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1、Chapter35 RealOptionsOptions,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20141AnAlternativetotheNPVRuleforCapitalInvestmentsDefinestochasticprocessesforthekeyunderlyingvariablesanduserisk-neutralvaluationThisapproach(knownastherealoptionsapproach)islik
2、elytodoabetterjobatvaluinggrowthoptions,abandonmentoptions,etcthanNPVOptions,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20142TheProblemwithusingNPVtoValueOptionsConsidertheexamplefromChapter13:risk-freerate=12%;strikeprice=$21Supposethattheexpectedret
3、urnrequiredbyinvestorsintherealworldonthestockis16%.Whatdiscountrateshouldweusetovalueanoptionwithstrikeprice$21?Options,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20143StockPrice=$22Stockprice=$20StockPrice=$18CorrectDiscountRatesareCounter-Intuitive
4、Correctdiscountrateforacalloptionis42.6%Correctdiscountrateforaputoptionis–52.5%Options,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20144GeneralApproachtoValuationWecanvalueanyassetdependentonavariableqbyReducingtheexpectedgrowthrateofqbylswherelisthem
5、arketpriceofq-riskandsisthevolatilityofqAssumingthatallinvestorsarerisk-neutralOptions,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20145ExtensiontoManyUnderlyingVariablesWhenthereareseveralunderlyingvariablesqiwereducethegrowthrateofeachonebyitsmarketp
6、riceofrisktimesitsvolatilityandthenbehaveasthoughtheworldisrisk-neutralNotethatthevariablesdonothavetobepricesoftradedsecuritiesOptions,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20146EstimatingtheMarketPriceofRiskUsingCAPM(equation35.2,page795)Option
7、s,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20147TypesofOptionsAbandonmentExpansionContractionOptiontodeferOptiontoextendlifeOptions,Futures,andOtherDerivatives,9thEdition,Copyright©JohnC.Hull20148ExampleofApplicationofRealOptionsApproachtoValuingAma
8、zon.comatendof1999(BusinessSnapshot35.1;SchwartzandMoon)Estimatestochasticprocessesforthecompany’ssalesrevenueanditsaveragegrowthra
