Modeling stock prices in a portfolio using multidimensional geometric brownian motion

Modeling and forecasting stock prices of public corporates are important studies in financial analysis, due to their stock price characteristics. Stocks investments give a wide variety of risks. Taking a portfolio of several stocks is one way to minimize risk. Stochastic process of single stock pric...

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Bibliographic Details
Published in:Journal of physics. Conference series 2018-05, Vol.1025 (1), p.12122
Main Authors: Maruddani, Di Asih I, Trimono
Format: Article
Language:English
Subjects:
Brownian motion
Department stores
Mathematical models
Mean Absolute Percentage Error
Modelling
Multidimensional Geometric Brownian Motion
Physics
Prices
Pricing
Stochastic Differential Equation
Stochastic processes
Two Dimensional Ito's Lemma
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Summary:Modeling and forecasting stock prices of public corporates are important studies in financial analysis, due to their stock price characteristics. Stocks investments give a wide variety of risks. Taking a portfolio of several stocks is one way to minimize risk. Stochastic process of single stock price movements model can be formulated in Geometric Brownian Motion (GBM) model. But for a portfolio that consist more than one corporate stock, we need an expansion of GBM Model. In this paper, we use multidimensional Geometric Brownian Motion model. This paper aims to model and forecast two stock prices in a portfolio. These are PT. Matahari Department Store Tbk and PT. Telekomunikasi Indonesia Tbk on period January 4, 2016 until April 21, 2017. The goodness of stock price forecast value is based on Mean Absolute Percentage Error (MAPE). As the results, we conclude that forecast two stock prices in a portfolio using multidimensional GBM give less MAPE than using GBM for single stock price respectively. We conclude that multidimensional GBM is more appropriate for modeling stock prices, because the price of each stock affects each other.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1025/1/012122