IDEAS home Printed from https://ideas.repec.org/p/mtl/montec/09-2015.html
   My bibliography  Save this paper

Nonparametric Estimation of the Leverage Effect : A Trade-off between Robustness and Efficiency

Author

Listed:
  • Ilze KALNINA
  • Dacheng XIU

Abstract

We consider two new approaches to nonparametric estimation of the leverage effect. The first approach uses stock prices alone. The second approach uses the data on stock prices as well as a certain volatility instrument, such as the CBOE volatility index (VIX) or the Black-Scholes implied volatility. The theoretical justification for the instrument-based estimator relies on a certain invariance property, which can be exploited when high frequency data is available. The price-only estimator is more robust since it is valid under weaker assumptions. However, in the presence of a valid volatility instrument, the price-only estimator is inefficient as the instrument-based estimator has a faster rate of convergence. We consider two empirical applications, in which we study the relationship between the leverage effect and the debt-to-equity ratio, credit risk, and illiquidity.

Suggested Citation

  • Ilze KALNINA & Dacheng XIU, 2015. "Nonparametric Estimation of the Leverage Effect : A Trade-off between Robustness and Efficiency," Cahiers de recherche 09-2015, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    • Handle: RePEc:mtl:montec:09-2015
    as

    Download full text from publisher

    File URL: http://www.cireqmontreal.com/wp-content/uploads/cahiers/09-2015-cah.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Wu, De-Min, 1973. "Alternative Tests of Independence Between Stochastic Regressors and Disturbances," Econometrica, Econometric Society, vol. 41(4), pages 733-750, July.
    2. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well," Management Science, INFORMS, vol. 55(12), pages 1914-1932, December.
    3. Segal, Gill & Shaliastovich, Ivan & Yaron, Amir, 2015. "Good and bad uncertainty: Macroeconomic and financial market implications," Journal of Financial Economics, Elsevier, vol. 117(2), pages 369-397.
    4. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 345-382, July.
    5. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    6. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
    7. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous‐time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323, October.
    8. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    9. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    10. Yacine Aït-Sahalia & Jean Jacod, 2012. "Analyzing the Spectrum of Asset Returns: Jump and Volatility Components in High Frequency Data," Journal of Economic Literature, American Economic Association, vol. 50(4), pages 1007-1050, December.
    11. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    12. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 1-37.
    13. Mencía, Javier & Sentana, Enrique, 2013. "Valuation of VIX derivatives," Journal of Financial Economics, Elsevier, vol. 108(2), pages 367-391.
    14. Christie, Andrew A., 1982. "The stochastic behavior of common stock variances : Value, leverage and interest rate effects," Journal of Financial Economics, Elsevier, vol. 10(4), pages 407-432, December.
    15. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
    16. Tim Bollerslev & Natalia Sizova & George Tauchen, 2011. "Volatility in Equilibrium: Asymmetries and Dynamic Dependencies," Review of Finance, European Finance Association, vol. 16(1), pages 31-80.
    17. Amihud, Yakov, 2002. "Illiquidity and stock returns: cross-section and time-series effects," Journal of Financial Markets, Elsevier, vol. 5(1), pages 31-56, January.
    18. Aït-Sahalia, Yacine & Fan, Jianqing & Li, Yingying, 2013. "The leverage effect puzzle: Disentangling sources of bias at high frequency," Journal of Financial Economics, Elsevier, vol. 109(1), pages 224-249.
