Modelling Share Prices Discussion 2022

Running header: Share prices 1
Modelling Share Prices
Name:
Course:
Instructor:
Institution:
Date:

prices 2
1. Downer Limited
Downer is company whose main purpose is to create, design, and maintain buildings and
infrastructure. Moreover, it the company is one of the leading providers of integrated services in both
New Zealand and Australia. The company aims at creating the effective space environment by building
efficient customer relationships through providing applicable and effective solutions. Notably, the
company has been in existence for approximately 150 years and has stable financial position thus it
qualifies in various security exchange platforms, such as the New Zealand and Australia. As a result, the
company is commonly referred ASX 100; besides, it possesses 88% of the Spotless Group Holdings
Limited (SPO). Therefore, this paper, seeks to analyze the behavior and performance of financial shares
of Downer EDI Limited.
2. Visualization
The following graph exhibits the share price (daily closing price) of Downer EDI limited for three
consecutive months (march, April, and may). The graph exhibits fluctuations on the share prices.

prices 3
3. Modelling of Share prices
In the financial sector, stock represent a share of ownership in a company thus investors buy
stocks with an expectation of yielding income generated from dividends and growth in value. There are
two factors that determine the current share prices, which include the past history of stock prices and the
any new information about the stock (Agustini, et al., 2018, 1). As a result, the stock prices assume a
Markov process, whereby the expected future prices rely on the present price. One of the techniques used
in the modelling of share prices is the stochastic modelling (Geometric Brownian motion) (GBM). The
Brownian motion, also known as the Winer process has been extensively used in physics to explain the
motion of a particle, subjected to a large number of smaller molecular shocks or disturbances (Imperial,
2018). Notably, the Brownian motion takes negative values thus it is not effective in modeling the share
prices; however, to curb this challenge the non-negative variation of BM, known as the GBM, S(t)
adopted (Imperial, 2018, 3). The GBM is defined by
S(t) = S0 exp X(t)
Whereby X(t) = μ + σ2/2
S0 is the initial value
S(t) is the Share price on the day (t)
μ is the drift
σ is the volatility
Notably, unlike the fixed-income investment the share price has variability associated with
randomness and the underlying Brownian motion, which could drop in value thus causing lose of money
by investors (Agustini, et al., 2018, 1).
i. Drift μ