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Combined multiplicative–Heston model for stochastic volatility

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  • Dashti Moghaddam, M.
  • Serota, R.A.

Abstract

We consider a model of stochastic volatility which combines features of the multiplicative model for large volatilities and of the Heston model for small volatilities. The steady-state distribution in this model is a Beta Prime and is characterized by the power-law behavior at both large and small volatilities. We discuss the reasoning behind using this model as well as consequences for our recent analyses of distributions of stock returns and realized volatility.

Suggested Citation

  • Dashti Moghaddam, M. & Serota, R.A., 2021. "Combined multiplicative–Heston model for stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    • Handle: RePEc:eee:phsmap:v:561:y:2021:i:c:s0378437120306671
    DOI: 10.1016/j.physa.2020.125263
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    References listed on IDEAS

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    1. Michael A. Kouritzin, 2015. "Microstructure Models with Short-Term Inertia and Stochastic Volatility," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-17, October.
    2. Ma, Tao & Serota, R.A., 2014. "A model for stock returns and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 89-115.
    3. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    4. Perelló, J & Porrà, J.M & Montero, M & Masoliver, J, 2000. "Black–Scholes option pricing within Itô and Stratonovich conventions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(1), pages 260-274.
    5. Adrian Dragulescu & Victor Yakovenko, 2002. "Probability distribution of returns in the Heston model with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 443-453.
    6. Michael A. Kouritzin & Anne Mackay, 2020. "Branching Particle Pricers With Heston Examples," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(01), pages 1-29, February.
    7. Richard D. F. Harris & C. Coskun Küçüközmen, 2001. "The Empirical Distribution of UK and US Stock Returns," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 28(5‐6), pages 715-740, June.
    8. Michael A. Kouritzin, 2016. "Explicit Heston Solutions and Stochastic Approximation for Path-dependent Option Pricing," Papers 1608.02028, arXiv.org, revised Apr 2018.
    9. Josep Perello & Jaume Masoliver & Jean-Philippe Bouchaud, 2004. "Multiple time scales in volatility and leverage correlations: a stochastic volatility model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 11(1), pages 27-50.
    10. Silva, A. Christian & Yakovenko, Victor M., 2007. "Stochastic volatility of financial markets as the fluctuating rate of trading: An empirical study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 278-285.
    11. Cheng Yan & Bo Zhao, 2019. "Withdrawn: A general jump‐diffusion process to price volatility derivatives," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(1), pages 15-37, January.
    12. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    13. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    14. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    15. Austin Gerig & Javier Vicente & Miguel A. Fuentes, 2009. "Model for Non-Gaussian Intraday Stock Returns," Papers 0906.3841, arXiv.org, revised Dec 2009.
    16. Giulia Livieri & Saad Mouti & Andrea Pallavicini & Mathieu Rosenbaum, 2018. "Rough volatility: Evidence from option prices," IISE Transactions, Taylor & Francis Journals, vol. 50(9), pages 767-776, September.
    17. Behfar, Stefan Kambiz, 2016. "Long memory behavior of returns after intraday financial jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 716-725.
    18. Miguel A Fuentes & Austin Gerig & Javier Vicente, 2009. "Universal Behavior of Extreme Price Movements in Stock Markets," PLOS ONE, Public Library of Science, vol. 4(12), pages 1-4, December.
    19. Michael A. Kouritzin, 2018. "Explicit Heston Solutions And Stochastic Approximation For Path-Dependent Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-45, February.
    20. Miguel A. Fuentes & Austin Gerig & Javier Vicente, 2009. "Universal Behavior of Extreme Price Movements in Stock Markets," Papers 0912.5448, arXiv.org.
    21. Praetz, Peter D, 1972. "The Distribution of Share Price Changes," The Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January.
    22. Josep Perello & Jaume Masoliver, 2002. "Stochastic volatility and leverage effect," Papers cond-mat/0202203, arXiv.org.
    23. Jean-Philippe Bouchaud & Andrew Matacz & Marc Potters, 2001. "The leverage effect in financial markets: retarded volatility and market panic," Science & Finance (CFM) working paper archive 0101120, Science & Finance, Capital Fund Management.
    24. Ma, Tao & Holden, John G. & Serota, R.A., 2013. "Distribution of wealth in a network model of the economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(10), pages 2434-2441.
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