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Expectations, Price Fluctuations and Lorenz Attractor

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  • Olkhov, Victor

Abstract

This paper describes expectations and Buy-Sell transactions of selected Stokes between economic agents and Exchange on economic space as ground for modeling trading volume and price fluctuations. We study simple model of mutual relations between transactions and expectations and derive economic equations that describe disturbances of price, trading volume and expectations. We obtain simple harmonic oscillations for price fluctuations. We show that our model economic equations can take form of Lorenz attractor. Our approximation of transactions and expectations and economic equations on disturbances of price, trading volume and expectations allows apply dynamical systems methods for modeling chaotic behavior of economic and financial systems.

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  • Olkhov, Victor, 2018. "Expectations, Price Fluctuations and Lorenz Attractor," MPRA Paper 89105, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:89105
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    as
    1. Markus K. Brunnermeier & Jonathan A. Parker, 2005. "Optimal Expectations," American Economic Review, American Economic Association, vol. 95(4), pages 1092-1118, September.
    2. Laurent Calvet & Adlai Fisher, 2002. "Multifractality In Asset Returns: Theory And Evidence," The Review of Economics and Statistics, MIT Press, vol. 84(3), pages 381-406, August.
    3. Tanaka, Mari & Bloom, Nicholas & David, Joel M. & Koga, Maiko, 2020. "Firm performance and macro forecast accuracy," Journal of Monetary Economics, Elsevier, vol. 114(C), pages 26-41.
    4. Douglas K. Pearce, 1983. "Stock prices and the economy," Economic Review, Federal Reserve Bank of Kansas City, vol. 68(Sep), pages 7-22.
    5. Hansen, Lars Peter & Sargent, Thomas J., 1980. "Formulating and estimating dynamic linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 7-46, May.
    6. John Heaton & Deborah Lucas, 2000. "Stock prices and fundamentals," Proceedings, Federal Reserve Bank of San Francisco, issue Apr.
    7. Sargent, Thomas J. & Wallace, Neil, 1976. "Rational expectations and the theory of economic policy," Journal of Monetary Economics, Elsevier, vol. 2(2), pages 169-183, April.
    8. Gontis, V. & Havlin, S. & Kononovicius, A. & Podobnik, B. & Stanley, H.E., 2016. "Stochastic model of financial markets reproducing scaling and memory in volatility return intervals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1091-1102.
    9. Tine Janžek & Petra Ziherl, 2013. "Overview of models and methods for measuring economic agent’s expectations," IFC Bulletins chapters, in: Bank for International Settlements (ed.), Proceedings of the Sixth IFC Conference on "Statistical issues and activities in a changing environment", Basel, 28-29 August 2012., volume 36, pages 172-179, Bank for International Settlements.
    10. Campbell, John Y., 1987. "Stock returns and the term structure," Journal of Financial Economics, Elsevier, vol. 18(2), pages 373-399, June.
    11. Alejandro-Quiñones, Ángel L. & Bassler, Kevin E. & Field, Michael & McCauley, Joseph L. & Nicol, Matthew & Timofeyev, Ilya & Török, Andrew & Gunaratne, Gemunu H., 2006. "A theory of fluctuations in stock prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 383-392.
    12. Starr,Ross M., 2011. "General Equilibrium Theory," Cambridge Books, Cambridge University Press, number 9780521533867.
    13. Olkhov, Victor, 2016. "Finance, risk and economic space," MPRA Paper 87172, University Library of Munich, Germany.
    14. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    15. John Y. Campbell & John Cochrane, 1999. "Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," Journal of Political Economy, University of Chicago Press, vol. 107(2), pages 205-251, April.
    16. van Binsbergen, Jules H. & Koijen, Ralph S.J., 2017. "The term structure of returns: Facts and theory," Journal of Financial Economics, Elsevier, vol. 124(1), pages 1-21.
    17. Gopikrishnan, P. & Plerou, V. & Gabaix, X. & Amaral, L.A.N. & Stanley, H.E., 2001. "Price fluctuations and market activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 137-143.
    18. J Vernon Henderson & Tim Squires & Adam Storeygard & David Weil, 2018. "The Global Distribution of Economic Activity: Nature, History, and the Role of Trade1," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(1), pages 357-406.
    19. Charles F. Manski, 2018. "Survey Measurement of Probabilistic Macroeconomic Expectations: Progress and Promise," NBER Macroeconomics Annual, University of Chicago Press, vol. 32(1), pages 411-471.
    20. Starr,Ross M., 2011. "General Equilibrium Theory," Cambridge Books, Cambridge University Press, number 9780521826457.
    21. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    22. Keim, Donald B. & Stambaugh, Robert F., 1986. "Predicting returns in the stock and bond markets," Journal of Financial Economics, Elsevier, vol. 17(2), pages 357-390, December.
    23. Massimiliano Caporin & Luca Corazzini & Michele Costola, 2014. "Measuring the Behavioral Component of Financial Fluctuations: An Analysis Based on the S&P 500," CREATES Research Papers 2014-33, Department of Economics and Business Economics, Aarhus University.
    24. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
    25. Robin Greenwood & Andrei Shleifer, 2014. "Expectations of Returns and Expected Returns," The Review of Financial Studies, Society for Financial Studies, vol. 27(3), pages 714-746.
