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ECG590I Asset Pricing. Lecture 10: Binomial Trees
1
10
Binomial Trees
10.1
Onestep model
1.
Model structure
John Seater, North Carolina State University, Fall 2007
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2
There is only one time interval
(
t
0
; t
1
)
There are only two possible outcomes for
S
High, with probability
p
Low, with probability
1
±
p
In the diagram above, Low is shown below Initial and High is above
Initial, implying that one of the outcome is an increase in value and
the other is a decrease.
In general however, both outcomes could be increases or decreases. We
study the general model later.
John Seater, North Carolina State University, Fall 2007
ECG590I Asset Pricing. Lecture 10: Binomial Trees
3
2.
Pricing a call option: numerical example
(a)
Setup
The riskfree rate is
r
= 0
:
25
K
= 45
.
John Seater, North Carolina State University, Fall 2007
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4
(b)
Notice that
S
0
does not equal the discounted expected value of
S
1
:
S
0
= 32
<
1
1 +
r
E
[
S
1
]
=
1
1 + 0
:
25
[
p
60 + (1
±
p
)
30]
=
4
5
1
2
60 +
1
2
30
±
= 36
John Seater, North Carolina State University, Fall 2007
ECG590I Asset Pricing. Lecture 10: Binomial Trees
5
(c)
Pricing the call: riskless portfolio method
Consider the following portfolio:
Long
shares of stock
Short one call
Find the value of
that makes the portfolio riskless
If the stock rises to 60, the portfolio is worth
±
15
If the stock falls to 30, the portfolio is worth
.
To be riskless, the portfolio must have the same value for either
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This note was uploaded on 10/05/2009 for the course ECG 590 taught by Professor Msmorril during the Fall '08 term at N.C. State.
 Fall '08
 msmorril

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