2010FRMPart1-ValuationandRiskModelsSampleExam20100404byDMCQiangJingFRM1.Astockthatiscurrentlytradingat$50andcaneithermoveto$55or$45overthenext6-monthperiod.Thecontinuouslycompoundedrisk-freerateis2.25percent.Whatistherisk-neutralprobabilityofanupmovement?A)0.6655.B)0.6565.C)0.5656.D)0.5566.2.Astockcurrentlytradesat$50.Attheendofthreemonths,thestockwilleitherbe$55or$45.Thecontinuouslycompoundedrisk-freerateofinterestis5percentperyear.Thevalueofa3-monthEuropeancalloptionwithastrikepriceof$50isclosestto:A)$2.78.B)$2.89.C)$2.55.D)$2.25.3.Astockthatcurrentlytradesat$40caneithermoveupordownby5percenteachyear.Thecontinuouslycompoundedrisk-freerateis4percent.Anover-the-counterEuropeancalloptionwith2yearsuntilexpirationissetupsothatthestrikepriceisdeterminedbytheformula$40+[(yearstoexpiration+1)×0.5]inperiodswhenthestockpriceincreases.Inperiodswhenthestockpricedeclines,thestrikepriceis$40.Whatisthevalueofthis2-yearspecializedOTCcalloption?A)$3.12.B)$2.74.C)$3.27.D)$2.56.4.ThedifferencebetweenaMonteCarlosimulationandahistoricalsimulationisthatahistoricalsimulationusesrandomlyselectedvariablesfrompastdistributions,whileaMonteCarlosimulation:A)usesrandomlyselectedvariablesfromfuturedistributions.B)usesvariablesbasedonrouletteodds.C)usesacomputertogeneraterandomvariables.D)projectsvariablesbasedonaprioriprinciples.5.Whencomparingafat-taileddistributiontoanotherwisesimilarnormaldistribution,thefat-taileddistributionoftenhas:A)alowerprobabilitymassataroundonestandarddeviation.B)adifferentmeanandstandarddeviation.C)anequalprobabilitymassclosetothemean.D)alowerprobabilitymassatmorethanthreestandarddeviations.6.ManyanalystsprefertouseMonteCarlosimulationratherthanhistoricalsimulationbecause:A)itismucheasiertogeneratetherequiredvariables.B)pastdistributionscannotaddresschangesincorrelationsoreventsthathavenothappenedbefore.C)pastdataisoftenproprietaryanddifficulttoobtain.D)computerscanmanipulatetheoreticaldatamuchmorequicklythanhistoricaldata.7.Valueatrisk(VAR)isa