    19. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
    20. Bollerslev, Tim & Li, Sophia Zhengzi & Todorov, Viktor, 2016. "Roughing up beta: Continuous versus discontinuous betas and the cross section of expected stock returns," Journal of Financial Economics, Elsevier, vol. 120(3), pages 464-490.
    21. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    22. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2005. "Correcting the Errors: Volatility Forecast Evaluation Using High-Frequency Data and Realized Volatilities," Econometrica, Econometric Society, vol. 73(1), pages 279-296, January.
    23. Christina D. Wang & Per A. Mykland, 2014. "The Estimation of Leverage Effect With High-Frequency Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 197-215, March.
    24. Bjørn Eraker, 2004. "Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices," Journal of Finance, American Finance Association, vol. 59(3), pages 1367-1404, June.
    25. Andrew J. Patton & Michela Verardo, 2012. "Does Beta Move with News? Firm-Specific Information Flows and Learning about Profitability," Review of Financial Studies, Society for Financial Studies, vol. 25(9), pages 2789-2839.
    26. Bandi, Federico M. & Renò, Roberto, 2012. "Time-varying leverage effects," Journal of Econometrics, Elsevier, vol. 169(1), pages 94-113.
    27. Michael Pitt & Sheheryar Malik & Arnaud Doucet, 2014. "Simulated likelihood inference for stochastic volatility models using continuous particle filtering," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(3), pages 527-552, June.
    28. Andersen, Torben G. & Fusari, Nicola & Todorov, Viktor, 2015. "The risk premia embedded in index options," Journal of Financial Economics, Elsevier, vol. 117(3), pages 558-584.
    29. 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.
    30. Mathias Vetter, 2012. "Estimation of Correlation for Continuous Semimartingales," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(4), pages 757-771, December.
    31. Tim Bollerslev & Julia Litvinova & George Tauchen, 2006. "Leverage and Volatility Feedback Effects in High-Frequency Data," Journal of Financial Econometrics, Oxford University Press, vol. 4(3), pages 353-384.
    32. Jacquier, Eric & Polson, Nicholas G. & Rossi, P.E.Peter E., 2004. "Bayesian analysis of stochastic volatility models with fat-tails and correlated errors," Journal of Econometrics, Elsevier, vol. 122(1), pages 185-212, September.
    33. Peter Carr & Liuren Wu, 2009. "Variance Risk Premiums," Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 1311-1341, March.
    34. Song, Zhaogang & Xiu, Dacheng, 2016. "A tale of two option markets: Pricing kernels and volatility risk," Journal of Econometrics, Elsevier, vol. 190(1), pages 176-196.
    35. Pastor, Lubos & Stambaugh, Robert F., 2003. "Liquidity Risk and Expected Stock Returns," Journal of Political Economy, University of Chicago Press, vol. 111(3), pages 642-685, June.
    36. Viktor Todorov & George Tauchen, 2011. "Volatility Jumps," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 356-371, July.
    37. Yacine Aït-Sahalia & Jianqing Fan & Roger J. A. Laeven & Christina Dan Wang & Xiye Yang, 2017. "Estimation of the Continuous and Discontinuous Leverage Effects," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1744-1758, October.
    38. Kalnina, Ilze, 2011. "Subsampling high frequency data," Journal of Econometrics, Elsevier, vol. 161(2), pages 262-283, April.
    39. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
    40. Bollerslev, Tim & Kretschmer, Uta & Pigorsch, Christian & Tauchen, George, 2009. "A discrete-time model for daily S & P500 returns and realized variations: Jumps and leverage effects," Journal of Econometrics, Elsevier, vol. 150(2), pages 151-166, June.