    26. Benjamin M. Friedman & David I. Laibson, 1989. "Economic Implications of Extraordinary Movements in Stock Prices," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 20(2), pages 137-190.
    27. Jean-Michel Grandmont, 1992. "Expectations Driven Nonlinear Business Cycles," Cowles Foundation Discussion Papers 1022, Cowles Foundation for Research in Economics, Yale University.
    28. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    29. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
    30. Hansen, Lars Peter, 2013. "Uncertainty Outside and Inside Economic Models," Nobel Prize in Economics documents 2013-7, Nobel Prize Committee.
    31. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
    32. Richard H. Thaler, 2018. "From Cashews to Nudges: The Evolution of Behavioral Economics," American Economic Review, American Economic Association, vol. 108(6), pages 1265-1287, June.
    33. V. Plerou & P. Gopikrishnan & X. Gabaix & L. A. N. Amaral & H. E. Stanley, 2001. "Price fluctuations, market activity and trading volume," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 262-269.
    34. Fama, Eugene F., 1998. "Market efficiency, long-term returns, and behavioral finance," Journal of Financial Economics, Elsevier, vol. 49(3), pages 283-306, September.
    35. Jeff Dominitz & Charles F. Manski, 2011. "Measuring and interpreting expectations of equity returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(3), pages 352-370, April.
    36. V. Plerou & P. Gopikrishnan & L. A. N. Amaral & M. Meyer & H. E. Stanley, 1999. "Scaling of the distribution of price fluctuations of individual companies," Papers cond-mat/9907161, arXiv.org.
    37. Olkhov, Victor, 2016. "On Economic Space notion," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 372-381.
    38. Arrow, Kenneth J, 1974. "General Economic Equilibrium: Purpose, Analytic Techniques, Collective Choice," American Economic Review, American Economic Association, vol. 64(3), pages 253-272, June.
    39. Charles F. Manski, 2004. "Measuring Expectations," Econometrica, Econometric Society, vol. 72(5), pages 1329-1376, September.
    40. Blume, Lawrence E. & Easley, David, 1984. "Rational expectations equilibrium: An alternative approach," Journal of Economic Theory, Elsevier, vol. 34(1), pages 116-129, October.
    41. Erhan Bayraktar & Ulrich Horst & Ronnie Sircar, 2007. "Queueing Theoretic Approaches to Financial Price Fluctuations," Papers math/0703832, arXiv.org.
    42. Vygintas Gontis & Shlomo Havlin & Aleksejus Kononovicius & Boris Podobnik & H. Eugene Stanley, 2015. "Stochastic model of financial markets reproducing scaling and memory in volatility return intervals," Papers 1507.05203, arXiv.org, revised Oct 2016.
    43. Sohei Kaihatsu & Takushi Kurozumi, 2014. "Sources of Business Fluctuations: Financial or Technology Shocks?," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(2), pages 224-242, April.
    44. Olkhov, Victor, 2017. "Quantitative Description of Financial Transactions and Risks," MPRA Paper 87316, University Library of Munich, Germany.
    45. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
    46. Nathan S. Balke & Mark E. Wohar, 2001. "Explaining stock price movements: is there a case for fundamentals?," Economic and Financial Policy Review, Federal Reserve Bank of Dallas, issue Q III, pages 22-34.
    47. Lucas, Robert Jr., 1972. "Expectations and the neutrality of money," Journal of Economic Theory, Elsevier, vol. 4(2), pages 103-124, April.
    48. Segnon, Mawuli & Lux, Thomas, 2013. "Multifractal models in finance: Their origin, properties, and applications," Kiel Working Papers 1860, Kiel Institute for the World Economy (IfW Kiel).
    49. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    50. Finn Kydland & Edward C. Prescott, 1980. "A Competitive Theory of Fluctuations and the Feasibility and Desirability of Stabilization Policy," NBER Chapters, in: Rational Expectations and Economic Policy, pages 169-198, National Bureau of Economic Research, Inc.
    51. Carbone, A. & Castelli, G. & Stanley, H.E., 2004. "Time-dependent Hurst exponent in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 267-271.
    52. Benoit Mandelbrot & Adlai Fisher & Laurent Calvet, 1997. "A Multifractal Model of Asset Returns," Cowles Foundation Discussion Papers 1164, Cowles Foundation for Research in Economics, Yale University.
    53. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2003. "A theory of power-law distributions in financial market fluctuations," Nature, Nature, vol. 423(6937), pages 267-270, May.
    54. Brock, William A. & Sayers, Chera L., 1988. "Is the business cycle characterized by deterministic chaos?," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 71-90, July.
    55. Anishchenko, V.S. & Vadivasova, T.E. & Okrokvertskhov, G.A. & Strelkova, G.I., 2003. "Correlation analysis of dynamical chaos," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 325(1), pages 199-212.
    56. 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..
    57. Olkhov, Victor, 2017. "Quantitative wave model of macro-finance," International Review of Financial Analysis, Elsevier, vol. 50(C), pages 143-150.
    58. Stanley, H. Eugene & Plerou, Vasiliki & Gabaix, Xavier, 2008. "A statistical physics view of financial fluctuations: Evidence for scaling and universality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3967-3981.
    59. Wändi Bruine de Bruin & Michael F. Bryan & Simon M. Potter & Giorgio Topa & Wilbert Van der Klaauw, 2008. "Rethinking the measurement of household inflation expectations: preliminary findings," Staff Reports 359, Federal Reserve Bank of New York.
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    Cited by:

