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

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  • 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
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    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.
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    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.
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    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.

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