Application of Business Analytics to Real Life Real World

Business Analytics 1
APPLICATION OF BUSINESS ANALYTICS TO REAL LIFE REAL WORLD
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Business Analytics 2
Question 1
σ t- Refers to the variance per unit time and is usually used to giver order of random noise.
μt - refers to the expected return per unit time thus it controls drift.
σ t and μt are not constant. They vary with time.
Assumptions
a) It is assumed that stock prices satisfy the condition ds= μSdt +σ SdW.
b) All securities are assumed to be infinitely divisible.
c) The assumption that no dividends at the end of trading year is made.
d) It is assumed that trading is continuous and no short selling
e) taxes and costs of transactions are assumed to be zero
Question 2
7/19/2018 8/8/2018 8/28/2018 9/17/2018 10/7/2018 10/27/2018 11/16/2018
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A time series plot for Closing price,S(t) for British Petrolium p.l.c.
(BP) share price
Date
share price
Question 2 is practically done in excel. The stock prices from 1st august 2018 to 31st October
2018 is from www.yahoofinance .com is attached in excel sheet 1 are historical stock price data.

Business Analytics 3
Question 3
For a share price to be represented as geometric Brownian motion must meet the following
condition:
S(t) = S0 eW t .............................. equation (1)
Where W t = W 0 + σ Bt + μt
From equation (1), S(t) is lognormally distributed with W 0 + σ Bt and variance σ 2 t
r(t) = S (t )−S (t−1)
S (t−1) ~ N( μ,σ )
Where:
S ( t ) is the closing price for time, t
S ¿) is the closing price for period t-1
r(t) = S (t )−S (t−1)
S (t−1) ~ μδt +σ ∅ √ δ t
δt = 1 day = 1
30 month
μ is the mean
∅ ~ N(0,1)
σ is the annualized volatility
Simplifying r(t) gives :
S (t )−S (t−1)
S (t−1) = μδt +σ ∅ √δ t
S ( t )−S (t−1) = S(t−1)μδt +S(t−1)σ ∅ √δ t
S(t) = S(t-1)(1+μδt +σ ∅ √δ t)
Therefore,