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Option pricing for stochastic volatility model with infinite activity Lévy jumps


  • Gong, Xiaoli
  • Zhuang, Xintian


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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    References listed on IDEAS

    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Kim, Young Shin & Rachev, Svetlozar T. & Bianchi, Michele Leonardo & Mitov, Ivan & Fabozzi, Frank J., 2011. "Time series analysis for financial market meltdowns," Journal of Banking & Finance, Elsevier, vol. 35(8), pages 1879-1891, August.
    3. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    4. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    5. Sven Klingler & Young Shin Kim & Svetlozar T. Rachev & Frank J. Fabozzi, 2013. "Option pricing with time-changed Lévy processes," Applied Financial Economics, Taylor & Francis Journals, vol. 23(15), pages 1231-1238, August.
    6. Zaevski, Tsvetelin S. & Kim, Young Shin & Fabozzi, Frank J., 2014. "Option pricing under stochastic volatility and tempered stable Lévy jumps," International Review of Financial Analysis, Elsevier, vol. 31(C), pages 101-108.
    7. Sun, Qi & Xu, Weidong, 2015. "Pricing foreign equity option with stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 89-100.
    8. Podobnik, Boris & Ivanov, Plamen Ch. & Grosse, Ivo & Matia, Kaushik & Eugene Stanley, H., 2004. "ARCH–GARCH approaches to modeling high-frequency financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 216-220.
    9. Rashidi Ranjbar, Hedieh & Seifi, Abbas, 2015. "A path-independent method for barrier option pricing in hidden Markov models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 440(C), pages 1-8.
    10. Abdelrazeq, Ibrahim, 2015. "Model verification for Lévy-driven Ornstein–Uhlenbeck processes with estimated parameters," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 26-35.
    11. Björn Fastrich & Peter Winker, 2014. "Combining Forecasts with Missing Data: Making Use of Portfolio Theory," Computational Economics, Springer;Society for Computational Economics, vol. 44(2), pages 127-152, August.
    12. Todorov, Viktor, 2011. "Econometric analysis of jump-driven stochastic volatility models," Journal of Econometrics, Elsevier, vol. 160(1), pages 12-21, January.
    13. Sharif Mozumder & Ghulam Sorwar & Kevin Dowd, 2013. "Option pricing under non-normality: a comparative analysis," Review of Quantitative Finance and Accounting, Springer, vol. 40(2), pages 273-292, February.
    14. Küchler, Uwe & Tappe, Stefan, 2013. "Tempered stable distributions and processes," Stochastic Processes and their Applications, Elsevier, vol. 123(12), pages 4256-4293.
    15. Xiao, Weilin & Zhang, Weiguo & Zhang, Xili & Chen, Xiaoyan, 2014. "The valuation of equity warrants under the fractional Vasicek process of the short-term interest rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 320-337.
    16. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    17. Thiemo Krink & Sandra Paterlini, 2011. "Multiobjective optimization using differential evolution for real-world portfolio optimization," Computational Management Science, Springer, vol. 8(1), pages 157-179, April.
    18. Wang, Xiao-Tian & Zhao, Zhong-Feng & Fang, Xiao-Fen, 2015. "Option pricing and portfolio hedging under the mixed hedging strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 424(C), pages 194-206.
    19. Rosinski, Jan, 2007. "Tempering stable processes," Stochastic Processes and their Applications, Elsevier, vol. 117(6), pages 677-707, June.
    20. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    21. Ole E. Barndorff-Nielsen, 1997. "Processes of normal inverse Gaussian type," Finance and Stochastics, Springer, vol. 2(1), pages 41-68.
    22. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    Cited by:

    1. repec:eee:phsmap:v:518:y:2019:i:c:p:22-29 is not listed on IDEAS
    2. 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.
    3. repec:eee:phsmap:v:485:y:2017:i:c:p:91-103 is not listed on IDEAS
    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. repec:eee:phsmap:v:483:y:2017:i:c:p:83-93 is not listed on IDEAS


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