Analytically pricing variance and volatility swaps with stochastic volatility, stochastic equilibrium level and regime switching
This paper proposes a new model with a two-factor stochastic equilibrium volatility level that can be used to price variance and volatility swaps with nonlinear payoff. The adopted model uses the CIR process as the volatility process with the constant equilibrium level replaced with a stochastic one...
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| Published in | Expert systems with applications Vol. 217; p. 119592 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.05.2023
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| Abstract | This paper proposes a new model with a two-factor stochastic equilibrium volatility level that can be used to price variance and volatility swaps with nonlinear payoff. The adopted model uses the CIR process as the volatility process with the constant equilibrium level replaced with a stochastic one, and at the same time incorporates the regime switching mechanics in order to better describe the underlying price. To better understand how the introduced regime switching impacts both swap prices, we also conduct numerical experiments to compare our results with those obtained without regime switching.
•We propose a new stochastic volatility model with two-factor equilibrium volatility level.•We introduce economic cycles by incorporating regime switching.•We analytically evaluate variance and volatility swaps. |
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| AbstractList | This paper proposes a new model with a two-factor stochastic equilibrium volatility level that can be used to price variance and volatility swaps with nonlinear payoff. The adopted model uses the CIR process as the volatility process with the constant equilibrium level replaced with a stochastic one, and at the same time incorporates the regime switching mechanics in order to better describe the underlying price. To better understand how the introduced regime switching impacts both swap prices, we also conduct numerical experiments to compare our results with those obtained without regime switching.
•We propose a new stochastic volatility model with two-factor equilibrium volatility level.•We introduce economic cycles by incorporating regime switching.•We analytically evaluate variance and volatility swaps. |
| ArticleNumber | 119592 |
| Author | He, Xin-Jiang Lin, Sha |
| Author_xml | – sequence: 1 givenname: Sha surname: Lin fullname: Lin, Sha email: linsha@mail.zjgsu.edu.cn organization: Collaborative Innovation Center of Statistical Data Engineering Technology & Application, Zhejiang Gongshang University, Hangzhou, China – sequence: 2 givenname: Xin-Jiang orcidid: 0000-0003-1429-5463 surname: He fullname: He, Xin-Jiang email: xinjiang@zjut.edu.cn organization: School of Economics, Zhejiang University of Technology, Hangzhou, China |
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| Cites_doi | 10.1080/1350486042000254024 10.1111/j.1467-9965.2010.00436.x 10.1016/0378-4266(95)00034-8 10.1007/s11579-020-00287-6 10.1080/13504860600659222 10.1016/j.amc.2019.02.063 10.1007/s11579-019-00242-0 10.1007/s11579-020-00281-y 10.1016/j.cam.2015.04.036 10.1093/imaman/dpab013 10.1080/14697688.2012.676208 10.3905/jod.1999.319129 10.1016/j.orl.2012.12.008 10.1080/14697680400000040 10.1111/mafi.12016 10.1016/j.matcom.2022.09.006 10.1016/j.ejor.2015.03.026 10.1007/s10479-018-2941-9 10.1016/j.jfineco.2005.09.005 10.1016/j.econmod.2013.11.009 10.1016/0304-4076(90)90093-9 10.3934/math.2023243 10.1016/j.matcom.2020.09.011 10.1016/j.eswa.2022.118742 |
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| Keywords | Stochastic volatility Variance/volatility swaps Analytical solution Regime switching Two-factor stochastic equilibrium level |
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10.1016/j.eswa.2023.119592_b21 article-title: Variance swap with mean reversion, multifactor stochastic volatility and jumps publication-title: European Journal of Operational Research doi: 10.1016/j.ejor.2015.03.026 – volume: 282 start-page: 27 issue: 1 year: 2019 ident: 10.1016/j.eswa.2023.119592_b1 article-title: Closed-form variance swap prices under general affine GARCH models and their continuous-time limits publication-title: Annals of Operations Research doi: 10.1007/s10479-018-2941-9 – volume: 82 start-page: 227 issue: 1 year: 2006 ident: 10.1016/j.eswa.2023.119592_b2 article-title: Estimation of continuous-time models with an application to equity volatility dynamics publication-title: Journal of Financial Economics doi: 10.1016/j.jfineco.2005.09.005 – volume: 37 start-page: 296 year: 2014 ident: 10.1016/j.eswa.2023.119592_b8 article-title: Pricing foreign equity options with regime-switching publication-title: Economic Modelling doi: 10.1016/j.econmod.2013.11.009 – volume: 45 start-page: 39 issue: 1 year: 1990 ident: 10.1016/j.eswa.2023.119592_b10 article-title: Analysis of time series subject to changes in regime publication-title: Journal of Econometrics doi: 10.1016/0304-4076(90)90093-9 – volume: 8 start-page: 4875 issue: 2 year: 2023 ident: 10.1016/j.eswa.2023.119592_b16 article-title: Analytical approximation of European option prices under a new two-factor non-affine stochastic volatility model publication-title: AIMS Mathematics doi: 10.3934/math.2023243 – volume: 181 start-page: 1 year: 2021 ident: 10.1016/j.eswa.2023.119592_b20 article-title: A generalized antithetic variates Monte-Carlo simulation method for pricing of Asian option in a Markov regime-switching model publication-title: Mathematics and Computers in Simulation doi: 10.1016/j.matcom.2020.09.011 – volume: 212 year: 2023 ident: 10.1016/j.eswa.2023.119592_b14 article-title: A new nonlinear stochastic volatility model with regime switching stochastic mean reversion and its applications to option pricing publication-title: Expert Systems with Applications doi: 10.1016/j.eswa.2022.118742 – volume: 20 start-page: 76 issue: 5 year: 2007 ident: 10.1016/j.eswa.2023.119592_b3 article-title: Realized volatility and variance: Options via swaps publication-title: Risk |
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| SubjectTerms | Analytical solution Regime switching Stochastic volatility Two-factor stochastic equilibrium level Variance/volatility swaps |
| Title | Analytically pricing variance and volatility swaps with stochastic volatility, stochastic equilibrium level and regime switching |
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