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1、CHAPTER73realoptionsInthisChapter...?theapplicationofderivativestheoryoutsideof?nance?optimalinvestment73.1INTRODUCTIONWe’veseentheword‘option’usedtodescribea?nancialcontractcontainingsomeelementofchoice.Andthatchoiceismadecomplicated,andinteresting,bytherandomn
2、essunderpinningthe?nancialmarkets.Buthigh?nanceisnottheonlyareainwhichrandomnessandchoiceplayimportantroles,everydecisioninlifecouldbeinterpretedastryingtomakethebestchoice,givenanunknownfuture.Inthischapterwewillseehowmanyoftheideasofderivativestheorycanbeappli
3、edtootherwalksoflife,andwe’llalsoseeafewmoreideasaswell.ThisisthesubjectofRealoptions.73.2FINANCIALOPTIONSANDREALOPTIONSThekeypointsthatrelate?nancialoptiontheoryandRealoptiontheoryareasfollows:?Randomnessconcerningthefutureintroducestheideaofexaminingprobabilit
4、ydistributionsforoutcomes;?Decisionsshouldbemadeoptimally,thereissomequestionoverthetiming;?Decisionsmaybepartiallyorwhollyirreversible.InthischapterwewillslowlybuilduptheconceptsandmathusedinRealoptiontheory.Inparticular,welookatprojectvaluation,optimalentryint
5、oandexitfromabusiness,andoptimallyandsequentiallyinvesting.Mostofthemathisverysimilartowhatwe’veseenalready.1152PartFiveadvancedtopics73.3ANINTRODUCTORYEXAMPLE:ABANDONMENTOFAMACHINEYouownafactorythatproducesgoodswithapro?tabilityofPwhichisrealizedcontinuously.So
6、thatPdtisthepro?tmadebetweentimestandt+dt.ThefactoryhasanaturallifespanofT.IfPisaconstantthenthepresentvalueofallthefuturepro?tsV(t)satis?esdV?rV+P=0(73.1)dtwithV(T)=0.NoticethatIhavediscountedattherisk-freerate;wemaybediscountingatadifferentratelateron.Thesolut
7、ionofthisisjustPV=1?e?r(T?t).rAslongasP>0thenVisalwayspositiveandtherewouldbenoreasontoclosedownthefactory.IfPisadeterministicfunctionoftimethenwecanstillsolve(73.1).IfPgoesnegativeforsuf?cientlylongthenitmightbeworthwhileclosingthefactorydown.Sincethisisacomp
8、letelydeterministicproblemyoujustwaituntilV=0.Youcouldevenopenupthefactorylateronifconditionsimprove.Let’snotworryaboutthisuntillaterinthechapter.Morerealistically,su
