IDEAS home Printed from https://ideas.repec.org/a/bpj/ecqcon/v29y2014i2p157-166n7.html
   My bibliography  Save this article

Leverage Effect for Volatility with Generalized Laplace Error

Author

Listed:
  • Javed Farrukh

    (School of Economics and Management, Lund University, Sweden)

  • Podgórski Krzysztof

    (School of Economics and Management, Lund University, Sweden)

Abstract

We propose a new model that accounts for the asymmetric response of volatility to positive (`good news') and negative (`bad news') shocks in economic time series – the so-called leverage effect. In the past, asymmetric powers of errors in the conditionally heteroskedastic models have been used to capture this effect. Our model is using the gamma difference representation of the generalized Laplace distributions that efficiently models the asymmetry. It has one additional natural parameter, the shape, that is used instead of power in the asymmetric power models to capture the strength of a long-lasting effect of shocks. Some fundamental properties of the model are provided including the formula for covariances and an explicit form for the conditional distribution of `bad' and `good' news processes given the past – the property that is important for statistical fitting of the model. Relevant features of volatility models are illustrated using S&P 500 historical data.

Suggested Citation

  • Javed Farrukh & Podgórski Krzysztof, 2014. "Leverage Effect for Volatility with Generalized Laplace Error," Stochastics and Quality Control, De Gruyter, vol. 29(2), pages 157-166, December.
    • Handle: RePEc:bpj:ecqcon:v:29:y:2014:i:2:p:157-166:n:7
    DOI: 10.1515/eqc-2014-0015
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/eqc-2014-0015
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/eqc-2014-0015?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. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. Bruno Feunou & Roméo Tédongap, 2012. "A Stochastic Volatility Model With Conditional Skewness," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(4), pages 576-591, July.
    5. Verhoeven, Peter & McAleer, Michael, 2004. "Fat tails and asymmetry in financial volatility models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(3), pages 351-361.
    6. Morten B. Jensen & Asger Lunde, 2001. "The NIG-S&ARCH model: a fat-tailed, stochastic, and autoregressive conditional heteroskedastic volatility model," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 1-10.
    7. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    8. 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.
    9. Jondeau, Eric & Rockinger, Michael, 2003. "Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1699-1737, August.
    10. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(1), pages 107-131, April.
    11. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    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. Javed Farrukh & Podgórski Krzysztof, 2017. "Tail Behavior and Dependence Structure in the APARCH Model," Journal of Time Series Econometrics, De Gruyter, vol. 9(2), pages 1-48, July.

    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. Javed Farrukh & Podgórski Krzysztof, 2017. "Tail Behavior and Dependence Structure in the APARCH Model," Journal of Time Series Econometrics, De Gruyter, vol. 9(2), pages 1-48, July.
    2. Giulia Di Nunno & Kęstutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From Constant to Rough: A Survey of Continuous Volatility Modeling," Mathematics, MDPI, vol. 11(19), pages 1-35, October.
    3. Alistair Mees & Berndt Pilgram, 2000. "Non-Linear Markov Modelling Using Canonical Variate Analysis: Forecasting Exchange Rate Volatility," Econometric Society World Congress 2000 Contributed Papers 1162, Econometric Society.
    4. Sylvia J. Soltyk & Felix Chan, 2023. "Modeling time‐varying higher‐order conditional moments: A survey," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 33-57, February.
    5. Eskandar A. Tooma, 2003. "Modeling and Forecasting Egyptian Stock Market Volatility Before and After Price Limits," Working Papers 0310, Economic Research Forum, revised Apr 2003.
    6. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521770415, June.
    7. 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.
    8. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034, Decembrie.
    9. 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.
    10. Giulia Di Nunno & Kk{e}stutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From constant to rough: A survey of continuous volatility modeling," Papers 2309.01033, arXiv.org, revised Sep 2023.
    11. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038, Elsevier.
    12. Subbotin, Alexandre, 2009. "Volatility Models: from Conditional Heteroscedasticity to Cascades at Multiple Horizons," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 15(3), pages 94-138.
    13. Milton Abdul Thorlie & Lixin Song & Muhammad Amin & Xiaoguang Wang, 2015. "Modeling and forecasting of stock index volatility with APARCH models under ordered restriction," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(3), pages 329-356, August.
    14. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
    15. Gürtler, Marc & Rauh, Ronald, 2012. "Challenging traditional risk models by a non-stationary approach with nonparametric heteroscedasticity," Working Papers IF41V1, Technische Universität Braunschweig, Institute of Finance.
    16. Ho, Hwai-Chung, 2015. "Sample quantile analysis for long-memory stochastic volatility models," Journal of Econometrics, Elsevier, vol. 189(2), pages 360-370.
    17. Kononovicius, A. & Ruseckas, J., 2015. "Nonlinear GARCH model and 1/f noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 74-81.
    18. Thilo A. Schmitt & Rudi Schafer & Holger Dette & Thomas Guhr, 2015. "Quantile Correlations: Uncovering temporal dependencies in financial time series," Papers 1507.04990, arXiv.org.
    19. Nigel Wilkins, 2004. "Indirect Estimation of Long Memory Volatility Models," Econometric Society 2004 Far Eastern Meetings 459, Econometric Society.
    20. Alberola, Ricardo, 2007. "Estimating Volatility Returns Using ARCH Models. An Empirical Case: The Spanish Energy Market," Revista Lecturas de Economía, Universidad de Antioquia, CIE, May.

    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:bpj:ecqcon:v:29:y:2014:i:2:p:157-166:n:7. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.