FBE559.slides.07

# FBE559.slides.07

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Unformatted text preview: always get \$1500. Note: the answer doesn’t depend on the ”true” probability of USC making it to the Rose Bowl. Risk-Neutral Approach Constructing replicating strategies to price options is cool, but tedious. If all we care about is pricing, there is a shortcut. Start with the one-period example: uS = 75 S0 = 50 dS = 25 and the interest rate is 10%. Consider the “up” and “down” digital options: 1 0 and 0 1 C0 1 0 Consider a portfolio (a, b ) where a is the number of shares of the stock held b is the dollar amount invested in the riskless bond. We want to ﬁnd (a, b ) so that 75a + 1.1b = 1 25a + 1.1b = 0. There is a unique solution a = 0.02 and b = −0.4545. So the price of the digital up option is: 50a + 1b = .5455 = .6/1.1 Similarly, the price of the down digital option is .4/1.1. Using Digital Options Now, consider a security with the following payoﬀ: CFu CFd = CFu × 1 0 + CFd × 0 1 No free-lunch requires: PV(CF ) = du CFu + dd CFd = 0.6 0.4 CFu + CFd . 1.1 1.1 wh...
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## This document was uploaded on 10/28/2013.

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