IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/2161.html
   My bibliography  Save this paper

An empirical model of volatility of returns and option pricing

Author

Listed:
  • McCauley, Joseph L.
  • Gunaratne, Gemunu H.

Abstract

This paper reports several entirely new results on financial market dynamics and option pricing We observe that empirical distributions of returns are much better approximated by an exponential distribution than by a Gaussian. This exponential distribution of asset prices can be used to develop a new pricing model for options (in closed algebraic form) that is shown to provide valuations that agree very well with those used by traders. We show how the Fokker-Planck formulation of fluctuations can be used with a local volatility (diffusion coeffficient) to generate an exponential distribution for asset returns, and also how fat tails for extreme returns are generated dynamically by a simple generalization of our new volatility model. Nonuniqueness in deducing dynamics from empirical data is discussed and is shown to have no practical effect over time scales much less than one hundred years. We derive an option pricing pde and explain why it‘s superfluous, because all information required to price options in agreement with the delta-hedge is already included in the Green function of the Fokker-Planck equation for a special choice of parameters. Finally, we also show how to calculate put and call prices for a stretched exponential returns density.

Suggested Citation

  • McCauley, Joseph L. & Gunaratne, Gemunu H., 2003. "An empirical model of volatility of returns and option pricing," MPRA Paper 2161, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:2161
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/2161/1/MPRA_paper_2161.pdf
    File Function: original version
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Gemunu H. Gunaratne & Joseph L. McCauley, 2002. "A theory for Fluctuations in Stock Prices and Valuation of their Options," Papers cond-mat/0209475, arXiv.org.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Giacomo Bormetti & Sofia Cazzaniga, 2011. "Multiplicative noise, fast convolution, and pricing," Papers 1107.1451, arXiv.org.
    2. de Mattos Neto, Paulo S.G. & Silva, David A. & Ferreira, Tiago A.E. & Cavalcanti, George D.C., 2011. "Market volatility modeling for short time window," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3444-3453.
    3. Shi, Leilei, 2006. "Does security transaction volume–price behavior resemble a probability wave?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 419-436.
    4. Decamps, Marc & De Schepper, Ann & Goovaerts, Marc, 2004. "Applications of δ-function perturbation to the pricing of derivative securities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(3), pages 677-692.
    5. McCauley, Joseph l., 2004. "Thermodynamic analogies in economics and finance: instability of markets," MPRA Paper 2159, University Library of Munich, Germany.
    6. Shu-Heng Chen & Sai-Ping Li, 2011. "Econophysics: Bridges over a Turbulent Current," Papers 1107.5373, arXiv.org.
    7. McCauley, Joseph L., 2003. "Scaling, correlations, and cascades in finance and turbulence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 213-221.
    8. McCauley, Joseph L., 2003. "Thermodynamic analogies in economics and finance: instability of markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 199-212.
    9. Bucsa, G. & Jovanovic, F. & Schinckus, C., 2011. "A unified model for price return distributions used in econophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3435-3443.
    10. Seemann, Lars & Hua, Jia-Chen & McCauley, Joseph L. & Gunaratne, Gemunu H., 2012. "Ensemble vs. time averages in financial time series analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 6024-6032.
    11. Bassler, Kevin E. & McCauley, Joseph L. & Gunaratne, Gemunu H., 2006. "Nonstationary increments, scaling distributions, and variable diffusion processes in financial markets," MPRA Paper 2126, University Library of Munich, Germany.
    12. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    13. Giacomo Bormetti & Sofia Cazzaniga, 2014. "Multiplicative noise, fast convolution and pricing," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 481-494, March.
    14. Ramos, Antônio M.T. & Carvalho, J.A. & Vasconcelos, G.L., 2016. "Exponential model for option prices: Application to the Brazilian market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 161-168.
    15. Joesph L. McCauley, 2002. "Self-Financing, Replicating Hedging Strategies, an incomplete thermodynamic analogy," Papers cond-mat/0203304, arXiv.org.

    More about this item

    Keywords

    Market instability; market dynamics; finance; option pricing;

    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • G0 - Financial Economics - - General
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

    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:pra:mprapa:2161. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter) or (Rebekah McClure). General contact details of provider: http://edirc.repec.org/data/vfmunde.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.