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The EWMA Heston model

Author

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  • Léo Parent

    (PRISM Sorbonne - Pôle de recherche interdisciplinaire en sciences du management - UP1 - Université Paris 1 Panthéon-Sorbonne)

Abstract

This paper introduces the exponentially weighted moving average (EWMA) Heston model, a Markovian stochastic volatility model able to capture a wide range of empirical features related to volatility dynamics while being more tractable for simulations than rough volatility models based on fractional processes. After presenting the model and its principal characteristics, our analysis focuses on the use of its associated Euler-discretization scheme as a time-series generator for Monte-Carlo simulations. Using this discretization scheme, and on the basis of S&P500 empirical time series, we show that the EWMA Heston model is overall consistent with market data, making it a credible alternative to other existing stochastic volatility models. Keywords: tohsti voltility modelD reston modelD qudrti rough reston modelD umh e'etD timeEreversl symmetryD voltility distriutionD returns distriutionF JEL classication: gISD gQPD qIHD qIRD qIUF

Suggested Citation

  • Léo Parent, 2022. "The EWMA Heston model," Post-Print hal-04431111, HAL.
    • Handle: RePEc:hal:journl:hal-04431111
    Note: View the original document on HAL open archive server: https://hal.science/hal-04431111
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    References listed on IDEAS

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    1. P. Blanc & J. Donier & J.-P. Bouchaud, 2017. "Quadratic Hawkes processes for financial prices," Quantitative Finance, Taylor & Francis Journals, vol. 17(2), pages 171-188, February.
    2. Stéphane Goutte & Amine Ismail & Huyên Pham, 2017. "Regime-switching stochastic volatility model: estimation and calibration to VIX options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 24(1), pages 38-75, January.
    3. 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.
    4. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    5. Gilles Zumbach, 2009. "Time reversal invariance in finance," Quantitative Finance, Taylor & Francis Journals, vol. 9(5), pages 505-515.
    6. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    7. Markku Lanne & Pentti Saikkonen, 2005. "Non-linear GARCH models for highly persistent volatility," Econometrics Journal, Royal Economic Society, vol. 8(2), pages 251-276, July.
    8. Belkhouja, Mustapha & Boutahary, Mohamed, 2011. "Modeling volatility with time-varying FIGARCH models," Economic Modelling, Elsevier, vol. 28(3), pages 1106-1116, May.
    9. Roger Lord & Remmert Koekkoek & Dick Van Dijk, 2010. "A comparison of biased simulation schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 177-194.
    10. Ross A. Maller & Gernot Muller & Alex Szimayer, 2008. "GARCH modelling in continuous time for irregularly spaced time series data," Papers 0805.2096, arXiv.org.
    11. 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.
    12. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737, September.
    13. Omar El Euch & Mathieu Rosenbaum, 2019. "The characteristic function of rough Heston models," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 3-38, January.
    14. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 7(2), pages 174-196, Spring.
    15. Gishan Dissanaike, 1997. "Do Stock Market Investors Overreact?," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 24(1), pages 27-50.
    16. De Bondt, Werner F M & Thaler, Richard H, 1987. "Further Evidence on Investor Overreaction and Stock Market Seasonalit y," Journal of Finance, American Finance Association, vol. 42(3), pages 557-581, July.
    17. Paul Lynch & Gilles Zumbach, 2003. "Market heterogeneities and the causal structure of volatility," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 320-331.
    18. Thierry Bochud & Damien Challet, 2007. "Optimal approximations of power laws with exponentials: application to volatility models with long memory," Quantitative Finance, Taylor & Francis Journals, vol. 7(6), pages 585-589.
    19. Brandt, Michael W. & Jones, Christopher S., 2006. "Volatility Forecasting With Range-Based EGARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 470-486, October.
    20. Eduardo Abi Jaber & Omar El Euch, 2019. "Multi-factor approximation of rough volatility models," Post-Print hal-01697117, HAL.
    21. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    22. David G. Hobson & L. C. G. Rogers, 1998. "Complete Models with Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 27-48, January.
    23. Gilles Zumbach, 2010. "Volatility conditional on price trends," Quantitative Finance, Taylor & Francis Journals, vol. 10(4), pages 431-442.
    24. Jim Gatheral & Paul Jusselin & Mathieu Rosenbaum, 2020. "The quadratic rough Heston model and the joint S&P 500/VIX smile calibration problem," Papers 2001.01789, arXiv.org.
    25. Gishan Dissanaike, 1997. "Do Stock Market Investors Overreact?," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 24(1), pages 27-50, January.
    26. Stéphane Goutte & Amine Ismail & Huyên Pham, 2017. "Regime-switching Stochastic Volatility Model : Estimation and Calibration to VIX options," Working Papers hal-01212018, HAL.
    27. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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