IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v62y2023i1d10.1007_s10614-022-10271-5.html
   My bibliography  Save this article

Modeling Tail Dependence Using Stochastic Volatility Model

Author

Listed:
  • See-Woo Kim

    (KB Securities Co. Ltd.)

  • Yong-Ki Ma

    (Kongju National University)

  • Ciprian Necula

    (Bucharest University of Economic Studies)

Abstract

As one can see in many previous well-known papers, an one–factor stochastic volatility model has its limitation to fit the market dynamics. Based on empirical facts that the market volatility can be well explained by the combination of short-term and long-term volatilities, a multi–scale stochastic volatility model that is governed by two factors evolving on different time-scales: a fast mean-reverting factor and a persistent, slow mean-reverting factor is applied to capture the dynamics of two assets in this paper. The validity of the model was tested by calibration against the market return distribution of the S&P 500 and Dow Jones Industrial Average Indices. Based on this multiscale model, an analytically approximate formula, in terms of the Gaussian copula, was obtained for the joint transition density and the parameters of this density were estimated using daily data from the S&P 500 and DAX Indices.

Suggested Citation

  • See-Woo Kim & Yong-Ki Ma & Ciprian Necula, 2023. "Modeling Tail Dependence Using Stochastic Volatility Model," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 129-147, June.
  • Handle: RePEc:kap:compec:v:62:y:2023:i:1:d:10.1007_s10614-022-10271-5
    DOI: 10.1007/s10614-022-10271-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10614-022-10271-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10614-022-10271-5?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. Davide Meneguzzo & Walter Vecchiato, 2004. "Copula sensitivity in collateralized debt obligations and basket default swaps," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 24(1), pages 37-70, January.
    2. A. Ronald Gallant & Chien-Te Hsu & George Tauchen, 1999. "Using Daily Range Data To Calibrate Volatility Diffusions And Extract The Forward Integrated Variance," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 617-631, November.
    3. Ben-Zhang Yang & Xiaoping Lu & Guiyuan Ma & Song-Ping Zhu, 2020. "Robust Portfolio Optimization with Multi-Factor Stochastic Volatility," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 264-298, July.
    4. Yong-Ki Ma, 2015. "Modeling the Dependency Structure of Integrated Intensity Processes," PLOS ONE, Public Library of Science, vol. 10(8), pages 1-10, August.
    5. Dominique Guegan & Jing Zang, 2009. "Pricing bivariate option under GARCH-GH model with dynamic copula: application for Chinese market," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 777-795.
    6. Peter Christoffersen & Kris Jacobs & Karim Mimouni, 2010. "Volatility Dynamics for the S&P500: Evidence from Realized Volatility, Daily Returns, and Option Prices," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 3141-3189, August.
    7. Jaegi Jeon & Geonwoo Kim & Jeonggyu Huh, 2021. "Consistent and efficient pricing of SPX and VIX options under multiscale stochastic volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(5), pages 559-576, May.
    8. A. Colin Cameron & Tong Li & Pravin K. Trivedi & David M. Zimmer, 2004. "Modelling the differences in counted outcomes using bivariate copula models with application to mismeasured counts," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 566-584, December.
    9. Dominique Guegan & Jing Zhang, 2009. "Pricing bivariate option under GARCH-GH model with dynamic copula: application for Chinese market," Post-Print halshs-00368336, HAL.
    10. Kim, See-Woo & Kim, Jeong-Hoon, 2019. "Variance swaps with double exponential Ornstein-Uhlenbeck stochastic volatility," The North American Journal of Economics and Finance, Elsevier, vol. 48(C), pages 149-169.
    11. Ben-Zhang Yang & Xiaoping Lu & Guiyuan Ma & Song-Ping Zhu, 2019. "Robust portfolio optimization with multi-factor stochastic volatility," Papers 1910.06872, arXiv.org, revised Jun 2020.
    12. 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.
    13. Dominique Guegan & Jing Zhang, 2009. "Pricing bivariate option under GARCH-GH model with dynamic copula: application for Chinese market," PSE-Ecole d'économie de Paris (Postprint) halshs-00368336, HAL.
    14. Yong-Ki Ma & Jeong-Hoon Kim, 2010. "Pricing the credit default swap rate for jump diffusion default intensity processes," Quantitative Finance, Taylor & Francis Journals, vol. 10(8), pages 809-817.
    15. Kim, Jeong-Hoon & Ma, Yong-Ki & Park, Chan Yeol, 2016. "Joint survival probability via truncated invariant copula," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 68-76.
