paul wilmott on quantitative finance speculating with options

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1、CHAPTER59speculatingwithoptionsInthisChapter...•howtofindthepresentvalueoftherealexpectedpayoff(andwhyyoushouldwanttoknowthis)•severalwaystomodelassetpricedrift•howtocloseyouroptionpositionoptimally•whenandwhennottohedge59.1INTRODUCTIONAlmosteverythingIhavesho

2、wnyousofarisaboutfindingpricingequationsforderivativecontractsusinghedgingarguments.Thereisaverypowerfulreasonwhysuchargumentsshouldgiveoptionpricesinthemarketregardlessofwhetherornotinvestorsactuallyhedgetheoption.Thereasonissimple:Iftheoptionisnotpricedatthe

3、Black–Scholesfairvalueandhedgingispossibletheneither•theoptionpriceistoolow,inwhichcasesomeonewillbuyit,hedgeawaytheriskandmakearisklessprofitor•theoptionpriceistoohigh,inwhichcasesomeonewillartificiallyreplicatethepayoffandchargelessforthiscontract.Bothofthese

4、areexamplesofmarketinefficiencieswhichwoulddisappearquicklyinpractice(toagreaterorlesserextent).However,afewminutesspentonatypicaltradingfloorwillconvinceyouthatoptioncontractsareoftenboughtforspeculationandthatthevalueofanoptiontoaspeculatorandthechoiceofexpir

5、ydateandstrikepricedependstronglyonhismarketview,somethingthatisirrelevantintheBlack–Scholesworld.Moreover,manyOTCandothercontractsareusedtooffsetrisksoutsidethemarket,andifeveryderivativeishedgedbybothwriterandpurchaserthenthewholethingispointless,oratbestas

6、eriesofhedgingandmodelingcompetitions.InthischapterIshowpossiblewaysinwhichaspeculatorcanchooseanoptioncontractsoastoprofitfromhisviewifitturnsouttobecorrect.954PartFiveadvancedtopicsThroughoutthischapterIusetheword‘value’tomeantheworthofanoptiontoaspeculatora

7、ndthiswillnotnecessarilybetheBlack–Scholes‘fair’value.Togetaroundtheobviouscriticismthatwhatfollowsisnonsenseinacompletemarket,inwhichdeltahedgingispossible,I’mgoingtotakethepointofviewthattheinvestorcanvalueacontractatotherthantheBlack–Scholesvaluebecauseofm

8、arketincompleteness,forwhateverreasonyoulike.Thecauseofincompletenessmaybetransactioncosts,restrictionsonsalesorpurchases,uncertainparameters,generalmodelerrorsetc.Thusany‘arbitrage’thaty