    41. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    42. Mark Broadie & Mikhail Chernov & Michael Johannes, 2007. "Model Specification and Risk Premia: Evidence from Futures Options," Journal of Finance, American Finance Association, vol. 62(3), pages 1453-1490, June.
    43. repec:dau:papers:123456789/1392 is not listed on IDEAS
    44. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201, Decembrie.
    45. Torben G. Andersen & Oleg Bondarenko & Maria T. Gonzalez-Perez, 2015. "Exploring Return Dynamics via Corridor Implied Volatility," Review of Financial Studies, Society for Financial Studies, vol. 28(10), pages 2902-2945.
    46. Alexander Alvarez & Fabien Panloup & Monique Pontier & Nicolas Savy, 2012. "Estimation of the instantaneous volatility," Statistical Inference for Stochastic Processes, Springer, vol. 15(1), pages 27-59, April.
    47. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
    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. Carsten H. Chong & Viktor Todorov, 2023. "Asymptotic Expansions for High-Frequency Option Data," Papers 2304.12450, arXiv.org.
    2. Aït-Sahalia, Yacine & Kalnina, Ilze & Xiu, Dacheng, 2020. "High-frequency factor models and regressions," Journal of Econometrics, Elsevier, vol. 216(1), pages 86-105.
    3. Todorov, Viktor, 2021. "Higher-order small time asymptotic expansion of Itô semimartingale characteristic function with application to estimation of leverage from options," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 671-705.
    4. Huiling Yuan & Yulei Sun & Lu Xu & Yong Zhou & Xiangyu Cui, 2022. "A new volatility model: GQARCH‐ItÔ model," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 345-370, May.
    5. Carsten H. Chong & Viktor Todorov, 2023. "Volatility of Volatility and Leverage Effect from Options," Papers 2305.04137, arXiv.org, revised Jan 2024.
    6. Giacomo Toscano & Maria Cristina Recchioni, 2020. "Bias optimal vol-of-vol estimation: the role of window overlapping," Papers 2004.04013, arXiv.org, revised Jul 2021.
    7. Bibinger, Markus & Neely, Christopher & Winkelmann, Lars, 2019. "Estimation of the discontinuous leverage effect: Evidence from the NASDAQ order book," Journal of Econometrics, Elsevier, vol. 209(2), pages 158-184.
    8. Yang, Xinxin & Zheng, Xinghua & Chen, Jiaqi, 2021. "Testing high-dimensional covariance matrices under the elliptical distribution and beyond," Journal of Econometrics, Elsevier, vol. 221(2), pages 409-423.
    9. Mingmian Cheng & Norman R. Swanson, 2019. "Fixed and Long Time Span Jump Tests: New Monte Carlo and Empirical Evidence," Econometrics, MDPI, vol. 7(1), pages 1-32, March.
    10. Giacomo Toscano & Maria Cristina Recchioni, 2022. "Bias-optimal vol-of-vol estimation: the role of window overlapping," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 137-185, June.
    11. Yuan, Huiling & Zhou, Yong & Xu, Lu & Sun, Yulei & Cui, Xiangyu, 2020. "A New Volatility Model: GQARCH-Ito Model," SocArXiv hkzdr, Center for Open Science.
    12. Zhi Liu, 2022. "Testing for the Presence of the Leverage Effect without Estimation," Mathematics, MDPI, vol. 10(14), pages 1-16, July.
    13. Huang, Jing-Zhi & Ni, Jun & Xu, Li, 2022. "Leverage effect in cryptocurrency markets," Pacific-Basin Finance Journal, Elsevier, vol. 73(C).
    14. Carsten Chong & Marc Hoffmann & Yanghui Liu & Mathieu Rosenbaum & Gr'egoire Szymanski, 2022. "Statistical inference for rough volatility: Central limit theorems," Papers 2210.01216, arXiv.org, revised Jul 2023.
    15. Giacomo Toscano & Giulia Livieri & Maria Elvira Mancino & Stefano Marmi, 2021. "Volatility of volatility estimation: central limit theorems for the Fourier transform estimator and empirical study of the daily time series stylized facts," Papers 2112.14529, arXiv.org, revised Sep 2022.
    16. Curato, Imma Valentina & Sanfelici, Simona, 2022. "Stochastic leverage effect in high-frequency data: a Fourier based analysis," Econometrics and Statistics, Elsevier, vol. 23(C), pages 53-82.