    1. Olkhov, Victor, 2019. "New Essentials of Economic Theory," MPRA Paper 95065, University Library of Munich, Germany.
    2. Olkhov, Victor, 2019. "New Essentials of Economic Theory I. Assumptions, Economic Space and Variables," MPRA Paper 93085, University Library of Munich, Germany.
    3. Olkhov, Victor, 2019. "New essentials of economic theory II. Economic transactions, expectations and asset pricing," MPRA Paper 93428, University Library of Munich, Germany.
    4. Olkhov, Victor, 2019. "New Essentials of Economic Theory III. Economic Applications," MPRA Paper 94053, University Library of Munich, Germany.
    5. Olkhov, Victor, 2019. "Econophysics of Asset Price, Return and Multiple Expectations," MPRA Paper 91587, University Library of Munich, Germany.
    6. Olkhov, Victor, 2022. "Economic Policy - the Forth Dimension of the Economic Theory," MPRA Paper 112685, University Library of Munich, Germany.
    7. Olkhov, Victor, 2019. "Methods of Economic Theory: Variables, Transactions and Expectations as Functions of Risks," MPRA Paper 95628, University Library of Munich, Germany.
    8. Victor Olkhov, 2019. "Financial Variables, Market Transactions, and Expectations as Functions of Risk," IJFS, MDPI, vol. 7(4), pages 1-27, November.

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    More about this item

    Keywords

    Financial Transactions; Expectations; Economic Space; Stochastic Prices;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • E00 - Macroeconomics and Monetary Economics - - General - - - General
    • E03 - Macroeconomics and Monetary Economics - - General - - - Behavioral Macroeconomics
    • E30 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - General (includes Measurement and Data)
    • G02 - Financial Economics - - General - - - Behavioral Finance: Underlying Principles
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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