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compensation to bear risk Binomial Stock Example I: Another Alternate Solution
We want to price the call option:
Stock: 100 150
50 Bond: 95 100
100 C0 =??? 25
0 Riskneutral pricing works for the stock itself, so for some q :
0.95(q 150 + (1 − q )50) = 100
In words: the discounted expected payoﬀ of the stock using the
riskneutral probabilities and the riskfree rate is the price of the
stock. Binomial Stock Example I: Another Alternate Solution When we solve, we get 95q + 45 = 100, or
q= 55
.
95 So the call price is:
C0 = 0.95
Jump to Method #1 55
55
× 25 + (1 − ) × 0
95
95 Jump to Method #2 = 13.75 Binomial Stock Example I: Another Alternate Solution Also notice using this we can price any other option we want.
A put struck at 90 will cost:
P0 = 0.95 55
55
× 0 + (1 − ) × 40
95
95 = 16 Thus once we have q we don’t have to start over with two
equations/two unknowns or computing the ∆ Ways to compute Binomial Option Price Now we have three ways to compute the price:
1 Find replicating portf...
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This document was uploaded on 10/28/2013.
 Spring '13

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