1
The Black-Scholes Model
Brief introduction
to stochastic processes (from
Ch. 13 and focusing on the lecture notes)
Markov process
Wi
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Wiener process
Generalized Wiener process
Ito process
Modeling stock prices – Geometric Brownian Motion
Black-Scholes-Merton model (reading:14.4-13.9,
14.11-14.12)
Markov Process
Markov process
stochastic process for which only the present
value of a variable is relevant for predicting
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the future.
The past history of the variable is
irrelevant.
Markov property of stock prices is
consistent with the weak form of market
efficiency.
Wiener Process
A Wiener process is a particular type of Markov
stochastic process with mean change of zero and a
variance rate of 1.0 per year.
A variable
z
follows a Wiener process if it has the
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A variable
z
follows a Wiener process if it has the
following two properties:
Property 1
: The change in
z
during a short period of time
t
is
, where
~
(0,1).
Property 2
:
The value change of
z
for any two different short
intervals of time are independent.
This property implies that z
follows a Markov process
z
t

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