), The random character of stock market prices, MIT Press, Cambridge, MA, 1964, pp. Geometric Brownian motion has been extensively used as a model for stock prices, commodity prices, growth in demand for products and services, and real options analysis (Benninga & Tolkowsky 2002; Nembhard, Shi & Aktan 2002; Thorsen 1998). Assuming the historical data is stored in a variable named ‘electricitydata’, the, You may receive emails, depending on your. Kitagawa, G. & Sato, S., 2001, ‘Monte carlo smoothing and self-organising state space model’, in A. Doucet, N. de Freitas & N. Gordon (eds. & Stoffer, D.S., 2008, ‘Fitting stochastic volatility models in the presence of irregular sampling via particle methods and the EM algorithm’, Journal of Time Series Analysis 29(5), 811–833. The algorithm is as follows: The algorithm for the filtering is an extension of Godsill, Doucet and West’s (2004) and Kim and Stoffer’s (2008) algorithms. It can also follow GBM based on the Gaussian process. Choose a web site to get translated content where available and see local events and offers. & Siddique, A., 2000, ‘Conditional skewness in asset pricing tests’, Journal of Finance 55, 1263–1295. https://doi.org/10.1287/opre.7.2.145. (1995) and Nagahara (1996) revealed that the return distributions of Japanese stocks are fat-tailed and skewed. 193. The normal distribution is one of the most usually applied distributions. Duplantier, B., 2005, ‘Le mouvement brownien, “divers et ondoyant”’, Seminaire Poincare 1, 155–212. Table 3 summarises the estimated parameters for both the GBM normal and student’s t-distribution. Hence, the constant instantaneous expected drift assumption of the standard Brownian process is substituted with the constant expected rate of return in the geometric Brownian process (Hull 2000). The student’s t GBM model was compared and evaluated with the normal GBM model. A particle filter technique based on student’s t-distribution is developed to estimate the random effects and parameters for the extended model. The notation dt is an infinitely approaching 0 time difference between time points t and t - 1 and the last term involves random dBt ~ N(0, dt) increment to Brownian motion process. Practical/managerial implications: The proposed model which is heavier tailed than the normal does not only provide an approximate solution to non-normal estimation problem. Sattayatham, P., Intrasit, A. The functions provided by MATLAB enabled us to develop the techniques based on the student’s t GBM model and a strategy for fitting the model. Equivalently, S is lognormally distributed. Geometric Brownian motion (GBM), a stochastic differential equation, can be used to model phenomena that are subject to fluctuation and exhibit long-term trends, such as stock prices and the market value of goods. The GBM normal and student’s t–based particle filter method are then run on the simulated prices process, and the average MAPE is calculated. 0. https://doi.org/10.1287/mnsc.44.12.1650, Theodossiou, P., 2000, Skewed generalized error distribution of financial assets and option pricing, School of Business, Rutgers University, New Jersey, Newark. USA. The most used are the normal, the lognormal and the non-Gaussian stable distributions. Jarque C.M, Bera A.K., 1980. The significant kurtosis indicates that return distribution has sharp peaks compared to a normal distribution. This method applies the concept of sampling-importance-resampling (SIR) (Rubin 1987). was the project leader and was responsible for most of the theoretical and experimental work done. The log-likelihood for the GBM student’s t-distribution model is higher than that of the model for the GBM normal for each of the five stock series. 193, Estimation of Geometric Brownian Motion Parameters for Oil Price Analysis, Jakob Croghan, Iowa State UniversityFollow How to estimate parameters μ and σ of geometric Brownian Motion. John K. Jackman, Iowa State UniversityFollow https://doi.org/10.1016/j.nonrwa.2004.08.012, Theodossiou, P., 1998, ‘Financial data and the Skewed generalized T distribution’, Management Science 44(12), 1650–1661. Ross, S., 2000, Introduction to probability models, 7th edn., Harcourt Academic Press, New York. in Cootner, P.H. We apply the above-described methodology to model the stock prices of five firms of the NSE – each from five different sectors, namely the banking sector (Guaranteed Trust Bank [GTB]), oil and gas sector (Oando), construction sector (Julius Berger [Jberger]), health care sector (GlaxoSmith) and industrial goods sector (Chemical & Allied Product [CAP]) over the period 02 January 2010 to 31 December 2014. Theodossiou (1998) advocated the use of a skewed generalised t-distribution, which combines the student’s t and skewed student’s t, to model return distributions. Lieberman, B.M., 1989, ‘Capacity utilization: Theoretical models and empirical tests’, European Journal of Operational Research 40, 155–168. Table 1 reports the descriptive statistics for all the five selected indices. Harvey, C.R. Geometric Brownian motion (GBM) is a stochastic process. https://doi.org/10.1287/mnsc.48.8.1086.166. Kitagawa, G., 1996, ‘Monte Carlo filter and smoother for non-Gaussian nonlinear state space models’, Journal of Computational and Graphical. Follow 28 views (last 30 days) Duda R. on 30 Jun 2019. It has also been used for representing future demand in capacity studies (Lieberman 1989; Ryan 2006; Whitt 1981).
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