    16. A. Colin Cameron & Tong Li & Pravin K. Trivedi & David M. Zimmer, 2004. "Modelling the differences in counted outcomes using bivariate copula models with application to mismeasured counts," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 566-584, December.
    17. Necula, Ciprian, 2010. "Modeling the Dependency Structure of Stock Index Returns using a Copula Function Approach," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(3), pages 93-106, September.
    18. Deng, Guohe, 2020. "Pricing perpetual American floating strike lookback option under multiscale stochastic volatility model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    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. Aït-Sahalia, Yacine & Li, Chenxu & Li, Chen Xu, 2021. "Closed-form implied volatility surfaces for stochastic volatility models with jumps," Journal of Econometrics, Elsevier, vol. 222(1), pages 364-392.
    2. Christophe Chorro & Dominique Guegan & Florian Ielpo, 2010. "Option pricing for GARCH-type models with generalized hyperbolic innovations," Post-Print halshs-00469529, HAL.
    3. Dominique Guegan & Jing Zhang, 2010. "Change analysis of a dynamic copula for measuring dependence in multivariate financial data," Post-Print halshs-00368334, HAL.
    4. Cyril Caillault, Dominique Guégan, 2009. "Forecasting VaR and Expected Shortfall Using Dynamical Systems: A Risk Management Strategy," Frontiers in Finance and Economics, SKEMA Business School, vol. 6(1), pages 26-50, April.
    5. Christophe Chorro & Dominique Guegan & Florian Ielpo, 2012. "Option Pricing for GARCH-type Models with Generalized Hyperbolic Innovations," Post-Print hal-00511965, HAL.
    6. Christophe Chorro & Dominique Guegan & Florian Ielpo, 2012. "Option Pricing for GARCH-type Models with Generalized Hyperbolic Innovations," PSE-Ecole d'économie de Paris (Postprint) hal-00511965, HAL.
    7. Dominique Guegan & Jing Zhang, 2010. "Change analysis of a dynamic copula for measuring dependence in multivariate financial data," PSE-Ecole d'économie de Paris (Postprint) halshs-00368334, HAL.
    8. Cyril Caillault & Dominique Guegan, 2009. "Forecasting VaR and Expected Shortfall using Dynamical Systems: A Risk Management Strategy," PSE-Ecole d'économie de Paris (Postprint) halshs-00375765, HAL.
    9. Cai, Ning & Li, Chenxu & Shi, Chao, 2021. "Pricing discretely monitored barrier options: When Malliavin calculus expansions meet Hilbert transforms," Journal of Economic Dynamics and Control, Elsevier, vol. 127(C).
    10. Asai, Manabu & McAleer, Michael, 2015. "Leverage and feedback effects on multifactor Wishart stochastic volatility for option pricing," Journal of Econometrics, Elsevier, vol. 187(2), pages 436-446.
    11. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.
    12. Huber, Christoph & Huber, Jürgen & Kirchler, Michael, 2021. "Market shocks and professionals’ investment behavior – Evidence from the COVID-19 crash," Journal of Banking & Finance, Elsevier, vol. 133(C).
    13. Wanling Huang & Artem Prokhorov, 2014. "A Goodness-of-fit Test for Copulas," Econometric Reviews, Taylor & Francis Journals, vol. 33(7), pages 751-771, October.
    14. 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.
    15. Katarzyna Bien & Ingmar Nolte & Winfried Pohlmeier, 2008. "A multivariate integer count hurdle model: theory and application to exchange rate dynamics," Studies in Empirical Economics, in: Luc Bauwens & Winfried Pohlmeier & David Veredas (ed.), High Frequency Financial Econometrics, pages 31-48, Springer.
    16. Chandra Bhat & Ipek Sener, 2009. "A copula-based closed-form binary logit choice model for accommodating spatial correlation across observational units," Journal of Geographical Systems, Springer, vol. 11(3), pages 243-272, September.
    17. Coppejans, Mark & Gallant, A. Ronald, 2002. "Cross-validated SNP density estimates," Journal of Econometrics, Elsevier, vol. 110(1), pages 27-65, September.
    18. Jaegi Jeon & Geonwoo Kim & Jeonggyu Huh, 2019. "Consistent and Efficient Pricing of SPX and VIX Options under Multiscale Stochastic Volatility," Papers 1909.10187, arXiv.org.
    19. Huber, Christoph & Huber, Jürgen & Kirchler, Michael, 2022. "Volatility shocks and investment behavior," Journal of Economic Behavior & Organization, Elsevier, vol. 194(C), pages 56-70.
    20. Meddahi, N., 2001. "An Eigenfunction Approach for Volatility Modeling," Cahiers de recherche 2001-29, Centre interuniversitaire de recherche en économie quantitative, CIREQ.

    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:kap:compec:v:62:y:2023:i:1:d:10.1007_s10614-022-10271-5. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.