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Multiple time scales and the exponential Ornstein-Uhlenbeck stochastic volatility model

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  • Jaume Masoliver
  • Josep Perello

Abstract

We study the exponential Ornstein-Uhlenbeck stochastic volatility model and observe that the model shows a multiscale behavior in the volatility autocorrelation. It also exhibits a leverage correlation and a probability profile for the stationary volatility which are consistent with market observations. All these features make the model quite appealing since it appears to be more complete than other stochastic volatility models also based on a two-dimensional diffusion. We finally present an approximate solution for the return probability density designed to capture the kurtosis and skewness effects.

Suggested Citation

  • Jaume Masoliver & Josep Perello, 2005. "Multiple time scales and the exponential Ornstein-Uhlenbeck stochastic volatility model," Papers cond-mat/0501639, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/0501639
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    Cited by:

    1. Oliver Pfante & Nils Bertschinger, 2019. "Information-Theoretic Analysis Of Stochastic Volatility Models," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 22(01), pages 1-21, February.
    2. Andrea Barletta & Elisa Nicolato & Stefano Pagliarani, 2019. "The short‐time behavior of VIX‐implied volatilities in a multifactor stochastic volatility framework," Mathematical Finance, Wiley Blackwell, vol. 29(3), pages 928-966, July.
    3. Cai, Mei-Ling & Chen, Zhang-HangJian & Li, Sai-Ping & Xiong, Xiong & Zhang, Wei & Yang, Ming-Yuan & Ren, Fei, 2022. "New volatility evolution model after extreme events," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    4. Mei-Ling Cai & Zhang-HangJian Chen & Sai-Ping Li & Xiong Xiong & Wei Zhang & Ming-Yuan Yang & Fei Ren, 2022. "New volatility evolution model after extreme events," Papers 2201.03213, arXiv.org.
    5. Oliver Pfante & Nils Bertschinger, 2019. "Volatility Inference And Return Dependencies In Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 1-44, May.
    6. M A Sánchez-Granero & J E Trinidad-Segovia & J Clara-Rahola & A M Puertas & F J De las Nieves, 2017. "A model for foreign exchange markets based on glassy Brownian systems," PLOS ONE, Public Library of Science, vol. 12(12), pages 1-22, December.
    7. Alexander Subbotin & Thierry Chauveau & Kateryna Shapovalova, 2009. "Volatility Models: from GARCH to Multi-Horizon Cascades," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00390636, HAL.
    8. Jun-Jie Chen & Bo Zheng & Lei Tan, 2013. "Agent-Based Model with Asymmetric Trading and Herding for Complex Financial Systems," PLOS ONE, Public Library of Science, vol. 8(11), pages 1-11, November.
    9. Giacomo Bormetti & Valentina Cazzola & Danilo Delpini, 2009. "Option pricing under Ornstein-Uhlenbeck stochastic volatility: a linear model," Papers 0905.1882, arXiv.org, revised May 2010.
    10. Xingchen Wan & Jie Yang & Slavi Marinov & Jan-Peter Calliess & Stefan Zohren & Xiaowen Dong, 2020. "Sentiment Correlation in Financial News Networks and Associated Market Movements," Papers 2011.06430, arXiv.org, revised Feb 2021.
    11. Jun-jie Chen & Bo Zheng & Lei Tan, 2014. "Agent-based model with asymmetric trading and herding for complex financial systems," Papers 1407.5258, arXiv.org.
    12. Cyrille Dubarry & Randal Douc, 2014. "Calibrating the exponential Ornstein--Uhlenbeck multiscale stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 443-456, March.
    13. Patrick Chan & Ronnie Sircar & Iosif Zimbidis, 2025. "Optimal Trading under Instantaneous and Persistent Price Impact, Predictable Returns and Multiscale Stochastic Volatility," Papers 2507.17162, arXiv.org.
    14. Alexandre Subbotin, 2009. "Volatility Models: from Conditional Heteroscedasticity to Cascades at Multiple Horizons," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 15(3), pages 94-138.
    15. Mario Gutiérrez-Roig & Carlota Segura & Jordi Duch & Josep Perelló, 2016. "Market Imitation and Win-Stay Lose-Shift Strategies Emerge as Unintended Patterns in Market Direction Guesses," PLOS ONE, Public Library of Science, vol. 11(8), pages 1-19, August.
    16. Miccichè, S., 2016. "Understanding the determinants of volatility clustering in terms of stationary Markovian processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 186-197.
    17. Nils Bertschinger & Oliver Pfante, 2015. "Inferring Volatility in the Heston Model and its Relatives -- an Information Theoretical Approach," Papers 1512.08381, arXiv.org.
    18. Kim, See-Woo & Kim, Jeong-Hoon, 2019. "Variance swaps with double exponential Ornstein-Uhlenbeck stochastic volatility," The North American Journal of Economics and Finance, Elsevier, vol. 48(C), pages 149-169.
    19. Yunhong Lyu & Sévérien Nkurunziza, 2023. "Inference in generalized exponential O–U processes," Statistical Inference for Stochastic Processes, Springer, vol. 26(3), pages 581-618, October.
    20. Buchbinder, G.L. & Chistilin, K.M., 2007. "Multiple time scales and the empirical models for stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 168-178.

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