ps5sol - 70-492 Investment AnalysisProblem Set 5:...

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Unformatted text preview: 70-492 Investment AnalysisProblem Set 5: Derivatives1. a) LetSTbe the S&P 500 value per dollar invested,Payoff from fund =.95 ifST<.95,STif 0.95< ST<1.15,1.15 ifST>1.15,which is depicted in Figure 1.b) Payoff from call = max{ST-x,}.Payoff from put = max{x-ST,}.To replicate the payoff from the fun, we can invest $1 in S&P500, purchasing a put with strikingpricex= 0.95, and sell a call with striking pricex= 1.15. Here is how the plan worksPayoff =ST+ 0.95-ST= 0.95ifST<.95STif 0.95< ST<1.15-(ST-1.15) +ST= 1.15 ifST>1.15From put-call parity,C(x)-P(x) =ST-x(1 +r)T,which givesP(x) =C(x)-ST+x(1 +r)T(1)The total cost of the replicating strategy isP(0.95) +ST-C(1.15).(2)Using (1) we haveC(0.95)-ST+.95(1 +r)T+ST-C(1.15) =C(0.95)-C(1.15) +.95(1 +r)TThe above equation indicates that we can buy a call with a strike price of 0.95, sell a call withstrike price of 1.15, and invest in bond with face value of 0.95....
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This note was uploaded on 01/20/2012 for the course INVESTMENT 101 taught by Professor Unknown during the Spring '08 term at Carnegie Mellon.

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ps5sol - 70-492 Investment AnalysisProblem Set 5:...

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