FRM一级基础段估值与风险模型（打印版）.docx

该【FRM一级基础段估值与风险模型（打印版） 】是由【经管专家】上传分享，文档一共【78】页，该文档可以免费在线阅读，需要了解更多关于【FRM一级基础段估值与风险模型（打印版） 】的内容，可以使用淘豆网的站内搜索功能，选择自己适合的文档，以下文字是截取该文章内的部分文字，如需要获得完整电子版，请下载此文档到您的设备，方便您编辑和打印。ValuationandRiskModels,83▁?????Т??????TopicWeightingsinFRMPart?-235Framework?BondMarket??BondValuationBondMarketRisk???OptionsValuation???BinomialTreesTheBlack-Scholes-MertonModelOptionSensitivityMeasuresMarketRiskModels?MeasuresofFinancialRisk??CalculatingandApplyingVaRMeasuringandMonitoringVolatilityCreditRiskModels?ExternalandInternalCreditRatingCountryRiskMeasuringCreditRisk????OperationalRiskModelsStressTesting3-235BondMarketTopic1:&LComponents4-235Reviews??SpotRatezAt-periodspotrate,orzerorate,,+R???1+F?,??????=1+R???RT?RT????e????×e??,??????=e?????F?,?=T??T?5-235Spot,ForwardRates?%Maturity(year)%%%%%%%%%%%%%%%%%%%%%(year)?%F?.?,?%21+1+=1+2F?.?,?=%6-235BasicValuationMethod?hepriceofabond??C?C?C?(1+S?)?C?(1+y)?P=++??+=?1+S?(1+S?)????zSupposethata2-yearTreasurybondwithaprincipalof$100providescouponsattherateof6%:TreasuryZeroRatesMaturity(Years)ZeroRate(%)(pounded)=3e??.??×?.?+3e??.???×?+3e??.???×?.?+103e??.???×?.?=-235DiscountFactor?DiscountFactorzThediscountfactor,d(t),foratermof(t)years,givesthepresentvalueofoneunitofcurrency($1)tobereceivedattheendofthatterm.???rtmdt=1+ordt=e????%%.50%.00%.50%.00%%%%%%%%%%%%%%%%%?year?8-235BasicValuationMethod?ExampleThetablebelowshowsselectedT-bondpricesforsemiannualcoupon,$%-%104-22+4%2332Bond1:100+100××=101+=%%:100××+100+100×d1=×d1=104+9-235BasicValuationMethod???PricingBondusingDiscountFactors,SpotRates,orForwardRateszAssumea1-yeartreasurybondthatpaysa8%semi-(%)DiscountFactor6MonthForwardRate(%)-235BasicValuationMethodPricingBondusingDiscountFactors,SpotRates,orForwardRateszCalculatetheBondPriceusingDiscountFactorsPrice=$4×+$104×=$$%2$%Price=+=$?11+1+2zCalculatetheBondPriceusingForwardRates$%2$104×Price=+=$%%21+1+1+11-235ReplicationMethodLawofoneprice:zAbsentconfoundingfactors(.,liquidity,financing,taxes,creditrisk),,,thatis,,urbecausefactorsasionallyconsideredinthewaytheinstrumentsarepriced,-235ReplicationMethod?ExampleThreebondyieldsandpricesareshownbelow?MaturityYTMCouponPrice(%ofpar)%6%6%0%0%6%-%.Isthereanarbitrageopportunityusingthesethreebonds?Ifso,describethetradesnecessarytoexploitthearbitrageopportunity?13-235ReplicationMethod?Example$$1001$6$6+$?+?=B?×+×=,,-235ReplicationMethod?ExampleTime=01year2years(costof2-year,6%-1,000,+60,000(coupon)+1,060,000(coupon)-60,000(maturity)couponbonds)(proceeds1-year,+57,%couponbonds)(proceed2-year,0%couponbonds)+1,049,-1,060,000+106,(maturity)15-235BasicValuationMethod?PriceofanAnnuityzAnannuitywithsemiannualpaymentsisasecuritythatmakesapaymentc/2everysixmonthsforTyearsbutnevermakesafinal“principal”payment(.,FV=0).Thepriceofanannuity,A(T),isgivenby:??Cy1A=1?y21+?