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The emergence of bull and bear dynamics in a nonlinear model of interacting markets. (English) Zbl 1176.91082

Summary: We develop a three-dimensional nonlinear dynamic model in which the stock markets of two countries are linked through the foreign exchange market. Connections are due to the trading activity of heterogeneous speculators. Using analytical and numerical tools, we seek to explore how the coupling of the markets may affect the emergence of bull and bear market dynamics. The dimension of the model can be reduced by restricting investors’ trading activity, which enables the dynamic analysis to be performed stepwise, from low-dimensional cases up to the full three-dimensional model. In our paper we focus mainly on the dynamics of the one- and two- dimensional cases, with numerical experiments and some analytical results, and also show that the main features persist in the three-dimensional model.

MSC:

91B60 Trade models
91B54 Special types of economic markets (including Cournot, Bertrand)
37N40 Dynamical systems in optimization and economics
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References:

[1] R. H. Day and W. Huang, “Bulls, bears and market sheep,” Journal of Economic Behavior and Organization, vol. 14, no. 3, pp. 299-329, 1990. · doi:10.1016/0167-2681(90)90061-H
[2] A. Kirman, “Epidemics of opinion and speculative bubbles in financial markets,” in Money and Financial Markets, M. Taylor, Ed., pp. 354-368, Blackwell, Oxford, UK, 1991.
[3] C. Chiarella, “The dynamics of speculative behaviour,” Annals of Operations Research, vol. 37, no. 1-4, pp. 101-123, 1992. · Zbl 0777.90008 · doi:10.1007/BF02071051
[4] P. De Grauwe, H. Dewachter, and M. Embrechts, Exchange Rate Theory: Chaotic Models of Foreign Exchange Markets, Blackwell, Oxford, UK, 1993.
[5] W. Huang and R. H. Day, “Chaotically switching bear and bull markets: the derivation of stock price distributions from behavioral rules,” in Non-Linear Dynamics and Evolutionary Economics, R. H. Day and P. Chen, Eds., pp. 169-182, Oxford University Press, Oxford, UK, 1993.
[6] T. Lux, “Herd behavior, bubbles and crashes,” The Economic Journal, vol. 105, no. 431, pp. 881-896, 1995. · doi:10.2307/2235156
[7] T. Lux, “The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions,” Journal of Economic Behavior and Organization, vol. 33, no. 2, pp. 143-165, 1998. · doi:10.1016/S0167-2681(97)00088-7
[8] W. A. Brock and C. H. Hommes, “Heterogeneous beliefs and routes to chaos in a simple asset pricing model,” Journal of Economic Dynamics & Control, vol. 22, no. 8-9, pp. 1235-1274, 1998. · Zbl 0913.90042 · doi:10.1016/S0165-1889(98)00011-6
[9] C. Chiarella and X.-Z. He, “Asset price and wealth dynamics under heterogeneous expectations,” Quantitative Finance, vol. 1, no. 5, pp. 509-526, 2001. · doi:10.1088/1469-7688/1/5/303
[10] C. Chiarella and X.-Z. He, “Heterogeneous beliefs, risk and learning in a simple asset pricing model with a market maker,” Macroeconomic Dynamics, vol. 7, no. 4, pp. 503-536, 2003. · Zbl 1058.91031 · doi:10.1017/S1365100502020114
[11] J. D. Farmer and S. Joshi, “The price dynamics of common trading strategies,” Journal of Economic Behavior and Organization, vol. 49, no. 2, pp. 149-171, 2002. · doi:10.1016/S0167-2681(02)00065-3
[12] C. Chiarella, R. Dieci, and L. Gardini, “Speculative behaviour and complex asset price dynamics: a global analysis,” Journal of Economic Behavior and Organization, vol. 49, no. 2, pp. 173-197, 2002. · doi:10.1016/S0167-2681(02)00066-5
[13] C. Hommes, H. Huang, and D. Wang, “A robust rational route to randomness in a simple asset pricing model,” Journal of Economic Dynamics & Control, vol. 29, no. 6, pp. 1043-1072, 2005. · Zbl 1202.91110 · doi:10.1016/j.jedc.2004.08.003
[14] C. Hommes, “Heterogeneous agent models in economics and finance,” in Handbook of Computational Economics Vol. 2: Agent-Based Computational Economics, L. Tesfatsion and K. Judd, Eds., North-Holland, Amsterdam, The Netherlands, 2006.
