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Option pricing for stochastic volatility model with infinite activity Lévy jumps

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  • Gong, Xiaoli
  • Zhuang, Xintian

Abstract

The purpose of this paper is to apply the stochastic volatility model driven by infinite activity Lévy processes to option pricing which displays infinite activity jumps behaviors and time varying volatility that is consistent with the phenomenon observed in underlying asset dynamics. We specially pay attention to three typical Lévy processes that replace the compound Poisson jumps in Bates model, aiming to capture the leptokurtic feature in asset returns and volatility clustering effect in returns variance. By utilizing the analytical characteristic function and fast Fourier transform technique, the closed form formula of option pricing can be derived. The intelligent global optimization search algorithm called Differential Evolution is introduced into the above highly dimensional models for parameters calibration so as to improve the calibration quality of fitted option models. Finally, we perform empirical researches using both time series data and options data on financial markets to illustrate the effectiveness and superiority of the proposed method.

Suggested Citation

  • Gong, Xiaoli & Zhuang, Xintian, 2016. "Option pricing for stochastic volatility model with infinite activity Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 455(C), pages 1-10.
    • Handle: RePEc:eee:phsmap:v:455:y:2016:i:c:p:1-10
    DOI: 10.1016/j.physa.2016.02.064
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    Cited by:

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    2. Bin Xie & Weiping Li & Nan Liang, 2021. "Pricing S&P 500 Index Options with L\'evy Jumps," Papers 2111.10033, arXiv.org, revised Nov 2021.
    3. D’Amico, Guglielmo & Gismondi, Fulvio & Petroni, Filippo & Prattico, Flavio, 2019. "Stock market daily volatility and information measures of predictability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 518(C), pages 22-29.
    4. Gong, Xiaoli & Zhuang, Xintian, 2017. "American option valuation under time changed tempered stable Lévy processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 57-68.
    5. Alghalith, Moawia, 2020. "Pricing options under simultaneous stochastic volatility and jumps: A simple closed-form formula without numerical/computational methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    6. Moawia Alghalith & Wing-Keung Wong, 2022. "Option Pricing Under an Abnormal Economy: using the Square Root of the Brownian Motion," Advances in Decision Sciences, Asia University, Taiwan, vol. 26(Special), pages 4-18, December.
    7. Gong, Xiao-Li & Liu, Xi-Hua & Xiong, Xiong & Zhuang, Xin-Tian, 2019. "Non-Gaussian VARMA model with stochastic volatility and applications in stock market bubbles," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 129-136.
    8. Gong, Xiaoli & Zhuang, Xintian, 2017. "Pricing foreign equity option under stochastic volatility tempered stable Lévy processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 83-93.
    9. Lin, Zhongguo & Han, Liyan & Li, Wei, 2021. "Option replication with transaction cost under Knightian uncertainty," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    10. Gong, Xiaoli & Zhuang, Xintian, 2017. "Measuring financial risk and portfolio reversion with time changed tempered stable Lévy processes," The North American Journal of Economics and Finance, Elsevier, vol. 40(C), pages 148-159.
    11. Dufera, Tamirat Temesgen, 2024. "Fractional Brownian motion in option pricing and dynamic delta hedging: Experimental simulations," The North American Journal of Economics and Finance, Elsevier, vol. 69(PB).

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