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Uncertainty about fundamental, pessimistic and overconfident traders: a piecewise-linear maps approach. (English) Zbl 1480.91273

Summary: We analyze a financial market model with heterogeneous interacting agents where fundamentalists and chartists are considered. We assume that fundamentalists are homogeneous in their trading strategy but heterogeneous in their belief about the asset’s fundamental value. On the other hand, we consider that chartists, when they are optimistic become overconfident and they trade more than when they are pessimistic. Consequently, our model dynamics are driven by a one-dimensional piecewise-linear continuous map with three linear branches. We investigate the bifurcation structures in the map’s parameter space and describe the endogenous fear and greed market dynamics arising from our asset-pricing model.

MSC:

91G15 Financial markets
91B69 Heterogeneous agent models
Full Text: DOI

References:

[1] Anufriev, M.; Gardini, L.; Radi, D., Chaos, border collisions and stylized empirical facts in an asset pricing model with heterogeneous agents, Nonlinear Dyn., 102, 993-1017 (2020)
[2] Avrutin, V.; Gardini, L.; Sushko, I.; Tramontana, F., Continuous and Discontinuous Piecewise Smooth One-Dimensional Maps: Invariant Sets and Bifurcation Structures (2019), Singapore: World Scientific, Singapore · Zbl 1452.37002
[3] Bischi, GI; Chiarella, C.; Kopel, M.; Szidarovszky, F., Nonlinear Oligopolies (2010), New York: Springer, New York · Zbl 1182.91001
[4] Bischi, GI; Gallegati, M.; Gardini, L.; Leombruni, R.; Palestrini, A., Herd behavior and nonfundamental asset price fluctuations in financial markets, Macroecon. Dyn., 10, 4, 502 (2006) · Zbl 1278.91064
[5] Bischi, GI; Gardini, L.; Tramontana, F., Bifurcation curves in discontinuous maps, Discrete Contin. Dyn. Syst. B, 13, 2, 249 (2010) · Zbl 1187.37053
[6] Bischi, G.I., Lamantia, F.: Coexisting attractors and complex basins in discrete-time economic models. In: Nonlinear Dynamical Systems in Economics, pp. 187-231. Springer (2005) · Zbl 1310.91098
[7] Brianzoni, S.; Campisi, G., Dynamical analysis of a financial market with fundamentalists, chartists, and imitators, Chaos Solitons Fractals, 130, 109434 (2020)
[8] Brianzoni, S.; Mammana, C.; Michetti, E., Updating wealth in an asset pricing model with heterogeneous agents, Discrete Dyn. Nat. Soc., 2010, 386 (2010) · Zbl 1201.91066
[9] Brock, WA; Hommes, CH, Heterogeneous beliefs and routes to chaos in a simple asset pricing model, J. Econ. Dyn. Control, 22, 8-9, 1235-1274 (1998) · Zbl 0913.90042
[10] Campisi, G.; Muzzioli, S., Investor sentiment and trading behavior, Chaos Interdiscip. J. Nonlinear Sci., 30, 9, 093103 (2020) · Zbl 1451.91036 · doi:10.1063/5.0011636
[11] Campisi, G., Muzzioli, S.: Designing volatility indices for Austria, Finland and Spain. Financ. Mark. Portf. Manag. 1-87 (2021)
[12] Chiarella, C.; Dieci, R.; Gardini, L., Speculative behaviour and complex asset price dynamics: a global analysis, J. Econ. Behav. Organ., 49, 2, 173-197 (2002)
[13] Chiarella, C.; Dieci, R.; Gardini, L., The dynamic interaction of speculation and diversification, Appl. Math. Finance, 12, 1, 17-52 (2005) · Zbl 1113.91019
[14] Chiarella, C.; Dieci, R.; Gardini, L., Asset price and wealth dynamics in a financial market with heterogeneous agents, J. Econ. Dyn. Control, 30, 9-10, 1755-1786 (2006) · Zbl 1162.91473
