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Unformatted text preview: 12 = 49
7
7
7 54 Example 6.5. Knockout options. In these options when the price falls
below a certain level the option is worthless no matter what the value of the
stock is at the end. To illustrate consider the binomial model from Example
6.4: u = 3/2, d = 2/3, and r = 1/6. This time we suppose S0 24 and consider
a call (S3 28)+ with a knockout barrier at 20, that is if the stock price drops
below 20 the option becomes worthless. As we have computed the risk neutral
probability is p⇤ = 0.6 and the value recursion is
Vn (a) = 6
[.6Vn (aH ) + .4Vn (aT )],
7 with the extra boundary condition that if the price is 20 the value is 0.
81
53 54
H
30 HH H
36
HH36
HH
8
16.839 HH
24
H 24
HH
H
HH
H
8.660
4.114 HH
H
H 16
H 16
H
H
0
0 To check the answer note that the knockout feature eliminates one of the paths
to 36 so
V0 = (6/7)3 [(.6)3 · 53 + 2(.6)2 (.4) · 8] = 8.660 From this we see that the knockout barrier reduced the value of the option by
(6/7)3 (0.6)2 (0.4) · 8 = 0.7255. 6.4 Capital A...
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 Spring '10
 DURRETT
 The Land

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