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TheEquivalentMartingaleMeasureResult(Page635-36)
Options,Futures,andOtherDerivatives,8thEdition,Copyright©
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ForwardRiskNeutrality
Wewillrefertoaworldwherethemarketpriceofriskisthevolatilityofgasaworldthatisforwardriskneutralwithrespecttog.
IfEgdenotesexpectationsinaworldthatisFRNwrtg
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AlternativeChoicesfortheNumeraireSecurityg
MoneyMarketAccount
Zero-couponbondprice
Annuityfactor
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MoneyMarketAccountastheNumeraire
Themoneymarketaccountisanaccountthatstartsat$1andisalwaysinvestedattheshort-termrisk-freeinterestrate
Theprocessforthevalueoftheaccountis
dg=rgdt
-neutralworldwherel=0
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MoneyMarketAccountcontinued
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Zero-CouponBondMaturingattimeTasNumeraire
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ForwardPrices
InaworldthatisFRNwrtP(0,T),theexpectedvalueofasecurityattimeTisitsforwardprice
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InterestRates
InaworldthatisFRNwrtP(0,T2)theexpectedvalueofaninterestratelastingbetweentimesT1andT2istheforwardinterestrate
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AnnuityFactorastheNumeraire
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