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Diagnostics of Rational Expectation Financial Bubbles with Stochastic Mean-Reverting Termination Times

Listed author(s):
  • Li Lin
  • Didier Sornette
Registered author(s):

    We propose two rational expectation models of transient financial bubbles with heterogeneous arbitrageurs and positive feedbacks leading to self-reinforcing transient stochastic faster-than-exponential price dynamics. As a result of the nonlinear feedbacks, the termination of a bubble is found to be characterized by a finite-time singularity in the bubble price formation process ending at some potential critical time $\tilde{t}_c$, which follows a mean-reversing stationary dynamics. Because of the heterogeneity of the rational agents' expectations, there is a synchronization problem for the optimal exit times determined by these arbitrageurs, which leads to the survival of the bubble almost all the way to its theoretical end time. The explicit exact analytical solutions of the two models provide nonlinear transformations which allow us to develop novel tests for the presence of bubbles in financial time series. Avoiding the difficult problem of parameter estimation of the stochastic differential equation describing the price dynamics, the derived operational procedures allow us to diagnose bubbles that are in the making and to forecast their termination time. The tests performed on three financial markets, the US S&P500 index from 1 February 1980 to 31 October 2008, the US NASDAQ composite index from 1 January 1980 to 31 July 2008 and the Hong Kong Hang Seng index from 1 December 1986 to 30 November 2008, suggest the feasibility of advance bubble warning.

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    File URL: http://arxiv.org/pdf/0911.1921
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    Paper provided by arXiv.org in its series Papers with number 0911.1921.