=c/y16-235BondReturn?GrossRealizedReturnsP???+c?P?R?,???=P?zIfwewanttolookatthereturnoveralongerperiod,$98,$%(semi-pounding),thegrossrealizedreturnis:?98++×1+%=-235BondReturn?NetRealizedReturnszIncorporatesfundingcostP?+c?B?????????????R?,???=P?zContinuetheexample,assumingthatthefundstobuyarefinancedat%perannum(semi-pounding),realizedreturnis:?98×1+%?++×1+%39=-235BondReturn?:Supposeabondpays$40everysixmonthsforfouryearsandafinalpaymentof$1,$850,:TheYTMistheythatsolvesthefollowingequation:$40y$40y$40+$1000$850=++??+??y2?1+1+1+22FV=$1000;PV=-850;PMT=40;N=8;&37?I/Y=?YTM=%19-235BondReturnAssumptionthecouponpaymentscanbereinvestedataninterestrateequaltotheyieldtomaturitythebondisheldtomaturityIfthebondisnotheldtomaturity,theinvestorfacestheriskthathemayhavetosellforlessthanthepurchaseprice,resultingareturnthatislessthantheyieldtomaturity,,-235BondReturn?ExampleAbondwitha$100parvaluepaysa4%:year1:%;year2:5%;year3:%.:=++=??zComputetheYTM:441041+YTM?=++1+YTM1+YTM?FV=$100;PV=-;PMT=4;N=3??&37?,?<?<%21-235BondReturn?RelationshipbetweenSpotRatesandYTMCF?+YTMCF?1+YTM?CF?1+YTM?P=++??+1CF?+R?CF?1+R?CF?1+R?=++??+1??,-sloping,theyieldofthetwo-yearbondwillbebelowthetwo-yearspotrate(usetwo-yearbondasexample).zWhenthetermstructureofspotratesisdownward-sloping,theyieldofthetwo-yearbondwillbeabovethetwo--235BondReturnInterestRateInterestRate98765439876543ForwardCurveSpotCurveYieldCurveYieldCurveSpotCurveForwardCurve0123456789100**********Maturity(Year)Maturity(Year)Upward-SlopingTermStructureDownward-SlopingTermStructure23-235BondReturn?,,-slopingtrend,-slopingtrend,-235BondReturn???TheSpreadofaBondzThemarketpriceofasecurityisrecoveredbydiscountingabond’=++??1+f1+s1+f1+s1+f2+sc+F+1+f1+s1+f2+s…1+fT+s25-235P&LComponentspositionofP&LzThebond’sprofitandlossconsistsofboth:99Priceappreciation(ordepreciation);.,-carry::?Carry-roll-down:thepricechangeduetothepassageoftimewhereratesmoveasexpectedbutwithnochangeinthespread.?monassumptionwhenthecarryroll-downiscalculatedisthatforwardratesarerealized(.,theforwardrateforafutureperiodremainsunchangedaswemovethroughtime).26-235P&LComponentspositionofP&L?Ratechange:thepriceeffectofrateschangingfromtheintermediatetermstructuretothetermstructurethatactuallyprevailsattimet+1.?Thepriceappreciationduetoaspreadchangeisthepriceeffectduetothebond’sindividualspreadchangingfroms(t)tos(t+1).27-235P&LComponents?ExampleStartperiod201020112012priceP&L1-1Pricingdate:2010-1-1;annualcoupon=1InitialTermstructure2%3%4%%%%Pricingdate:2011-1-1;annualcoupon=1Carry-roll-Termstructure3%4%%%2%3%%%1-11-+-Roll-Down:+%1%3%1%--235P&LComponents11101P=+++=+%1+%1+%1+%1+%1+%1101P???????????????===+%1+%1+%1101P??????????=+1+%11+%1+%101P????????????=+=+3%1+3%1+4%29-235Exercise1?Thepriceofathree-yearzero---yearimpliedforwardratefromyear3toyear4?%%%%?Answer:D30-235