan, 2010. "Bias Corrections In Testing And Estimating Semiparametric, Single Index Models," Econometric Theory, Cambridge University Press, vol. 26(6), pages 1683-1718, December.
    18. Ait-Sahalia, Yacine & Bickel, Peter J. & Stoker, Thomas M., 2001. "Goodness-of-fit tests for kernel regression with an application to option implied volatilities," Journal of Econometrics, Elsevier, vol. 105(2), pages 363-412, December.
    19. Zhongjin Lu & Yingzi Zhu, 2010. "Volatility components: The term structure dynamics of VIX futures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 30(3), pages 230-256, March.
    20. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    Full references (including those not matched with items on IDEAS)

    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. Fernandes, Marcelo & Grammig, Joachim, 2005. "Nonparametric specification tests for conditional duration models," Journal of Econometrics, Elsevier, vol. 127(1), pages 35-68, July.
    2. Matthias R. Fengler & Helmut Herwartz & Christian Werner, 2012. "A Dynamic Copula Approach to Recovering the Index Implied Volatility Skew," Journal of Financial Econometrics, Oxford University Press, vol. 10(3), pages 457-493, June.
    3. Gao, Jiti & King, Maxwell, 2003. "Estimation and model specification testing in nonparametric and semiparametric econometric models," MPRA Paper 11989, University Library of Munich, Germany, revised Feb 2006.
    4. Li, Qi & Hsiao, Cheng & Zinn, Joel, 2003. "Consistent specification tests for semiparametric/nonparametric models based on series estimation methods," Journal of Econometrics, Elsevier, vol. 112(2), pages 295-325, February.
    5. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    6. René Garcia & Eric Ghysels & Eric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.
    7. E Fe-Rodriguez & C D Orme, 2005. "The Asymptotic Equivalence of Kernel-based Nonparametric Conditional Moment Test Statistics," Economics Discussion Paper Series 0504, Economics, The University of Manchester.
    8. Gang Li & Chu Zhang, 2010. "On the Number of State Variables in Options Pricing," Management Science, INFORMS, vol. 56(11), pages 2058-2075, November.
    9. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    10. Jinhyun Lee, 2013. "A Consistent Nonparametric Bootstrap Test of Exogeneity," Discussion Paper Series, School of Economics and Finance 201316, School of Economics and Finance, University of St Andrews.
    11. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    12. Calvet, Laurent E. & Fisher, Adlai J., 2008. "Multifrequency jump-diffusions: An equilibrium approach," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 207-226, January.
    13. Hsiao, Cheng & Li, Qi & Racine, Jeffrey S., 2007. "A consistent model specification test with mixed discrete and continuous data," Journal of Econometrics, Elsevier, vol. 140(2), pages 802-826, October.
    14. Masamune Iwasawa, 2015. "A Joint Specification Test for Response Probabilities in Unordered Multinomial Choice Models," Econometrics, MDPI, vol. 3(3), pages 1-31, September.
    15. Capelle-Blancard, G. & Jurczenko, E., 1999. "Une application de la formule de Jarrow et Rudd aux options sur indice CAC 40," Papiers d'Economie Mathématique et Applications 2000.05, Université Panthéon-Sorbonne (Paris 1).
    16. Kottaridi, Constantina & Stengos, Thanasis, 2010. "Foreign direct investment, human capital and non-linearities in economic growth," Journal of Macroeconomics, Elsevier, vol. 32(3), pages 858-871, September.
    17. Yoo, Seung-Hoon & Yang, Chang-Young, 2000. "Dealing with bottled water expenditures data with zero observations: a semiparametric specification," Economics Letters, Elsevier, vol. 66(2), pages 151-157, February.
    18. T. Stengos & E. Zacharias, 2006. "Intertemporal pricing and price discrimination: a semiparametric hedonic analysis of the personal computer market," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 371-386, April.
    19. Gonçalo Faria & João Correia-da-Silva, 2014. "A closed-form solution for options with ambiguity about stochastic volatility," Review of Derivatives Research, Springer, vol. 17(2), pages 125-159, July.
    20. David S. Bates, 1995. "Testing Option Pricing Models," NBER Working Papers 5129, National Bureau of Economic Research, Inc.

    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:gam:jjrfmx:v:13:y:2020:i:11:p:287-:d:447859. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.