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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. RiskNeutral 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 oneperiod 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 freelunch 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.
 Spring '13

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