paul wilmott on quantitative finance real options

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1、CHAPTER73realoptionsInthisChapter...•theapplicationofderivativestheoryoutsideoffinance•optimalinvestment73.1INTRODUCTIONWe’veseentheword‘option’usedtodescribeafinancialcontractcontainingsomeelementofchoice.Andthatchoiceismadecomplicated,andinteresting,bytherandomn

2、essunderpinningthefinancialmarkets.Buthighfinanceisnottheonlyareainwhichrandomnessandchoiceplayimportantroles,everydecisioninlifecouldbeinterpretedastryingtomakethebestchoice,givenanunknownfuture.Inthischapterwewillseehowmanyoftheideasofderivativestheorycanbeappli

3、edtootherwalksoflife,andwe’llalsoseeafewmoreideasaswell.ThisisthesubjectofRealoptions.73.2FINANCIALOPTIONSANDREALOPTIONSThekeypointsthatrelatefinancialoptiontheoryandRealoptiontheoryareasfollows:•Randomnessconcerningthefutureintroducestheideaofexaminingprobabilit

4、ydistributionsforoutcomes;•Decisionsshouldbemadeoptimally,thereissomequestionoverthetiming;•Decisionsmaybepartiallyorwhollyirreversible.InthischapterwewillslowlybuilduptheconceptsandmathusedinRealoptiontheory.Inparticular,welookatprojectvaluation,optimalentryint

5、oandexitfromabusiness,andoptimallyandsequentiallyinvesting.Mostofthemathisverysimilartowhatwe’veseenalready.1152PartFiveadvancedtopics73.3ANINTRODUCTORYEXAMPLE:ABANDONMENTOFAMACHINEYouownafactorythatproducesgoodswithaprofitabilityofPwhichisrealizedcontinuously.So

6、thatPdtistheprofitmadebetweentimestandt+dt.ThefactoryhasanaturallifespanofT.IfPisaconstantthenthepresentvalueofallthefutureprofitsV(t)satisfiesdV−rV+P=0(73.1)dtwithV(T)=0.NoticethatIhavediscountedattherisk-freerate;wemaybediscountingatadifferentratelateron.Thesolut

7、ionofthisisjustP
V=1−e−r(T−t).rAslongasP>0thenVisalwayspositiveandtherewouldbenoreasontoclosedownthefactory.IfPisadeterministicfunctionoftimethenwecanstillsolve(73.1).IfPgoesnegativeforsufficientlylongthenitmightbeworthwhileclosingthefactorydown.Sincethisisacomp

8、letelydeterministicproblemyoujustwaituntilV=0.Youcouldevenopenupthefactorylateronifconditionsimprove.Let’snotworryaboutthisuntillaterinthechapter.Morerealistically,su