Open Access
Subscription Access
Open Access
Subscription Access
Stock Market Modeling in the Langevin Formalism
Subscribe/Renew Journal
A Langevin formalism is proposed for stock market dynamics with modeling of various economic market features from first principles. Various processes and effects that occur in the stock market are mathematically incorporated in the said formulation. The Fokker Planck equation corresponding to the Langevin equation so obtained is solved and shows deviation from Gaussian behavior of the rate of change of stock price PDF. The deviation relates to factors such as market efficiency, market depth, liquidity of the relevant stock and informational asymmetries.
Keywords
Stock Market, Langevin Equation, Fokker Planck Equation, Black Scholes Model, Market Microstructure.
Subscription
Login to verify subscription
User
Font Size
Information
- Guillaume, D. M., Dacorogna, M. M., Dave, R. R., Muller, U. A., Olsen, R. B., & Pictet, O. V. (1997). From the bird’s eye view to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets. Finance and Stochastics, 1, 95–130.
- Mantegna, R., & Stanley, H. E. (1995). Scaling behaviour in the dynamics of an economic index. Nature: International Journal of Science, 376, 46–49.
- Cont, R., Potters, M., & Bouchaud, J. P. (1997). In Scale invariance and beyond (B. Dubrulle, F. Graner, D. Sornette, Eds.). EDP-Springer.
- R. Cont, cond-mat/9705075.
- Cizeau, P., Liu, Y., Meyer, M., Peng, C. K., & Stanley, H. E. (n.d.). Volatility distribution in the S&P500 Stock Index.,- cond-mat/9708143 and 970621.
- Potters, M., Cont, R., & Bouchaud, J. P. (1998). Financial markets as adaptive systems. Europhysics Letters, 41(3), 239–244.
- Sornette, D., Johansen, A., & Bouchaud, J. P. (1996). Stock market crashes, precursors and replicas. Journal of Physics, 6, 167–175.
- Feigenbaum, J. A., & Freund, P. G. O. (1996). Discrete scale invariance in stock markets before crashes. International Journal of Modern Physics, 10, 3737–3745.
- Vandewalle, N., Ausloos, M., Boveroux, P., & Minguet, A. (1998). How the financial crash of October 1997 could have been predicted. European Physical Journal B, 4, 139–141.
- Hull, J. (1997). Options, futures and other derivative securities (8th ed.). Upper Saddle River, NJ: Prentice-Hall.
- Grandmont, J. M. (1981). Handbook of mathematical economics (K. J. Arrow & M. D. Intriligator, Eds.). Elsevier.
- O’Hara, M. (1995). Market microstructure theory. Cambridge: Blackwell.
- Levy, M., Levy, H., & Solomon, S. (1995). Microscopic simulation of the stock market: The effect of microscopic diversity. Journal de Physique I, EDP Sciences, 5(8), 1087–1107.
- Bak, P., Paczuski, M., & Martin, S. (1997). Price variations in a stock market with many agents. Physica A: Statistical Mechanics and Its Applications, 246(3), 430–453.
- Caldarelli, G., Marsili, M., & Zhang, Y. C. (1997). A prototype model of stock exchange. Europhysics Letters, 40, 479–484.
- Cont, R., & Bouchaud, J. P. (2000). Macroeconomic Dynamics, in press; e-print, condmat/9712318.
- Hwa, T., & Kardar, M. (1992). Avalanches, hydrodynamics, and discharge events in models of sandpiles. Physical Review A, 45(10), 7002–7023.
- Hanggi, P., Talkner, P., & Borkovec, M. (1990). Reactionrate theory: Fifty years after Kramers. Reviews of Modern Physics, 52, 251.
- Johansen, A., & Sornette, D. (1998). Stock market crashes are outliers. European Physical Journal B, 1, 141–143.
- Markowitz, H. (1959). Portfolio selection efficient diversification of investment. New York, NY: John Wiley and Sons.
- Elton, E. J., & Gruber, M. J. (1995). Modern portfolio theory and investment analysis (5th ed.). New York: John Wiley and Sons.
Abstract Views: 261
PDF Views: 0