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The influences of delay time on the stability of a market model with stochastic volatility

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  • Li, Jiang-Cheng
  • Mei, Dong-Cheng

Abstract

The effects of the delay time on the stability of a market model are investigated, by using a modified Heston model with a cubic nonlinearity and cross-correlated noise sources. These results indicate that: (i) There is an optimal delay time τo which maximally enhances the stability of the stock price under strong demand elasticity of stock price, and maximally reduces the stability of the stock price under weak demand elasticity of stock price; (ii) The cross correlation coefficient of noises and the delay time play an opposite role on the stability for the case of the delay time <τo and the same role for the case of the delay time >τo. Moreover, the probability density function of the escape time of stock price returns, the probability density function of the returns and the correlation function of the returns are compared with other literatures.

Suggested Citation

  • Li, Jiang-Cheng & Mei, Dong-Cheng, 2013. "The influences of delay time on the stability of a market model with stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 763-772.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:4:p:763-772
    DOI: 10.1016/j.physa.2012.10.028
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    Citations

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    Cited by:

    1. Ausloos, Marcel & Eskandary, Ali & Kaur, Parmjit & Dhesi, Gurjeet, 2019. "Evidence for Gross Domestic Product growth time delay dependence over Foreign Direct Investment. A time-lag dependent correlation study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 527(C).
    2. Zhong, Guang-Yan & Li, Jiang-Cheng & Jiang, George J. & Li, Hai-Feng & Tao, Hui-Ming, 2018. "The time delay restraining the herd behavior with Bayesian approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 335-346.
    3. Chendur Kumaran, R. & Venkatesh, T.G. & Swarup, K.S., 2022. "Stochastic delay differential equations: Analysis and simulation studies," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    4. Ko, Bonggyun & Song, Jae Wook, 2018. "A simple analytics framework for evaluating mean escape time in different term structures with stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 398-412.

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