FBE559.slides.07

# 25 0 risk neutral pricing works for the stock itself

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Unformatted text preview: people act as if we don’t need 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 Risk-neutral 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 risk-neutral probabilities and the risk-free 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.

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