5. Binomial Tree Model
Reading: Chapter 12, Chapter 11 of
Luenberger
1

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5.1 A Toy Model That Could Later Be Made
Very Realistic
•
Suppose a stock is currently at price
S.
•
In a later time
t,
it could move up and down,
but only to one of the two
known
states:
•
We do not know the probability
p
that the
stock will go up, or (
1-p
) that it will go down.
So the stock price at
t
is
random
.
•
Is there a way to calculate
p?
How do we value
a call option
C
at
t=0
?
2
or
,
0.
Su
Sd u
d

How to make the toy model more realistic
(Chapter 11; will not cover in detail here)
•
Make
t
very small, and attach many
t
’
s
one
after the other.
•
Small fixed bistate changes in each
t
can add
to yield any value of change in a stock price at
larger time intervals.
•
We can match the historical volatility of this
stock with the volatility of the binomial tree
model to yield
3
and
t
t
u
e
d
e

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