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An analytical approximation formula for European option pricing under a new stochastic volatility model with regime-switching

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  • He, Xin-Jiang
  • Zhu, Song-Ping

Abstract

In this paper, an analytical approximation formula for pricing European options is obtained under a newly proposed hybrid model with the volatility of volatility in the Heston model following a Markov chain, the adoption of which is motivated by the empirical evidence of the existence of regime-switching in real markets. We first derive the coupled PDE (partial differential equation) system that governs the European option price, which is solved with the perturbation method. It should be noted that the newly derived formula is fast and easy to implement with only normal distribution function involved, and numerical experiments confirm that our formula could provide quite accurate option prices, especially for relatively short-tenor ones. Finally, empirical studies are carried out to show the superiority of our model based on S&P 500 returns and options with the time to expiry less than one month.

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  • He, Xin-Jiang & Zhu, Song-Ping, 2016. "An analytical approximation formula for European option pricing under a new stochastic volatility model with regime-switching," Journal of Economic Dynamics and Control, Elsevier, vol. 71(C), pages 77-85.
    • Handle: RePEc:eee:dyncon:v:71:y:2016:i:c:p:77-85
    DOI: 10.1016/j.jedc.2016.08.002
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    Cited by:

    1. Loretta Mastroeni, 2022. "Pricing Options with Vanishing Stochastic Volatility," Risks, MDPI, vol. 10(9), pages 1-16, September.
    2. Sha Lin & Xin-Jiang He, 2022. "Analytically Pricing European Options under a New Two-Factor Heston Model with Regime Switching," Computational Economics, Springer;Society for Computational Economics, vol. 59(3), pages 1069-1085, March.
    3. Lin, Sha & He, Xin-Jiang, 2020. "Pricing variance and volatility swaps with stochastic volatility, stochastic interest rate and regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    4. Liu, Yue & Sun, Huaping & Zhang, Jijian & Taghizadeh-Hesary, Farhad, 2020. "Detection of volatility regime-switching for crude oil price modeling and forecasting," Resources Policy, Elsevier, vol. 69(C).
    5. Ben-zhang Yang & Xinjiang He & Nan-jing Huang, 2019. "Equilibrium price and optimal insider trading strategy under stochastic liquidity with long memory," Papers 1901.00345, arXiv.org, revised Jan 2019.
    6. Li, Zhe & Zhang, Wei-Guo & Liu, Yong-Jun & Zhang, Yue, 2019. "Pricing discrete barrier options under jump-diffusion model with liquidity risk," International Review of Economics & Finance, Elsevier, vol. 59(C), pages 347-368.
    7. Xie, Yurong & Deng, Guohe, 2022. "Vulnerable European option pricing in a Markov regime-switching Heston model with stochastic interest rate," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    8. Bianca Reichert & Adriano Mendon a Souza, 2022. "Can the Heston Model Forecast Energy Generation? A Systematic Literature Review," International Journal of Energy Economics and Policy, Econjournals, vol. 12(1), pages 289-295.
    9. Jing, Bo & Li, Shenghong & Ma, Yong, 2021. "Consistent pricing of VIX options with the Hawkes jump-diffusion model," The North American Journal of Economics and Finance, Elsevier, vol. 56(C).
    10. Xin-Jiang He & Song-Ping Zhu, 2019. "Variance And Volatility Swaps Under A Two-Factor Stochastic Volatility Model With Regime Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-19, June.
    11. Lin, Sha & He, Xin-Jiang, 2021. "A closed-form pricing formula for forward start options under a regime-switching stochastic volatility model," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    12. Ali Nasir & Ambreen Khursheed & Kazim Ali & Faisal Mustafa, 2021. "A Markov Decision Process Model for Optimal Trade of Options Using Statistical Data," Computational Economics, Springer;Society for Computational Economics, vol. 58(2), pages 327-346, August.
    13. Bo Jing & Shenghong Li & Yong Ma, 2020. "Pricing VIX options with volatility clustering," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(6), pages 928-944, June.
    14. Li, Zhe & Zhang, Wei-Guo & Liu, Yong-Jun, 2018. "European quanto option pricing in presence of liquidity risk," The North American Journal of Economics and Finance, Elsevier, vol. 45(C), pages 230-244.
    15. Xin-Jiang He & Sha Lin, 2022. "An Analytical Approximation Formula for Barrier Option Prices Under the Heston Model," Computational Economics, Springer;Society for Computational Economics, vol. 60(4), pages 1413-1425, December.

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    More about this item

    Keywords

    European option; Regime-switching Heston model; Perturbation method; Empirical studies;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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