IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1009.5129.html
   My bibliography  Save this paper

A certain estimate of volatility through return for stochastic volatility models

Author

Listed:
  • Mikhail Martynov
  • Olga Rozanova

Abstract

We study the dependence of volatility on the stock price in the stochastic volatility framework on the example of the Heston model. To be more specific, we consider the conditional expectation of variance (square of volatility) under fixed stock price return as a function of the return and time. The behavior of this function depends on the initial stock price return distribution density. In particular, we show that the graph of the conditional expectation of variance is convex downwards near the mean value of the stock price return. For the Gaussian distribution this effect is strong, but it weakens and becomes negligible as the decay of distribution at infinity slows down.

Suggested Citation

  • Mikhail Martynov & Olga Rozanova, 2010. "A certain estimate of volatility through return for stochastic volatility models," Papers 1009.5129, arXiv.org, revised Jul 2011.
    • Handle: RePEc:arx:papers:1009.5129
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1009.5129
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Miccichè, Salvatore & Bonanno, Giovanni & Lillo, Fabrizio & Mantegna, Rosario N, 2002. "Volatility in financial markets: stochastic models and empirical results," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 756-761.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. DAI & Feng QIN & Zifu, 2005. "DF Structure Models for Options Pricing," The IUP Journal of Applied Economics, IUP Publications, vol. 0(6), pages 61-77, November.
    2. Michele Vodret & Iacopo Mastromatteo & Bence Tóth & Michael Benzaquen, 2023. "Microfounding GARCH models and beyond: a Kyle-inspired model with adaptive agents," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 18(3), pages 599-625, July.
    3. Lemmens, D. & Liang, L.Z.J. & Tempere, J. & De Schepper, A., 2010. "Pricing bounds for discrete arithmetic Asian options under Lévy models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(22), pages 5193-5207.
    4. Gilles Daniel & Nathan Joseph & David Bree, 2005. "Stochastic volatility and the goodness-of-fit of the Heston model," Quantitative Finance, Taylor & Francis Journals, vol. 5(2), pages 199-211.
    5. feng dai, 2004. "The Partial Distribution: Definition, Properties and Applications in Economy," Econometrics 0403008, University Library of Munich, Germany.
    6. Li, Chao & Shang, Pengjian, 2018. "Complexity analysis based on generalized deviation for financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 118-128.
    7. 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.
    8. Lisa Borland & Jean-Philippe Bouchaud & Jean-Francois Muzy & Gilles Zumbach, 2005. "The Dynamics of Financial Markets -- Mandelbrot's multifractal cascades, and beyond," Science & Finance (CFM) working paper archive 500061, Science & Finance, Capital Fund Management.
    9. Jaume Masoliver & Josep Perello, 2006. "Multiple time scales and the exponential Ornstein-Uhlenbeck stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 6(5), pages 423-433.
    10. 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).
    11. F. Baldovin & F. Camana & M. Caporin & M. Caraglio & A.L. Stella, 2015. "Ensemble properties of high-frequency data and intraday trading rules," Quantitative Finance, Taylor & Francis Journals, vol. 15(2), pages 231-245, February.
    12. 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.
    13. Lisa Borland & Jean-Philippe Bouchaud & Jean-Francois Muzy & Gilles Zumbach, 2005. "The Dynamics of Financial Markets -- Mandelbrot's multifractal cascades, and beyond," Papers cond-mat/0501292, arXiv.org.
    14. Aki-Hiro Sato & Paolo Tasca & Takashi Isogai, 2015. "Dynamic Interaction Between Asset Prices and Bank Behavior: A Systemic Risk Perspective," Papers 1504.07152, arXiv.org, revised Feb 2017.
    15. Andria, Joseph & di Tollo, Giacomo & Kalda, Jaan, 2022. "The predictive power of power-laws: An empirical time-arrow based investigation," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    16. De Domenico, Federica & Livan, Giacomo & Montagna, Guido & Nicrosini, Oreste, 2023. "Modeling and simulation of financial returns under non-Gaussian distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 622(C).
    17. G. L. Buchbinder & K. M. Chistilin, 2006. "Multiple time scales and the empirical models for stochastic volatility," Papers physics/0611048, arXiv.org.
    18. Linden, Mikael, 2005. "Estimating the distribution of volatility of realized stock returns and exchange rate changes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 352(2), pages 573-583.
    19. Kim, Kyungwon & Jung, Sean S., 2014. "Empirical analysis of structural change in Credit Default Swap volatility," Chaos, Solitons & Fractals, Elsevier, vol. 60(C), pages 56-67.
    20. Feng Dai & Ling Liang, 2005. "The Advance in Partial Distribution: A New Mathematical Tool for Economic Management," EERI Research Paper Series EERI_RP_2005_04, Economics and Econometrics Research Institute (EERI), Brussels.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1009.5129. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.