[15] Chiarella, C., He, X.Z., Huang, W., Zheng, H.: Estimating behavioural heterogeneity under regime switching. J. Econ. Behav. Organ. 83(3), 446-460 (2012) (The Great Recession: motivation for re-thinking paradigms in macroeconomic modeling). doi:10.1016/j.jebo.2012.02.014
[16] Cont, R., Empirical properties of asset returns: stylized facts and statistical issues, Quant. Finance, 1, 223-236 (2001) · Zbl 1408.62174
[17] Day, RH, Complex dynamics, market mediation and stock price behavior, North Am. Actuar. J., 1, 3, 1-16 (1997)
[18] Day, RH; Huang, W., Bulls, bears and market sheep, J. Econ. Behav. Organ., 14, 3, 299-329 (1990)
[19] De Grauwe, P.; Kaltwasser, PR, Animal spirits in the foreign exchange market, J. Econ. Dyn. Control, 36, 8, 1176-1192 (2012) · Zbl 1345.91007
[20] Dercole, F., Radi, D.: Does the “uptick rule” stabilize the stock market? Insights from adaptive rational equilibrium dynamics. Chaos Solitons Fractals 130, 109426 (2020) · Zbl 1489.91157
[21] Dieci, R.; Westerhoff, F., Heterogeneous speculators, endogenous fluctuations and interacting markets: a model of stock prices and exchange rates, J. Econ. Dyn. Control, 34, 4, 743-764 (2010) · Zbl 1202.91184
[22] Elyasiani, E.; Gambarelli, L.; Muzzioli, S., Moment risk premia and the cross-section of stock returns in the European stock market, J. Bank. Finance, 111, 105732 (2020)
[23] Elyasiani, E., Gambarelli, L., Muzzioli, S.: The skewness index: uncovering the relationship with volatility and market returns. Appl. Econ. 1-17 (2021)
[24] Föllmer, H.; Horst, U.; Kirman, A., Equilibria in financial markets with heterogeneous agents: a probabilistic perspective, J. Math. Econ., 41, 1-2, 123-155 (2005) · Zbl 1118.91044
[25] Franke, R.; Westerhoff, F., Why a simple herding model may generate the stylized facts of daily returns: explanation and estimation, J. Econ. Interact. Coord., 11, 1, 1-34 (2016)
[26] Gallegati, M.; Palestrini, A.; Rosser, JB, The period of financial distress in speculative markets: interacting heterogeneous agents and financial constraints, Macroecon. Dyn., 15, 1, 60-79 (2011) · Zbl 1273.91196
[27] Gardini, L.; Tramontana, F., Border collision bifurcation curves and their classification in a family of 1d discontinuous maps, Chaos Solitons Fractals, 44, 4-5, 248-259 (2011)
[28] Giot, P., Relationships between implied volatility indexes and stock index returns, J. Portf. Manag., 31, 3, 92-100 (2005)
[29] Glaser, M.; Weber, M., Overconfidence and trading volume, Geneva Risk Insur. Rev., 32, 1, 1-36 (2007)
[30] Gu, EG, On the existence of chaos in a discontinuous area-preserving map arising in financial markets, Int. J. Bifurc. Chaos, 28, 14, 1850177 (2018) · Zbl 1410.37035
[31] Gu, EG; Guo, J., BCB curves and contact bifurcations in piecewise linear discontinuous map arising in a financial market, Int. J. Bifurc. Chaos, 29, 2, 1950022 (2019) · Zbl 1411.37076
[32] He, XZ; Li, Y., Power-law behaviour, heterogeneity, and trend chasing, J. Econ. Dyn. Control, 31, 10, 3396-3426 (2007) · Zbl 1163.91530
[33] He, XZ; Zheng, H., Trading heterogeneity under information uncertainty, J. Econ. Behav. Organ., 130, 64-80 (2016)
[34] Huang, W., Day, R.: Chaotically switching bear and bull markets: the derivation of stock price distributions from behavioral rules. Nonlinear Dyn. Evol. Econ. 169-182 (1993)
[35] Huang, W.; Zheng, H., Financial crises and regime-dependent dynamics, J. Econ. Behav. Organ., 82, 2, 445-461 (2012)
[36] Huang, W.; Zheng, H.; Chia, WM, Financial crises and interacting heterogeneous agents, J. Econ. Dyn. Control, 34, 6, 1105-1122 (2010) · Zbl 1230.91150