[15] B. LeBaron, “Agent-based computational finance,” in Handbook of Computational Economics Vol. 2: Agent-Based Computational Economics, L. Tesfatsion and K. Judd, Eds., pp. 1187-1233, North-Holland, Amsterdam, The Netherlands, 2006.
[16] T. Lux, “Financial power laws: empirical evidence, models and mechanisms,” in Power Laws in the Social Sciences: Discovering Complexity and Non-Equilibrium Dynamics in the Social Universe, C. Cioffi-Revilla, Ed., Cambridge University Press, Cambridge, UK, 2008.
[17] F. Westerhoff, “Exchange rate dynamics: a nonlinear survey,” in Handbook of Research on Complexity, J. B. Rosser, Ed., Edward Elgar, Cheltenham, UK, 2009.
[18] C. Chiarella, R. Dieci, and X.-Z. He, “Heterogeneity, market mechanisms and asset price dynamics,” in Handbook of Financial Markets: Dynamics and Evolution, T. Hens and K. R. Schenk-Hoppe, Eds., pp. 277-344, North Holland, Amsterdam, The Netherlands, 2009.
[19] F. Westerhoff, “Multiasset market dynamics,” Macroeconomic Dynamics, vol. 8, no. 5, pp. 596-616, 2004. · Zbl 1134.91392 · doi:10.1017/S1365100504040040
[20] C. Chiarella, R. Dieci, and L. Gardini, “The dynamic interaction of speculation and diversification,” Applied Mathematical Finance, vol. 12, no. 1, pp. 17-52, 2005. · Zbl 1113.91019 · doi:10.1080/1350486042000260072
[21] F. H. Westerhoff and R. Dieci, “The effectiveness of Keynes-Tobin transaction taxes when heterogeneous agents can trade in different markets: a behavioral finance approach,” Journal of Economic Dynamics & Control, vol. 30, no. 2, pp. 293-322, 2006. · Zbl 1198.91162 · doi:10.1016/j.jedc.2004.12.004
[22] R. Dieci and F. Westerhoff, “Heterogeneous speculators, endogenous fluctuations and interacting markets: a model of stock prices and exchange rates,” Working paper, University of Bologna, Bologna, Italy, 2008. · Zbl 1202.91184
[23] R. Dieci, G.-I. Bischi, and L. Gardini, “From bi-stability to chaotic oscillations in a macroeconomic model,” Chaos, Solitons & Fractals, vol. 12, no. 5, pp. 805-822, 2001. · Zbl 1032.91093 · doi:10.1016/S0960-0779(00)00055-2
[24] X.-Z. He and F. H. Westerhoff, “Commodity markets, price limiters and speculative price dynamics,” Journal of Economic Dynamics & Control, vol. 29, no. 9, pp. 1577-1596, 2005. · Zbl 1198.91161 · doi:10.1016/j.jedc.2004.09.003
[25] C. Mira, L. Gardini, A. Barugola, and J.-C. Cathala, Chaotic Dynamics in Two-Dimensional Noninvertible Maps, vol. 20 of World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, World Scientific, River Edge, NJ, USA, 1996. · Zbl 0906.58027
[26] C. Grebogi, E. Ott, and J. A. Yorke, “Crises, sudden changes in chaotic attractors, and transient chaos,” Physica D, vol. 7, no. 1-3, pp. 181-200, 1983. · Zbl 0561.58029 · doi:10.1016/0167-2789(83)90126-4
[27] F. Tramontana, L. Gardini, R. Dieci, and F. Westerhoff, “The emergence of “bull and bear” dynamics in a nonlinear model of interacting markets,” in Nonlinear Dynamics in Economics, Finance and Social Sciences, C. Chiarella, G. I. Bischi, and L. Gardini, Eds., Springer, New York, NY, USA, 2009. · Zbl 1176.91082 · doi:10.1155/2009/310471
[28] R. W. Farebrother, “Simplified Samuelson conditions for cubit and quartic equations,” The Manchester School of Econonomics and Social Studies, vol. 41, no. 4, pp. 396-400, 1973. · doi:10.1111/j.1467-9957.1973.tb00090.x
[29] G. Gandolfo, Economic Dynamics: Methods and Models, vol. 16 of Advanced Textbooks in Economics, North-Holland, Amsterdam, The Netherlands, 2nd edition, 1980. · Zbl 0464.90001
[30] S. N. Elaydi, An Introduction to Difference Equations, Springer, New York, NY, USA, 1995. · Zbl 0855.39003
[31] K. Okuguchi and K. Irie, “The Shur and Samuelson conditions for a cubic equation,” The Manchester School of Econonomics and Social Studies, vol. 58, no. 4, pp. 414-418, 1990. · doi:10.1111/j.1467-9957.1990.tb00431.x
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