Unformatted text preview: the ﬁrst
equation from the second):
25 = 100x ⇒ x = 1
4 1
And also we have y = − 8 . So we must have PC = 1 PA − 1 PB .
4
8 Summary of old example
We have two future times (t = 1 and t = 2) and two assets with
diﬀerent cash ﬂows at those times (Bond A and Bond B), so we
can replicate any future cash ﬂows.
We do this by solving two equations and two unknowns. Binomial Stock Example I Stock: 100 150
50 Bond: 95 100
100 There are two random states of nature
bond and stock have diﬀerent payoﬀs in each states C0 =??? 25
0 Binomial Stock Example I (continued)
The previous solution carries over by changing t = 1 and t = 2 to
”up” state and ”down” state:
Stock: 100 Bond: 95 Call: C0 150
50 100
100 25
0 Binomial Stock Example I (continued)
If we buy x units of Bond A the stock and y units of Bond B the
zero coupon bond, then the cash ﬂows are:
CF in the down state is 50x + 100y
CF in the up state is 150x + 100y
So if we choose (x , y ) so that:
0 = 50x + 100y (match down state) 25 = 150x + 100y (match up state) We will replicate the option. The solut...
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 Spring '13
 Options, Mathematical finance, CF

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