[37] Jungeilges, J., Maklakova, E., Perevalova, T.: Asset price dynamics in a “bull and bear market”. Struct. Chang. Econ. Dyn. 56, 117-128 (2021)
[38] Lux, T.; Marchesi, M., Volatility clustering in financial markets: a microsimulation of interacting agents, Int. J. Theor. Appl. Finance, 3, 4, 675-702 (2000) · Zbl 0967.91072
[39] Naimzada, AK; Ricchiuti, G., Heterogeneous fundamentalists and imitative processes, Appl. Math. Comput., 199, 1, 171-180 (2008) · Zbl 1134.91508
[40] Naimzada, AK; Ricchiuti, G., Dynamic effects of increasing heterogeneity in financial markets, Chaos Solitons Fractals, 41, 4, 1764-1772 (2009) · Zbl 1198.91138
[41] Naimzada, AK; Ricchiuti, G., Complexity with heterogeneous fundamentalists and a multiplicative price mechanism, Econ. Notes Rev. Bank. Finance Monet. Econ., 43, 3, 233-247 (2014)
[42] Nusse, HE; Ott, E.; Yorke, JA, Border-collision bifurcations: an explanation for observed bifurcation phenomena, Phys. Rev. E, 49, 2, 1073 (1994)
[43] Nusse, HE; Yorke, JA, Border-collision bifurcations including period two to period three for piecewise smooth systems, Phys. D Nonlinear Phenom., 57, 1-2, 39-57 (1992) · Zbl 0760.58031
[44] Panchuk, A.; Sushko, I.; Westerhoff, F., A financial market model with two discontinuities: bifurcation structures in the chaotic domain, Chaos Interdiscip. J. Nonlinear Sci., 28, 5, 055908 (2018) · Zbl 1395.91525
[45] Sushko, I.; Tramontana, F.; Westerhoff, F.; Avrutin, V., Symmetry breaking in a bull and bear financial market model, Chaos Solitons Fractals, 79, 57-72 (2015) · Zbl 1354.91179
[46] Tramontana, F.; Gardini, L.; Dieci, R.; Westerhoff, F., The emergence of bull and bear dynamics in a nonlinear model of interacting markets, Discrete Dyn. Nat. Soc., 2009, 845 (2009) · Zbl 1176.91082
[47] Tramontana, F., Gardini, L., Westerhoff, F.: Intricate asset price dynamics and one-dimensional discontinuous maps. Nonlinear Econ. Dyn. 43-57 (2010)
[48] Tramontana, F., Westerhoff, F.: One-dimensional discontinuous piecewise-linear maps and the dynamics of financial markets. In: Global Analysis of Dynamic Models in Economics and Finance, pp. 205-227. Springer (2013) · Zbl 1296.91118
[49] Tramontana, F.; Westerhoff, F., Piecewise-linear maps and their application to financial markets, Front. Appl. Math. Stat., 2, 10 (2016)
[50] Tramontana, F.; Westerhoff, F.; Gardini, L., On the complicated price dynamics of a simple one-dimensional discontinuous financial market model with heterogeneous interacting traders, J. Econ. Behav. Organ., 74, 3, 187-205 (2010)
[51] Tramontana, F.; Westerhoff, F.; Gardini, L., The bull and bear market model of Huang and day: some extensions and new results, J. Econ. Dyn. Control, 37, 11, 2351-2370 (2013) · Zbl 1402.91152
[52] Tramontana, F.; Westerhoff, F.; Gardini, L., One-dimensional maps with two discontinuity points and three linear branches: mathematical lessons for understanding the dynamics of financial markets, Decis. Econ. Finance, 37, 1, 27-51 (2014) · Zbl 1302.91199
[53] Tramontana, F.; Westerhoff, F.; Gardini, L., A simple financial market model with chartists and fundamentalists: market entry levels and discontinuities, Math. Comput. Simul., 108, 16-40 (2015) · Zbl 1540.91065
[54] Westerhoff, FH, Greed, fear and stock market dynamics, Physica A, 343, 635-642 (2004)
[55] Whaley, RE, The investor fear gauge, J. Portf. Manag., 26, 3, 12-17 (2000)
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