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1、Chapter29 InterestRateDerivatives:TheStandardMarketModelsOptions,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20141TheComplicationsinValuingInterestRateDerivatives(page673)WeneedawholetermstructuretodefinethelevelofinterestratesatanytimeThe
2、stochasticprocessforaninterestrateismorecomplicatedthanthatforastockpriceVolatilitiesofdifferentpointsonthetermstructurearedifferentInterestratesareusedfordiscountingthepayoffaswellasfordefiningthepayoff.WhenOISdiscountingisusedforaproductwhosepayoffsdep
3、endonLIBOR,twotermstructuresmustbeconsideredOptions,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20142ApproachestoPricing InterestRateOptionsUseavariantofBlack’smodelUseano-arbitrage(yieldcurvebased)modelOptions,Futures,andOtherDerivatives,
4、9thEdition,Copyright©JohnC.Hull20143Black’sModelSimilartothemodelproposedbyFischerBlackforvaluingoptionsonfuturesin1976Assumesthatthevalueofaninterestrate,abondprice,orsomeothervariableataparticulartimeTinthefuturehasalognormaldistributionOptions,Futures
5、,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20144Black’sModelforEuropeanBondOptions(Equations29.1and29.2,page674)AssumethatthefuturebondpriceislognormalBoththebondpriceandthestrikepriceshouldbecashpricesnotquotedpricesOptions,Futures,andOtherDeri
6、vatives,9thEdition,Copyright©JohnC.Hull20145ForwardBondandForwardYieldApproximatedurationrelationbetweenforwardbondprice,FB,andforwardbondyield,yFwhereDisthe(modified)durationoftheforwardbondatoptionmaturityOptions,Futures,andOtherDerivatives,9thEdition,
7、Copyright©JohnC.Hull20146YieldVolsvsPriceVols(Equation29.4,page677)Thisrelationshipimpliesthefollowingapproximationwheresyistheforwardyieldvolatility,sBistheforwardpricevolatility,andy0istoday’sforwardyieldOftensyisquotedwiththeunderstandingthatthisrelat
8、ionshipwillbeusedtocalculatesBOptions,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20147TheoreticalJustificationforBondOptionModelOptions,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20148Capsan
