FBE559.slides.07

The solution has subtracting the rst equation from

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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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