An Econophysics Model of Financial Bubbles
Author(s)
Bodo Herzog
ABSTRACT
Usually financial crises go along with bubbles in asset prices, such as the housing bubble in the US in 2007. This paper attempts to build a mathematical model of financial bubbles from an econophysics, and thus a new perspective. I find that agents identify bubbles only with a time delay. Furthermore, I demonstrate that the detection of bubbles is different on either the individual or collective point of view. Second, I utilize the findings for a new definition of asset bubbles in finance. Finally, I extend the model to the study of asset price dynamics with news. In conclusion, the model provides unique insights into the properties and developments of financial bubbles.
Usually financial crises go along with bubbles in asset prices, such as the housing bubble in the US in 2007. This paper attempts to build a mathematical model of financial bubbles from an econophysics, and thus a new perspective. I find that agents identify bubbles only with a time delay. Furthermore, I demonstrate that the detection of bubbles is different on either the individual or collective point of view. Second, I utilize the findings for a new definition of asset bubbles in finance. Finally, I extend the model to the study of asset price dynamics with news. In conclusion, the model provides unique insights into the properties and developments of financial bubbles.
Cite this paper
Herzog, B. (2015) An Econophysics Model of Financial Bubbles. Natural Science, 7, 55-63. doi: 10.4236/ns.2015.71006.
Herzog, B. (2015) An Econophysics Model of Financial Bubbles. Natural Science, 7, 55-63. doi: 10.4236/ns.2015.71006.
References
[1] Protter, P. (2013) A Mathematical Theory of Financial Bubbles. Paris-Princeton Lectures on Mathematical Finance, 2081, 1-108. [2] Pindyck, R.S. and Wang, N. (2009) The Economic and Policy Consequences of Catastrophes. MIT Sloan School Working Paper No. 4751-09, 1-26. [3] Barro, R.J. (2009) Rare Disasters and Asset Markets in the Twentieth Century. American Economic Review, 99, 243-264.
http://dx.doi.org/10.1257/aer.99.1.243 [4] Bikhchandani, S. and Sharma, S. (2000) Herd Behavior in Financial Markets: A Review. IMF Working Paper No. 00/48. [5] Diamond, D. and Dybvig, P. (1983) Bank Runs, Deposit Insurance, and Liquidity. Journal of Political Economy, 91, 401-409.
http://dx.doi.org/10.1086/261155 [6] DeLong, J.B., Schleifer, A., Summers, L. and Waldman, R. (1990) Positive Feedback Investment Strategies and Destabilizing Rational Speculation. Journal of Finance, 45, 379-395.
http://dx.doi.org/10.2307/2328662 [7] Froot, K., Scharfstein, D. and Stein, J. (1992) Herd on the Street: Informational Efficiencies in a Market with Short-Term Speculation. Journal of Finance, 47, 1461-1484.
http://dx.doi.org/10.1111/j.1540-6261.1992.tb04665.x [8] Lux, T. and Marchesi, M. (1999) Scaling and Criticality in a Stochastic Multiagent Model of a Financial Market. Nature, 397, 498-500.
http://dx.doi.org/10.1038/17290 [9] Banerjee, A. (1992) A Simple Model of Herd Behavior. Quarterly Journal of Economics, 107, 797-818.
http://dx.doi.org/10.2307/2118364 [10] Bikhchandani, S., Hirshleifer, D. and Welch, I. (1992) A Theory of Fads, Fashion, Custom and Cultural Change as Informational Cascades. Journal of Political Economy, 100, 992-1026.
http://dx.doi.org/10.1086/261849 [11] Bikhchandani, S., Hirshleifer, D. and Welch, I. (1998) Learning from the Behavior of Others: Conformity, Fads and Informational Cascades. Journal of Economic Perspectives, 12, 151-170.
http://dx.doi.org/10.1257/jep.12.3.151 [12] Devenov, A. and Welch, I. (1996) Rational Herding in Financial Economics. European Economic Review, 40, 603-615.
http://dx.doi.org/10.1016/0014-2921(95)00073-9 [13] Calvo, G. and Mendoza, E. (1998) Rational Herd Behavior and Globalization of Securities Markets. Mimeo, University of Maryland, College Park. [14] Maug, E. and Naik, N. (1996) Herding and Delegation Portfolio Management. Mimeo, London Business School, London. [15] Scharfstein, D. and Stein, J. (1990) Herd Behavior and Investment. American Economic Review, 80, 465-479. [16] Wemers, R. (1999) Mutual Fund Herding and the Impact on Stock Prices. Journal of Finance, 54, 581-622.
http://dx.doi.org/10.1111/0022-1082.00118 [17] Jain, A.K. and Gupta, S. (1987) Some Evidence on “Herding” Behavior of US Banks. Journal of Money, Credit and Banking, 19, 78-89.
http://dx.doi.org/10.2307/1992247 [18] Teh, L.L. and de Bondt, W.F.M. (1997) Herding Behavior and Stock Returns: An Exploratory Investigation. Swiss Journal of Economics and Statistics, 133, 293-323. [19] Graham, J.R. (1999) Herding among Investment Newsletters: Theory and Evidence. Journal of Finance, 54, 237-269.
