Markov Switching Model Analysis of Implied Volatility for Market Indexes with Applications to S&P 500 and DAX
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...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/753852 |
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| author | Luca Di Persio Samuele Vettori |
| author_facet | Luca Di Persio Samuele Vettori |
| author_sort | Luca Di Persio |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ca0eff58a1b049539aca4ac1e2fb3272 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-ca0eff58a1b049539aca4ac1e2fb32722025-02-03T05:58:38ZengWileyJournal of Mathematics2314-46292314-47852014-01-01201410.1155/2014/753852753852Markov Switching Model Analysis of Implied Volatility for Market Indexes with Applications to S&P 500 and DAXLuca Di Persio0Samuele Vettori1Department of Computer Science, University of Verona, Strada le Grazie 15, 37134 Verona, ItalyDepartment of Mathematics, University of Trento, Via Sommarive 14, 38123 Trento, ItalyWe 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.http://dx.doi.org/10.1155/2014/753852 |
| spellingShingle | Luca Di Persio Samuele Vettori Markov Switching Model Analysis of Implied Volatility for Market Indexes with Applications to S&P 500 and DAX Journal of Mathematics |
| title | Markov Switching Model Analysis of Implied Volatility for Market Indexes with Applications to S&P 500 and DAX |
| title_full | Markov Switching Model Analysis of Implied Volatility for Market Indexes with Applications to S&P 500 and DAX |
| title_fullStr | Markov Switching Model Analysis of Implied Volatility for Market Indexes with Applications to S&P 500 and DAX |
| title_full_unstemmed | Markov Switching Model Analysis of Implied Volatility for Market Indexes with Applications to S&P 500 and DAX |
| title_short | Markov Switching Model Analysis of Implied Volatility for Market Indexes with Applications to S&P 500 and DAX |
| title_sort | markov switching model analysis of implied volatility for market indexes with applications to s p 500 and dax |
| url | http://dx.doi.org/10.1155/2014/753852 |
| work_keys_str_mv | AT lucadipersio markovswitchingmodelanalysisofimpliedvolatilityformarketindexeswithapplicationstosp500anddax AT samuelevettori markovswitchingmodelanalysisofimpliedvolatilityformarketindexeswithapplicationstosp500anddax |