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Nonparametric Estimation of the Leverage Effect: A Trade-Off Between Robustness and Efficiency

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  • 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 Chicago Board Options Exchange (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 are 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 an empirical application, in which we study the relationship between the leverage effect and the debt-to-equity ratio, credit risk, and illiquidity. Supplementary materials for this article are available online.

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  • Ilze Kalnina & Dacheng Xiu, 2017. "Nonparametric Estimation of the Leverage Effect: A Trade-Off Between Robustness and Efficiency," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 384-396, January.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:517:p:384-396
    DOI: 10.1080/01621459.2016.1141687
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    Cited by:

    1. 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.
    2. Zhi Liu, 2022. "Testing for the Presence of the Leverage Effect without Estimation," Mathematics, MDPI, vol. 10(14), pages 1-16, July.
    3. Bollerslev, Tim & Todorov, Viktor, 2023. "The jump leverage risk premium," Journal of Financial Economics, Elsevier, vol. 150(3).
    4. Carsten H. Chong & Viktor Todorov, 2023. "Volatility of Volatility and Leverage Effect from Options," Papers 2305.04137, arXiv.org, revised Jan 2024.
    5. Huang, Jing-Zhi & Ni, Jun & Xu, Li, 2022. "Leverage effect in cryptocurrency markets," Pacific-Basin Finance Journal, Elsevier, vol. 73(C).
    6. 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 Jun 2024.
    7. Carsten H. Chong & Viktor Todorov, 2023. "Asymptotic Expansions for High-Frequency Option Data," Papers 2304.12450, arXiv.org.
    8. Aït-Sahalia, Yacine & Kalnina, Ilze & Xiu, Dacheng, 2020. "High-frequency factor models and regressions," Journal of Econometrics, Elsevier, vol. 216(1), pages 86-105.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    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.
    17. Yuan, Huiling & Zhou, Yong & Xu, Lu & Sun, Yulei & Cui, Xiangyu, 2020. "A New Volatility Model: GQARCH-Ito Model," SocArXiv hkzdr, Center for Open Science.
    18. Chong, Carsten H. & Todorov, Viktor, 2024. "Volatility of volatility and leverage effect from options," Journal of Econometrics, Elsevier, vol. 240(1).

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    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

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