IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v38y2008i3p769-777.html
   My bibliography  Save this article

A simple finite-difference stock market model involving intrinsic value

Author

Listed:
  • Melecký, Jan
  • Sergyeyev, Artur

Abstract

We suggest a deterministic delay difference model for the time series of the closing stock price and the intrinsic value of the stock. The most important new feature of this model is the equation describing the evolution of the intrinsic value. We present a general solution for the model in question and study the stability of the stationary points. Comparison with the real-world data shows that upon a suitable choice of parameters our model exhibits a behavior reasonably similar to that of the real stock, at least for shorter time ranges (those of several weeks).

Suggested Citation

  • Melecký, Jan & Sergyeyev, Artur, 2008. "A simple finite-difference stock market model involving intrinsic value," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 769-777.
  • Handle: RePEc:eee:chsofr:v:38:y:2008:i:3:p:769-777
    DOI: 10.1016/j.chaos.2007.01.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077907000355
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2007.01.016?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dieci, Roberto & Foroni, Ilaria & Gardini, Laura & He, Xue-Zhong, 2006. "Market mood, adaptive beliefs and asset price dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 520-534.
    2. Ivanova, K, 1999. "Toward a phase diagram for stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 270(3), pages 567-577.
    3. Farmer, J. Doyne & Joshi, Shareen, 2002. "The price dynamics of common trading strategies," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 149-171, October.
    4. Ide, Kayo & Sornette, Didier, 2002. "Oscillatory finite-time singularities in finance, population and rupture," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 307(1), pages 63-106.
    5. Chiarella, Carl & He, Xue-Zhong & Wang, Duo, 2006. "A behavioral asset pricing model with a time-varying second moment," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 535-555.
    6. Bouchaud, Jean-Philippe, 2002. "An introduction to statistical finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 313(1), pages 238-251.
    7. Gian-Italo Bischi & Vincenzo Valori, 2000. "Nonlinear effects in a discrete-time dynamic model of a stock market," Working Papers - Mathematical Economics 2000-01, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    8. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    9. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
    10. Sornette, Didier, 1998. "Linear stochastic dynamics with nonlinear fractal properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 250(1), pages 295-314.
    11. J. Barkley Rosser, Jr. & Honggang Li, 2004. "Market Dynamics and Stock Price Volatility," Computing in Economics and Finance 2004 91, Society for Computational Economics.
    12. Lux, Thomas, 1998. "The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(2), pages 143-165, January.
    13. Ausloos, M. & Vandewalle, N. & Boveroux, Ph. & Minguet, A. & Ivanova, K., 1999. "Applications of statistical physics to economic and financial topics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 274(1), pages 229-240.
    14. Jean-Philippe Bouchaud, 2002. "An introduction to statistical finance," Science & Finance (CFM) working paper archive 313238, Science & Finance, Capital Fund Management.
    15. D. Sornette & K. Ide, 2003. "Theory Of Self-Similar Oscillatory Finite-Time Singularities," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 267-275.
    16. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    17. Carl Chiarella, 1992. "The Dynamics of Speculative Behaviour," Working Paper Series 13, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    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. Sandrine Jacob Leal, 2015. "Fundamentalists, chartists and asset pricing anomalies," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1837-1850, November.
    2. Sandrine Jacob Leal, 2015. "Fundamentalists, Chartists and Asset pricing anomalies," Post-Print hal-01508002, HAL.
    3. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, November.
    4. Torsten Trimborn & Philipp Otte & Simon Cramer & Maximilian Beikirch & Emma Pabich & Martin Frank, 2020. "SABCEMM: A Simulator for Agent-Based Computational Economic Market Models," Computational Economics, Springer;Society for Computational Economics, vol. 55(2), pages 707-744, February.
    5. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186, Elsevier.
    6. Xue-Zhong He & Youwei Li, 2017. "The adaptiveness in stock markets: testing the stylized facts in the DAX 30," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 1071-1094, November.
    7. He, Xue-Zhong & Li, Youwei, 2007. "Power-law behaviour, heterogeneity, and trend chasing," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3396-3426, October.
    8. Jörn Dermietzel, 2008. "The Heterogeneous Agents Approach to Financial Markets – Development and Milestones," International Handbooks on Information Systems, in: Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), Handbook on Information Technology in Finance, chapter 19, pages 443-464, Springer.
    9. Hommes, C.H., 2005. "Heterogeneous Agent Models in Economics and Finance, In: Handbook of Computational Economics II: Agent-Based Computational Economics, edited by Leigh Tesfatsion and Ken Judd , Elsevier, Amsterdam 2006," CeNDEF Working Papers 05-03, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    10. Loretti I. Dobrescu & Mihaela Neamtu & Dumitru Opris, 2011. "A Discrete--Delay Dynamic Model for the Stock Market," Discussion Papers 2012-11, School of Economics, The University of New South Wales.
    11. Scheffknecht, Lukas & Geiger, Felix, 2011. "A behavioral macroeconomic model with endogenous boom-bust cycles and leverage dynamcis," FZID Discussion Papers 37-2011, University of Hohenheim, Center for Research on Innovation and Services (FZID).
    12. J. Doyne Farmer, 2002. "Market force, ecology and evolution," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 11(5), pages 895-953, November.
    13. J.-H. Steffi Yang & Satchell, S.E., 2002. "The Impact of Technical Analysis on Asset Price Dynamics," Cambridge Working Papers in Economics 0219, Faculty of Economics, University of Cambridge.
    14. Andrea Gaunersdorfer & Cars Hommes, 2007. "A Nonlinear Structural Model for Volatility Clustering," Springer Books, in: Gilles Teyssière & Alan P. Kirman (ed.), Long Memory in Economics, pages 265-288, Springer.
    15. Bauer, Christian & De Grauwe, Paul & Reitz, Stefan, 2009. "Exchange rate dynamics in a target zone--A heterogeneous expectations approach," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 329-344, February.
    16. Alessio Emanuele Biondo, 2019. "Order book modeling and financial stability," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(3), pages 469-489, September.
    17. Carl Chiarella & Xue-Zhong He & Duo Wang, 2004. "Statistical Properties of a Heterogeneous Asset Price Model with Time-Varying Second Moment," Research Paper Series 142, Quantitative Finance Research Centre, University of Technology, Sydney.
    18. Didier SORNETTE, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based Models," Swiss Finance Institute Research Paper Series 14-25, Swiss Finance Institute.
    19. Adam Majewski & Stefano Ciliberti & Jean-Philippe Bouchaud, 2018. "Co-existence of Trend and Value in Financial Markets: Estimating an Extended Chiarella Model," Papers 1807.11751, arXiv.org.
    20. LeBaron, Blake, 2006. "Agent-based Computational Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 24, pages 1187-1233, Elsevier.

    More about this item

    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:eee:chsofr:v:38:y:2008:i:3:p:769-777. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.