JMF  Vol.5 No.2 , May 2015
Prediction of Stock Price Movement Using Continuous Time Models
Abstract: Predicting stock price movement is generally accepted to be challenging such that until today it is continuously being attempted. This paper attempts to address the problem of stock price movement using continuous time models. Specifically, the paper provides comparative analysis of continuous time models—General Brownian Motion (GBM) and Variance Gamma (VG) in predicting the direction and accurate stock price levels using Monte Carlo methods—Quasi Monte Carlo (QMC) and Least Squares Monte Carlo (LSMC). The hit ratio and mean-absolute percentage error (MAPE) were used to evaluate the models. The empirical tests suggest that either the GBM model or VG model in any Monte Carlo method can be used to predict the direction of stock price movement. In terms of predicting the stock price values, the empirical findings suggest that the GBM model performs well in the QMC method and the VG model performs well in the LSMC method.
Cite this paper: Sonono, M. , Mashele, H. (2015) Prediction of Stock Price Movement Using Continuous Time Models. Journal of Mathematical Finance, 5, 178-191. doi: 10.4236/jmf.2015.52017.

[1]   Leung, M., Daouk, H. and Chen, A. (2000) Forecasting Stock Indices: A Comparison of Classification and Level Estimation Models. International Journal of Forecasting, 16, 173-190.

[2]   Maberly, E.D. (1986) The Informational Content of the Interday Price Change with Respect to Stock Index. Journal of Futures Markets, 6, 385-395.

[3]   Wu, Y. and Zhang, H. (1997) Forward Premiums as Unbiased Predictors of Future Currency Depreciation: A Non- Parametric Analysis. Journal of International Money and Finance, 16, 609-623.

[4]   Aggarwal, R. and Demaskey, A. (1997) Using Derivatives in Major Currencies for Cross-Hedging Currency Risks in Asian Emerging Markets. Journal of Future Markets, 17, 781-796.<781::AID-FUT3>3.0.CO;2-J

[5]   Imandoust, S. and Bolandraftar, M. (2014) Forecasting the Direction of Stock Market Index Movement Using Three Data Mining Techniques: The Case of Tehran Stock Exchange. International Journal of Engineering Research and Applications, 4, 106-117.

[6]   Abidin, S. and Jaffar, M.M. (2012) A Review on Geometric Brownian Motion in Forecasting the Share Prices in Bursa Malaysia. World Applied Sciences Journal, 17, 87-93.

[7]   Abidin, S. and Jaffar, M.M. (2014) Forecasting Share Prices of Small Size Companies in Bursa Malaysia. Applied Mathematics and Information Sciences, 8, 107-112.

[8]   Mandelbrot, B.B. (1963) TheVariation of Speculative Prices. Journal of Business, 36, 394-419.

[9]   Fama, E. (1965) The Behaviour of Stock Market Prices. Journal of Business, 64, 34-105.

[10]   Madan, D.B. and Seneta, E. (1990) The Variance Gamma Model for Share Market Returns. Journal of Business, 64, 511-524.

[11]   Glasserman, P. (2003) Monte Carlo Methods in Financial Engineering. Springer, Berlin.

[12]   Caflisch, R.E. (1998) Monte Carlo and Quasi-Monte Carlo Methods. Acta Numerica, 7, 1-49.

[13]   Corwin, J., Boyle, P. and Tan, K.S. (1996) Quasi-Monte Carlo Methods in Finance. Numerical Finance Management Science, 42, 926-938.

[14]   Shiryaev, A., Xu, Z.Q. and Zhou, X.Y. (2008) Thou Shalt Buy and Hold. Quantitative Finance, 8, 765-776.

[15]   Yam, S.C.P., Yung, S.P. and Zhou, W. (2012) Optimal Selling Time in Stock Market over a Finite Time Horizon. Acta Mathematicae Applicatae Sinica, English Series, 28, 557-570.

[16]   Bellman, R. (1957) Dynamic Programming. Princeton University Press, Princeton.

[17]   Longstaff, F.A. and Schwartz, E.S. (2001) Valuing American Options by Simulation: A Simple Least-Squares Approach. Review of Financial Studies, 14, 113-147.

[18]   Madan, D.B., Carr, P.P. and Chang, E.C. (1998) The Variance Gamma Process and Option Pricing. Review of Finance, 2, 79-105.

[19]   Carr, P., Geman, H., Madan, D.B. and Yor, M. (2002) The Fine Structure of Asset Returns: An Empirical Investigation. The Journal of Business, 75, 305-333.