A new nonlinear stochastic volatility model with regime switching stochastic mean reversion and its applications to option pricing
We establish a new nonlinear stochastic volatility model by modeling the volatility long-run mean with a particular stochastic process, whose parameters can jump between different regimes according to a Markov chain. Introducing the regime switching factor is consistent with the empirical evidence o...
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| Published in | Expert systems with applications Vol. 212; p. 118742 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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01.02.2023
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| Abstract | We establish a new nonlinear stochastic volatility model by modeling the volatility long-run mean with a particular stochastic process, whose parameters can jump between different regimes according to a Markov chain. Introducing the regime switching factor is consistent with the empirical evidence of the economic cycle and nonlinear volatility mean-reversion observed from market data. A closed-form solution that can be used to value European options has been successfully obtained based on the characteristic function approach, followed by some numerical examples comparing the models with and without regime switching.
•We propose a new nonlinear three-factor stochastic volatility model.•We capture economic cycles and nonlinear volatility mean-reversion.•We present a closed-form solution for European option pricing. |
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| AbstractList | We establish a new nonlinear stochastic volatility model by modeling the volatility long-run mean with a particular stochastic process, whose parameters can jump between different regimes according to a Markov chain. Introducing the regime switching factor is consistent with the empirical evidence of the economic cycle and nonlinear volatility mean-reversion observed from market data. A closed-form solution that can be used to value European options has been successfully obtained based on the characteristic function approach, followed by some numerical examples comparing the models with and without regime switching.
•We propose a new nonlinear three-factor stochastic volatility model.•We capture economic cycles and nonlinear volatility mean-reversion.•We present a closed-form solution for European option pricing. |
| ArticleNumber | 118742 |
| Author | He, Xin-Jiang Lin, Sha |
| Author_xml | – sequence: 1 givenname: Xin-Jiang surname: He fullname: He, Xin-Jiang email: xinjiang@zjut.edu.cn organization: School of Economics, Zhejiang University of Technology, Hangzhou, China – sequence: 2 givenname: Sha orcidid: 0000-0003-1692-8711 surname: Lin fullname: Lin, Sha email: linsha@mail.zjgsu.edu.cn organization: School of Finance, Zhejiang Gongshang University, Hangzhou, China |
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| Cites_doi | 10.1016/j.spl.2018.02.056 10.1111/j.1540-6261.1987.tb02568.x 10.2307/2330793 10.1007/s10957-017-1159-3 10.1016/j.cam.2013.10.021 10.1016/j.chaos.2020.110644 10.1111/j.1540-6261.2004.00666.x 10.1086/260062 10.1016/0304-405X(87)90009-2 10.1016/j.jfineco.2005.09.005 10.1016/0895-7177(89)90202-1 10.1002/fut.10019 10.1016/j.ejor.2013.10.028 10.1111/0022-1082.00083 10.1007/s10100-017-0508-5 10.1080/1350486X.2017.1333015 10.1016/0304-4076(90)90093-9 10.1007/s11579-020-00281-y 10.1093/rfs/6.2.327 10.1016/j.eneco.2009.05.001 10.1287/mnsc.1040.0276 10.1080/02331934.2016.1209672 10.1080/14697688.2012.676208 10.1007/s00186-010-0302-9 10.1016/j.cam.2014.01.021 |
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publication-title: Management Science doi: 10.1287/mnsc.1040.0276 – volume: 4 start-page: 74 year: 2004 ident: 10.1016/j.eswa.2022.118742_b22 article-title: Heston’s stochastic volatility model: Implementation, calibration and some extensions publication-title: Wilmott Magazine – volume: 66 start-page: 2135 issue: 12 year: 2017 ident: 10.1016/j.eswa.2022.118742_b23 article-title: Robust optimization in spline regression models for multi-model regulatory networks under polyhedral uncertainty publication-title: Optimization doi: 10.1080/02331934.2016.1209672 – year: 2012 ident: 10.1016/j.eswa.2022.118742_b24 – volume: 13 start-page: 687 issue: 5 year: 2013 ident: 10.1016/j.eswa.2022.118742_b9 article-title: Pricing variance and volatility swaps in a stochastic volatility model with regime switching: discrete observations case publication-title: Quantitative Finance doi: 10.1080/14697688.2012.676208 – start-page: 371 year: 2014 ident: 10.1016/j.eswa.2022.118742_b25 article-title: Optimal control of stochastic hybrid models in the framework of regime switches – start-page: 1 year: 2020 ident: 10.1016/j.eswa.2022.118742_b27 article-title: Stochastic differential games for optimal investment problems in a Markov regime-switching jump-diffusion market publication-title: Annals of Operations Research – volume: 71 start-page: 453 issue: 3 year: 2010 ident: 10.1016/j.eswa.2022.118742_b28 article-title: Comparison and robustification of Bayes and Black-Litterman models publication-title: Mathematical Methods of Operations Research doi: 10.1007/s00186-010-0302-9 – volume: 267 start-page: 1 year: 2014 ident: 10.1016/j.eswa.2022.118742_b2 article-title: Dynamic programming for a Markov-switching jump–diffusion publication-title: Journal of Computational and Applied Mathematics doi: 10.1016/j.cam.2014.01.021 |
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| Title | A new nonlinear stochastic volatility model with regime switching stochastic mean reversion and its applications to option pricing |
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