IDEAS home Printed from https://ideas.repec.org/a/hin/jjmath/753852.html

Markov Switching Model Analysis of Implied Volatility for Market Indexes with Applications to S&P 500 and DAX

Author

Listed:
  • Luca Di Persio
  • Samuele Vettori

Abstract

We adopt a regime switching approach to study concrete financial time series with particular emphasis on their volatility characteristics considered in a space-time setting. In particular the volatility parameter is treated as an unobserved state variable whose value in time is given as the outcome of an unobserved, discrete-time and discrete-state, stochastic process represented by a suitable Markov chain. We will take into account two different approaches for inference on Markov switching models, namely, the classical approach based on the maximum likelihood techniques and the Bayesian inference method realized through a Gibbs sampling procedure. Then the classical approach shall be tested on data taken from the Standard & Poor’s 500 and the Deutsche Aktien Index series of returns in different time periods. Computations are given for a four-state switching model and obtained numerical results are put beside by explanatory graphs which report the outcomes obtained exploiting both smoothing and filtering algorithms used in the estimation/calibration procedures we proposed to infer on the switching model parameters.

Suggested Citation

  • Luca Di Persio & Samuele Vettori, 2014. "Markov Switching Model Analysis of Implied Volatility for Market Indexes with Applications to S&P 500 and DAX," Journal of Mathematics, Hindawi, vol. 2014, pages 1-17, December.
    • Handle: RePEc:hin:jjmath:753852
    DOI: 10.1155/2014/753852
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/JMATH/2014/753852.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/JMATH/2014/753852.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/753852?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
    ---><---

    References listed on IDEAS

    as
    1. Sargan, John Denis & Bhargava, Alok, 1983. "Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk," Econometrica, Econometric Society, vol. 51(1), pages 153-174, January.
    2. Frédérique Bec & Anders Rahbek & Neil Shephard, 2008. "The ACR Model: A Multivariate Dynamic Mixture Autoregression," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(5), pages 583-618, October.
    3. Albert, James H & Chib, Siddhartha, 1993. "Bayes Inference via Gibbs Sampling of Autoregressive Time Series Subject to Markov Mean and Variance Shifts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 1-15, January.
    4. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    5. Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, vol. 1(1), pages 3-15, March.
    6. Chang-Jin Kim & Charles R. Nelson, 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262112388, December.
    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. Antonio N. Bojanic, 2021. "A Markov-Switching Model of Inflation in Bolivia," Economies, MDPI, vol. 9(1), pages 1-18, March.
    2. Jyothi Chittineni, 2018. "Indian Implied Volatility Index: A Macroeconomic Study," Applied Economics and Finance, Redfame publishing, vol. 5(5), pages 75-82, September.

    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. Billio, Monica & Casarin, Roberto & Ravazzolo, Francesco & van Dijk, Herman K., 2012. "Combination schemes for turning point predictions," The Quarterly Review of Economics and Finance, Elsevier, vol. 52(4), pages 402-412.
    2. Grace Lee, 2011. "Aggregate shocks decomposition for eight East Asian countries," Journal of the Asia Pacific Economy, Taylor & Francis Journals, vol. 16(2), pages 215-232.
    3. Chung-Ming Kuan, 2013. "Markov switching model (in Russian)," Quantile, Quantile, issue 11, pages 13-40, December.
    4. Firouz Fallahi & Gabriel Rodríguez, 2007. "Using Markov-Switching Models to Identify the Link between Unemployment and Criminality," Working Papers 0701E, University of Ottawa, Department of Economics.
    5. Liu Xiaochun & Luger Richard, 2018. "Markov-switching quantile autoregression: a Gibbs sampling approach," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(2), pages 1, April.
    6. Chuku Chuku & Paul Middleditch, 2020. "Characterizing Monetary and Fiscal Policy Rules and Interactions when Commodity Prices Matter," Manchester School, University of Manchester, vol. 88(3), pages 373-404, June.
    7. Myroslav Pidkuyko, 2014. "Dynamics of Consumption and Dividends over the Business Cycle," CERGE-EI Working Papers wp522, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    8. Andreas Graflund, 2000. "A Bayes Inference Approach to Testing Mean Reversion in the Swedish Stock Market," Econometric Society World Congress 2000 Contributed Papers 1363, Econometric Society.
    9. Kai Zheng & Weidong Xu & Xili Zhang, 2023. "Multivariate Regime Switching Model Estimation and Asset Allocation," Computational Economics, Springer;Society for Computational Economics, vol. 61(1), pages 165-196, January.
    10. Psaradakis Zacharias & Spagnolo Nicola, 2002. "Power Properties of Nonlinearity Tests for Time Series with Markov Regimes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 6(3), pages 1-16, November.
    11. Aliyu, Shehu Usman Rano, 2020. "What have we learnt from modelling stock returns in Nigeria: Higgledy-piggledy?," MPRA Paper 110382, University Library of Munich, Germany, revised 06 Jun 2021.
    12. Maddalena Cavicchioli, 2021. "OLS Estimation of Markov switching VAR models: asymptotics and application to energy use," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(3), pages 431-449, September.
    13. Stavros Degiannakis, 2015. "A Probit Model for the State of the Greek GDP Growth," IJFS, MDPI, vol. 3(3), pages 1-12, August.
    14. Shanshan Qin & Zhenni Tan & Yuehua Wu, 2024. "On robust estimation of hidden semi-Markov regime-switching models," Annals of Operations Research, Springer, vol. 338(2), pages 1049-1081, July.
    15. Muriel Nguiffo-Boyom, 2006. "Un indicateur de retournement conjoncturel pour la France : une application du modèle à facteur avec changements de régimes," Économie et Prévision, Programme National Persée, vol. 172(1), pages 101-114.
    16. Paap, Richard & Segers, Rene & van Dijk, Dick, 2009. "Do Leading Indicators Lead Peaks More Than Troughs?," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(4), pages 528-543.
    17. Chang-Jin Kim & Chris Murray, 1999. "Permanent and Transitory Nature of Recessions," Discussion Papers in Economics at the University of Washington 0041, Department of Economics at the University of Washington.
    18. Erica Fellinger Jusué & Tomás Mancha Navarro, 2008. "Stabilization policies in Argentina: an analysis from the perspective of inflation uncertainty," Working Papers 04/08, Instituto Universitario de Análisis Económico y Social.
    19. Andreas Graflund & Birger Nilsson, 2003. "Dynamic Portfolio Selection: the Relevance of Switching Regimes and Investment Horizon," European Financial Management, European Financial Management Association, vol. 9(2), pages 179-200, June.
    20. Matthieu Droumaguet & Tomasz Wozniak, 2012. "Bayesian Testing of Granger Causality in Markov-Switching VARs," Economics Working Papers ECO2012/06, European University Institute.

    More about this item

    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:hin:jjmath:753852. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.