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Unformatted text preview: l use the binomial model in (6.16) but
now suppose S0 = 8 and consider the put option with value V3 = (10 S3 )+ .
The value of this option depends only on the price so we can reduce the tree
considered above to: 189 6.3. CONCRETE EXAMPLES 64
0
32
H
0 HH
H
0
HH
16 16
H
H
0
0.96 HH
8
H8
0.1
H
H
H
H
1.728
2.4 HH
H
HH 4
HH 4
0.1866
1/2
HH
H
6
3.2 HH
H
H2
0.6
H
H
6 HH
HH 1
1
H
9 On the tree itself stock prices are above the nodes and option prices below. To
explain the computation of the option price note that by (6.17).
V2 (2) = 0.4[V3 (4) + V3 (1)] = 0.4 · [8 + 9] = 6.8 V2 (8) = 0.4[V3 (16) + V3 (2)] = 0.4 · [0 + 6] = 2.4 V2 (32) = 0 V1 (4) = 0.4[V2 (8) + V2 (2)] = 0.4 · [2.4 + 6] = 3.36 V1 (16) = 0.4[V2 (32) + V2 (8)] = 0.4 · [0 + 2.4] = 0.96 V0 (8) = 0.4[V1 (16) + V1 (40] = 0.4 · [0.96 + 3.36] = 1.728 Again if one only wants the option price then Theorem 6.5 is much quicker: 1
3
3
= 1.728
V0 = (4/5) · 6 · + 9 ·
8
8
However if we want to compute the replicating strategy
n (a) = Vn+1 (a...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).
 Spring '10
 DURRETT
 The Land

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