Abstract
A stochastic chartist–fundamentalist model of speculative asset dynamics in financial markets is developed. The model is represented by a stochastic delay-differential equation (SDDE). The SDDE is then solved using approximation and numerical Monte Carlo methods. The results show that for large time delays, the SDDE generates market-like stock price dynamics that reflect the memory effects of the time delay. The resultant dynamics agree with the empirical observation of the tendency of stock markets to deviate from pure random walk.
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References
Anufriev, M. (2007, April). Heterogeneous beliefs under different market architectures. Paper presented at the Workshop on Statistical Physics and Financial Markets, Abdus Salam International Center for Theoretical Physics (ICTP), Trieste, Italy.
Bukwar E. (2000) Introduction to the numerical analysis of stochastic delay differential equations. Journal of Computational and Applied Mathematics 125: 297–307
Chiarella, C. (2007, April). The stochastic price dynamics of speculative behavior. Paper presented at the Workshop on Statistical Physics and Financial Markets, Abdus Salam International Center for Theoretical Physics (ICTP), Trieste, Italy.
Chiarella C., Dieci R., Gardini L. (2002) Speculative behavior and complex asset price dynamics: A global analysis. Journal of Economic Behavior and Organization, 49(2): 173–197
Dibeh G. (2005) Speculative dynamics in a time delay model of asset prices. Physica A 355(1): 199–208
Dibeh G. (2007) Contagion effects in a chartist–fundamentalist model with time delays. Physica A 382(1): 52–57
Frank T. D. (2006) Time-dependent solutions for stochastic systems with delays: Perturbation theory and applications to financial physics. Physics Letters A 357: 275–283
Franke R., Sethi R. (1998) Cautious trend-seeking and complex asset price dynamics. Research in Economics 52(1): 61–79
Guillouzic S., L’Hereux I., Longtin A. (1999) Small delay approximation of stochastic delay differential equations. Physical Review E 59(4): 3970–3982
Guillouzic S., L’Hereux I., Longtin A. (2000) Rate processes in a delayed, stochastically driven, and overdamped system. Physical Review E 61(5): 4906–4914
Johnson H., Shanno D. (1987) Option pricing when the variance is changing. Journal of Financial and Quantitative Analysis 22(2): 143–152
Johnson N., Jefferies P., Hu P. M. (2002) Financial Market Complexity. Oxford University Press, Oxford
Kuchler U., Platen E. (2002) Weak discrete time approximation of stochastic differential equations with time delay. Mathematics and Computers in Simulation 59: 497–505
Lux T. (1995) Herd behavior, bubbles and crashes. Economic Journal 105: 881–896
Ohanian, L.E. (1996). When the bubble bursts: Psychology or Fundamentals? Business Review of the Federal Reserve Bank of Philadelphia (Jan–Feb), 3–13.
Pikovsky A., Kurths J. (1997) Coherence resonance in a noise-driven excitable system. Physical Review Letters 78: 775–778
Rumelin W. (1982) Numerical treatment of stochastic differential equations. SIAM Journal of Numerical Analysis 19: 604–613
Sethi R (1996) Endogenous Regime Switching in Speculative Markets. Structural Change and Economic Dynamics 7((1): 99–118
Tambe S. S., Inamdar S. R., Kulkarni B. D. (1995) Diffusive broadening of limit cycle in presence of noise: A case study of reversible Brusselator. Mathematcis and Computers in Simulation 39: 115–124
Westerhoff F. (2003) Speculative markets and the effectiveness of price limits. Journal of Economic Dynamics and Control 28: 493–508
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Dibeh, G., Harmanani, H.M. A Stochastic Chartist–Fundamentalist Model with Time Delays. Comput Econ 40, 105–113 (2012). https://doi.org/10.1007/s10614-012-9329-8
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DOI: https://doi.org/10.1007/s10614-012-9329-8