    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. Song, Zhaogang & Xiu, Dacheng, 2016. "A tale of two option markets: Pricing kernels and volatility risk," Journal of Econometrics, Elsevier, vol. 190(1), pages 176-196.
    2. Amengual, Dante & Xiu, Dacheng, 2018. "Resolution of policy uncertainty and sudden declines in volatility," Journal of Econometrics, Elsevier, vol. 203(2), pages 297-315.
    3. Kaeck, Andreas & Rodrigues, Paulo & Seeger, Norman J., 2017. "Equity index variance: Evidence from flexible parametric jump–diffusion models," Journal of Banking & Finance, Elsevier, vol. 83(C), pages 85-103.
    4. Andersen, Torben G. & Bollerslev, Tim & Dobrev, Dobrislav, 2007. "No-arbitrage semi-martingale restrictions for continuous-time volatility models subject to leverage effects, jumps and i.i.d. noise: Theory and testable distributional implications," Journal of Econometrics, Elsevier, vol. 138(1), pages 125-180, May.
    5. Bardgett, Chris & Gourier, Elise & Leippold, Markus, 2019. "Inferring volatility dynamics and risk premia from the S&P 500 and VIX markets," Journal of Financial Economics, Elsevier, vol. 131(3), pages 593-618.
    6. Bandi, F.M. & Renò, R., 2016. "Price and volatility co-jumps," Journal of Financial Economics, Elsevier, vol. 119(1), pages 107-146.
    7. Francesco Audrino & Yujia Hu, 2016. "Volatility Forecasting: Downside Risk, Jumps and Leverage Effect," Econometrics, MDPI, vol. 4(1), pages 1-24, February.
    8. Fulvio Corsi & Roberto Renò, 2012. "Discrete-Time Volatility Forecasting With Persistent Leverage Effect and the Link With Continuous-Time Volatility Modeling," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 368-380, January.
    9. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    10. Audrino, Francesco & Fengler, Matthias R., 2015. "Are classical option pricing models consistent with observed option second-order moments? Evidence from high-frequency data," Journal of Banking & Finance, Elsevier, vol. 61(C), pages 46-63.
    11. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    12. Bibinger, Markus & Neely, Christopher & Winkelmann, Lars, 2019. "Estimation of the discontinuous leverage effect: Evidence from the NASDAQ order book," Journal of Econometrics, Elsevier, vol. 209(2), pages 158-184.
    13. Du Du & Dan Luo, 2019. "The Pricing of Jump Propagation: Evidence from Spot and Options Markets," Management Science, INFORMS, vol. 67(5), pages 2360-2387, May.
    14. Veiga, Helena, 2006. "Volatility forecasts: a continuous time model versus discrete time models," DES - Working Papers. Statistics and Econometrics. WS ws062509, Universidad Carlos III de Madrid. Departamento de Estadística.
    15. Carverhill, Andrew & Luo, Dan, 2023. "A Bayesian analysis of time-varying jump risk in S&P 500 returns and options," Journal of Financial Markets, Elsevier, vol. 64(C).
    16. Andersen, Torben G. & Bollerslev, Tim & Huang, Xin, 2011. "A reduced form framework for modeling volatility of speculative prices based on realized variation measures," Journal of Econometrics, Elsevier, vol. 160(1), pages 176-189, January.
    17. Aït-Sahalia, Yacine & Karaman, Mustafa & Mancini, Loriano, 2020. "The term structure of equity and variance risk premia," Journal of Econometrics, Elsevier, vol. 219(2), pages 204-230.
    18. Juan Hoyo & Guillermo Llorente & Carlos Rivero, 2020. "A Testing Procedure for Constant Parameters in Stochastic Volatility Models," Computational Economics, Springer;Society for Computational Economics, vol. 56(1), pages 163-186, June.
    19. Qu, Yan & Dassios, Angelos & Zhao, Hongbiao, 2023. "Shot-noise cojumps: exact simulation and option pricing," LSE Research Online Documents on Economics 111537, London School of Economics and Political Science, LSE Library.
    20. Kaeck, Andreas & Alexander, Carol, 2012. "Volatility dynamics for the S&P 500: Further evidence from non-affine, multi-factor jump diffusions," Journal of Banking & Finance, Elsevier, vol. 36(11), pages 3110-3121.

    More about this item

    Keywords

    derivatives; VIX; implied volatility; high frequency data; spot correlation;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:mtl:montec:09-2015. 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: Sharon BREWER (email available below). General contact details of provider: https://edirc.repec.org/data/cdmtlca.html .

    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.