SOAmc-exam-mfe-0507

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1、ExamMFESpring2007FINALANSWERKEYQuestion#Answer1B2A3C4E5D6C7E8C9A10B11D12A13E14E15C16D17B18A19D**BEGINNINGOFEXAMINATION**ACTUARIALMODELS–FINANCIALECONOMICSSEGMENT1.OnApril30,2007,acommonstockispricedat$52.00.Youaregiventhefollowing:(i)Dividendsofequalam

2、ountswillbepaidonJune30,2007andSeptember30,2007.(ii)AEuropeancalloptiononthestockwithstrikepriceof$50.00expiringinsixmonthssellsfor$4.50.(iii)AEuropeanputoptiononthestockwithstrikepriceof$50.00expiringinsixmonthssellsfor$2.45.(iv)Thecontinuouslycompoun

3、dedrisk-freeinterestrateis6%.Calculatetheamountofeachdividend.(A)$0.51(B)$0.73(C)$1.01(D)$1.23(E)$1.45EXAMMFE:Spring2007-1-GOTONEXTPAGEActuarialModels–FinancialEconomicsSegment2.Foraone-periodbinomialmodelforthepriceofastock,youaregiven:(i)Theperiodiso

4、neyear.(ii)Thestockpaysnodividends.(iii)u=1.433,whereuisoneplustherateofcapitalgainonthestockifthepricegoesup.(iv)d=0.756,wheredisoneplustherateofcapitallossonthestockifthepricegoesdown.(v)Thecontinuouslycompoundedannualexpectedreturnonthestockis10%.Ca

5、lculatethetrueprobabilityofthestockpricegoingup.(A)0.52(B)0.57(C)0.62(D)0.67(E)0.72EXAMMFE:Spring2007-2-GOTONEXTPAGEActuarialModels–FinancialEconomicsSegment3.YouareaskedtodeterminethepriceofaEuropeanputoptiononastock.AssumingtheBlack-Scholesframeworkh

6、olds,youaregiven:(i)Thestockpriceis$100.(ii)Theputoptionwillexpirein6months.(iii)Thestrikepriceis$98.(iv)Thecontinuouslycompoundedrisk-freeinterestrateisr=0.055.(v)δ=0.01(vi)σ=0.50Calculatethepriceofthisputoption.(A)$3.50(B)$8.60(C)$11.90(D)$16.00(E)$2

7、0.40EXAMMFE:Spring2007-3-GOTONEXTPAGEActuarialModels–FinancialEconomicsSegment4.Forastock,youaregiven:.(i)Thecurrentstockpriceis$50.00.(ii)δ=0.08(iii)Thecontinuouslycompoundedrisk-freeinterestrateisr=0.04.(iv)Thepricesforone-yearEuropeancalls(C)underva

8、riousstrikeprices(K)areshownbelow:KC$40$9.12$50$4.91$60$0.71$70$0.00Youownfourspecialputoptionseachwithoneofthestrikepriceslistedin(iv).Eachoftheseputoptionscanonlybeexercisedimmediatelyoroneyearfromnow.Determinetheloweststrikepriceforw