http://dx.doi.org/10.1111/0022-1082.00103 [20] Galbraith, J.K. (1997) Savings, Investment, and Functional Efficiency: A Comparative Examination of National Financial Complexes: Comment. Chapter Comment, University of Michigan Press, Ann Arbor, 305-308. [21] Fransman, M. (2004) The Telecoms Boom and Bust 1996-2003 and the Role of Financial Markets. Journal of Evolutionary Economics, 14, 369-406. [22] Luhmann, N. (1994) Die Wirtschaft der Gesellschaft (suhrkamp taschenbuch wissenschaft). Suhrkamp Verlag, Berlin. [23] McCauley, J.L. (2004) Dynamics of Markets: Econophysics and Finance. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511606588
[1] Protter, P. (2013) A Mathematical Theory of Financial Bubbles. Paris-Princeton Lectures on Mathematical Finance, 2081, 1-108. [2] Pindyck, R.S. and Wang, N. (2009) The Economic and Policy Consequences of Catastrophes. MIT Sloan School Working Paper No. 4751-09, 1-26. [3] Barro, R.J. (2009) Rare Disasters and Asset Markets in the Twentieth Century. American Economic Review, 99, 243-264.
http://dx.doi.org/10.1257/aer.99.1.243 [4] Bikhchandani, S. and Sharma, S. (2000) Herd Behavior in Financial Markets: A Review. IMF Working Paper No. 00/48. [5] Diamond, D. and Dybvig, P. (1983) Bank Runs, Deposit Insurance, and Liquidity. Journal of Political Economy, 91, 401-409.
http://dx.doi.org/10.1086/261155 [6] DeLong, J.B., Schleifer, A., Summers, L. and Waldman, R. (1990) Positive Feedback Investment Strategies and Destabilizing Rational Speculation. Journal of Finance, 45, 379-395.
http://dx.doi.org/10.2307/2328662 [7] Froot, K., Scharfstein, D. and Stein, J. (1992) Herd on the Street: Informational Efficiencies in a Market with Short-Term Speculation. Journal of Finance, 47, 1461-1484.
http://dx.doi.org/10.1111/j.1540-6261.1992.tb04665.x [8] Lux, T. and Marchesi, M. (1999) Scaling and Criticality in a Stochastic Multiagent Model of a Financial Market. Nature, 397, 498-500.
http://dx.doi.org/10.1038/17290 [9] Banerjee, A. (1992) A Simple Model of Herd Behavior. Quarterly Journal of Economics, 107, 797-818.
http://dx.doi.org/10.2307/2118364 [10] Bikhchandani, S., Hirshleifer, D. and Welch, I. (1992) A Theory of Fads, Fashion, Custom and Cultural Change as Informational Cascades. Journal of Political Economy, 100, 992-1026.
http://dx.doi.org/10.1086/261849 [11] Bikhchandani, S., Hirshleifer, D. and Welch, I. (1998) Learning from the Behavior of Others: Conformity, Fads and Informational Cascades. Journal of Economic Perspectives, 12, 151-170.
http://dx.doi.org/10.1257/jep.12.3.151 [12] Devenov, A. and Welch, I. (1996) Rational Herding in Financial Economics. European Economic Review, 40, 603-615.
http://dx.doi.org/10.1016/0014-2921(95)00073-9 [13] Calvo, G. and Mendoza, E. (1998) Rational Herd Behavior and Globalization of Securities Markets. Mimeo, University of Maryland, College Park. [14] Maug, E. and Naik, N. (1996) Herding and Delegation Portfolio Management. Mimeo, London Business School, London. [15] Scharfstein, D. and Stein, J. (1990) Herd Behavior and Investment. American Economic Review, 80, 465-479. [16] Wemers, R. (1999) Mutual Fund Herding and the Impact on Stock Prices. Journal of Finance, 54, 581-622.
http://dx.doi.org/10.1111/0022-1082.00118 [17] Jain, A.K. and Gupta, S. (1987) Some Evidence on “Herding” Behavior of US Banks. Journal of Money, Credit and Banking, 19, 78-89.
http://dx.doi.org/10.2307/1992247 [18] Teh, L.L. and de Bondt, W.F.M. (1997) Herding Behavior and Stock Returns: An Exploratory Investigation. Swiss Journal of Economics and Statistics, 133, 293-323. [19] Graham, J.R. (1999) Herding among Investment Newsletters: Theory and Evidence. Journal of Finance, 54, 237-269.
http://dx.doi.org/10.1111/0022-1082.00103 [20] Galbraith, J.K. (1997) Savings, Investment, and Functional Efficiency: A Comparative Examination of National Financial Complexes: Comment. Chapter Comment, University of Michigan Press, Ann Arbor, 305-308. [21] Fransman, M. (2004) The Telecoms Boom and Bust 1996-2003 and the Role of Financial Markets. Journal of Evolutionary Economics, 14, 369-406. [22] Luhmann, N. (1994) Die Wirtschaft der Gesellschaft (suhrkamp taschenbuch wissenschaft). Suhrkamp Verlag, Berlin. [23] McCauley, J.L. (2004) Dynamics of Markets: Econophysics and Finance. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511606588