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    Date of creation: Nov 2009
    Handle: RePEc:arx:papers:0911.1921
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    1. Hommes, C.H. & Wagener, F.O.O., 2008. "Complex evolutionary systems in behavioral finance," CeNDEF Working Papers 08-05, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    2. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    3. Joseph Chen & Harrison Hong & Jeremy C. Stein, 2001. "Breadth of Ownership and Stock Returns," NBER Working Papers 8151, National Bureau of Economic Research, Inc.
    4. Markus K Brunnermeier, 2002. "Bubbles and Crashes," FMG Discussion Papers dp401, Financial Markets Group.
    5. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2008. "Heterogeneity, Market Mechanisms, and Asset Price Dynamics," Research Paper Series 231, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Jean-Philippe Bouchaud & Rama Cont, 1998. "A Langevin approach to stock market fluctuations and crashes," Science & Finance (CFM) working paper archive 500027, Science & Finance, Capital Fund Management.
    7. Shleifer, Andrei & Vishny, Robert W, 1997. " The Limits of Arbitrage," Journal of Finance, American Finance Association, vol. 52(1), pages 35-55, March.
    8. Jennifer Lynch Koski & Jeffrey Pontiff, 1999. "How Are Derivatives Used? Evidence from the Mutual Fund Industry," Journal of Finance, American Finance Association, vol. 54(2), pages 791-816, 04.
    9. Jarrow, Robert A, 1980. " Heterogeneous Expectations, Restrictions on Short Sales, and Equilibrium Asset Prices," Journal of Finance, American Finance Association, vol. 35(5), pages 1105-1113, December.
    10. B. M. Roehner & D. Sornette, 2000. ""Thermometers" of Speculative Frenzy," Papers cond-mat/0001353, arXiv.org.
    11. Refet Gurkaynak, 2005. "Econometric Tests of Asset Price Bubbles: Taking Stock," Finance 0504008, EconWPA.
    12. D. Sornette & J. V. Andersen, 2001. "A Nonlinear Super-Exponential Rational Model of Speculative Financial Bubbles," Papers cond-mat/0104341, arXiv.org, revised Apr 2002.
    13. Kent Daniel & David Hirshleifer & Avanidhar Subrahmanyam, 1998. "Investor Psychology and Security Market Under- and Overreactions," Journal of Finance, American Finance Association, vol. 53(6), pages 1839-1885, December.
    14. J. Doyne Farmer, 2002. "Market force, ecology and evolution," Industrial and Corporate Change, Oxford University Press, vol. 11(5), pages 895-953, November.
    15. Thomas Lux & D. Sornette, 1999. "On Rational Bubbles and Fat Tails," Papers cond-mat/9910141, arXiv.org.
    16. Lintner, John, 1969. "The Aggregation of Investor's Diverse Judgments and Preferences in Purely Competitive Security Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 4(04), pages 347-400, December.
    17. W. A. Brock, 1993. "Pathways to Randomness in the Economy: Emergent Nonlinearity and Chaos in Economics and Finance," Working Papers 93-02-006, Santa Fe Institute.
    18. Blanchard, Olivier Jean, 1979. "Speculative bubbles, crashes and rational expectations," Economics Letters, Elsevier, vol. 3(4), pages 387-389.
    19. J. Michael Harrison & David M. Kreps, 1978. "Speculative Investor Behavior in a Stock Market with Heterogeneous Expectations," The Quarterly Journal of Economics, Oxford University Press, vol. 92(2), pages 323-336.
    20. Brock,W.A. & Hommes,C.H., 1998. "Rational animal spirits," Working papers 23, Wisconsin Madison - Social Systems.
    21. De Bondt, Werner F M & Thaler, Richard, 1985. " Does the Stock Market Overreact?," Journal of Finance, American Finance Association, vol. 40(3), pages 793-805, July.
    22. Kaizoji, Taisei & Sornette, Didier, 2008. "Market Bubbles and Chrashes," MPRA Paper 15204, University Library of Munich, Germany.
    23. Almazan, Andres & Brown, Keith C. & Carlson, Murray & Chapman, David A., 2004. "Why constrain your mutual fund manager?," Journal of Financial Economics, Elsevier, vol. 73(2), pages 289-321, August.
    24. De Long, J. Bradford & Shleifer, Andrei & Summers, Lawrence H. & Waldmann, Robert J., 1990. "Noise Trader Risk in Financial Markets," Scholarly Articles 3725552, Harvard University Department of Economics.
    25. Duffie, Darrell & Garleanu, Nicolae & Pedersen, Lasse Heje, 2002. "Securities lending, shorting, and pricing," Journal of Financial Economics, Elsevier, vol. 66(2-3), pages 307-339.
    26. Utpal Bhattacharya, 2008. "The Causes and Consequences of Recent Financial Market Bubbles: An Introduction," Review of Financial Studies, Society for Financial Studies, vol. 21(1), pages 3-10, January.
    27. Barberis, Nicholas & Shleifer, Andrei & Vishny, Robert, 1998. "A model of investor sentiment," Journal of Financial Economics, Elsevier, vol. 49(3), pages 307-343, September.
    28. A. Corcos & J. -P. Eckmann & A. Malaspinas & Y. Malevergne & D. Sornette, 2001. "Imitation and contrarian behavior: hyperbolic bubbles, crashes and chaos," Papers cond-mat/0109410, arXiv.org.
    29. Jegadeesh, Narasimhan & Titman, Sheridan, 1993. " Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency," Journal of Finance, American Finance Association, vol. 48(1), pages 65-91, March.
    30. Jose A. Scheinkman & Wei Xiong, 2003. "Overconfidence and Speculative Bubbles," Journal of Political Economy, University of Chicago Press, vol. 111(6), pages 1183-1219, December.
    31. Harrison Hong & Jeffrey D. Kubik & Jeremy C. Stein, 2003. "The Neighbor's Portfolio: Word-of-Mouth Effects in the Holdings and Trade of Money Managers," NBER Working Papers 9711, National Bureau of Economic Research, Inc.
    32. Narasimhan Jegadeesh, 2001. "Profitability of Momentum Strategies: An Evaluation of Alternative Explanations," Journal of Finance, American Finance Association, vol. 56(2), pages 699-720, 04.
    33. Carhart, Mark M, 1997. " On Persistence in Mutual Fund Performance," Journal of Finance, American Finance Association, vol. 52(1), pages 57-82, March.
    34. Andersen, J.V. & Sornette, D., 2004. "Fearless versus fearful speculative financial bubbles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 337(3), pages 565-585.
    35. 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.
    36. Miller, Edward M, 1977. "Risk, Uncertainty, and Divergence of Opinion," Journal of Finance, American Finance Association, vol. 32(4), pages 1151-1168, September.
    37. Michael J. Cooper & Roberto C. Gutierrez & Allaudeen Hameed, 2004. "Market States and Momentum," Journal of Finance, American Finance Association, vol. 59(3), pages 1345-1365, 06.
    38. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    39. Nishant Dass & Massimo Massa & Rajdeep Patgiri, 2008. "Mutual Funds and Bubbles: The Surprising Role of Contractual Incentives," Review of Financial Studies, Society for Financial Studies, vol. 21(1), pages 51-99, January.
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