习题答案Stochastic Calculus for Finance I

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1、StevenE.ShreveStochasticCalculusforFinanceIStudent'sManual:SolutionstoSelectedExercisesDecember14,2004SpringerBerlinHeidelbergNewYorkHongKongLondonMilanParisTokyoContents1TheBinomialNo-ArbitragePricingModel::::::::::::::::11.7SolutionstoSelectedExercises..........

2、..................12ProbabilityTheoryonCoinTossSpace::::::::::::::::::::72.9SolutionstoSelectedExercises............................73StatePrices:::::::::::::::::::::::::::::::::::::::::::::::193.7SolutionstoSelectedExercises............................194American

3、DerivativeSecurities::::::::::::::::::::::::::::274.9SolutionstoSelectedExercises............................275RandomWalk:::::::::::::::::::::::::::::::::::::::::::::415.8SolutionstoSelectedExercises............................416Interest-Rate-DependentAssets::::

4、:::::::::::::::::::::::536.9SolutionstoSelectedExercises............................531TheBinomialNo-ArbitragePricingModel1.7SolutionstoSelectedExercisesExercise1.2.SupposeinthesituationofExample1.1.1thattheoptionsellsfor1:20attimezero.Consideranagentwhobeginswith

5、wealthX0=0andattimezerobuys
0sharesofstockand0options.Thenumbers
0and0canbeeitherpositiveornegativeorzero.Thisleavestheagentwithacashpositionof4
01:200.Ifthisispositive,itisinvestedinthemoneymarket;ifitisnegative,itrepresentsmoneyborrowedfromthemoneymarket.At

6、timeone,thevalueoftheagent'sportfolioofstock,optionandmoneymarketis+5X1=
0S1+0(S15)(4
0+1:200):4AssumethatbothHandThavepositiveprobabilityofoccurring.ShowthatifthereisapositiveprobabilitythatX1ispositive,thenthereisapositiveprobabilitythatX1isnegative.Inotherw

7、ords,onecannotndanarbitragewhenthetime-zeropriceoftheoptionis1:20.Solution.Consideringthecasesofaheadandofatailonthersttoss,andutilizingthenumbersgiveninExample1.1.1,wecanwrite:5X1(H)=8
0+30(4
0+1:200);45X1(T)=2
0+0
0(4
0+1:200)4Addingthese,wegetX1(H)+X1(T

8、)=10
0+3010
030=0;or,equivalently,21TheBinomialNo-ArbitragePricingModelX1(H)=X1(T):Inotherwords,eitherX1(H)andX1(T)arebothzero,ortheyhaveoppositesi