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1、Chapter20 VolatilitySmilesOptions,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20141WhatisaVolatilitySmile?ItistherelationshipbetweenimpliedvolatilityandstrikepriceforoptionswithacertainmaturityThevolatilitysmileforEuropeancalloptionsshouldbeexactlythe
2、sameasthatforEuropeanputoptionsThesameisatleastapproximatelytrueforAmericanoptionsOptions,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20142WhytheVolatilitySmileistheSameforEuropeanCallsandPutPut-callparityp+S0e−qT=c+Ke–rTholdsformarketprices(pmktandcm
3、kt)andforBlack-Scholes-Mertonprices(pbsandcbs)Asaresult,pmkt−pbs=cmkt−cbsWhenpbs=pmkt,itmustbetruethatcbs=cmktItfollowsthattheimpliedvolatilitycalculatedfromaEuropeancalloptionshouldbethesameasthatcalculatedfromaEuropeanputoptionwhenbothhavethesamestrikepriceandmatu
4、rityOptions,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20143TheVolatilitySmileforForeignCurrencyOptions(Figure20.1,page433)Options,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20144ImpliedVolatilityStrikePriceImpliedDistributionforForei
5、gnCurrencyOptionsOptions,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20145PropertiesofImpliedDistributionforForeignCurrencyOptionsBothtailsareheavierthanthelognormaldistributionItisalso“morepeaked”thanthelognormaldistributionOptions,Futures,andOtherDe
6、rivatives,9thEdition,Copyright©JohnC.Hull20146PossibleCausesofVolatilitySmileforForeignCurrenciesExchangerateexhibitsjumpsratherthancontinuouschangesVolatilityofexchangerateisstochasticOptions,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20147Historica
7、lAnalysisofExchangeRateChangesOptions,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20148RealWorld(%)NormalModel(%)>1SD25.0431.73>2SD5.274.55>3SD1.340.27>4SD0.290.01>5SD0.080.00>6SD0.030.00TheVolatilitySmileforEquityOptions(Figure20.3,page436)Options,Fu
8、tures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20149ImpliedVolatilityStrikePriceImpliedDistributionforEquityOptionsOptions,Futur
