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1、11BinomialOptionPricing:SelectedTopicshapter10introducedbinomialoptionpricing,focusingonhowthemodelcanbeusedCtocomputeEuropeanandAmericanoptionpricesforavarietyofunderlyingassets.Inthischapterwecontinuethediscussionofbinomialpricing,discussingselecte
2、dtopicsanddelvingmoredeeplyintotheeconomicsofthemodelanditsunderlyingassumptions.First,thebinomialmodelcanvalueoptionsthatmaybeearly-exercised.Weexamineearlyexerciseinmoredetail,andseethattheoptionpricingcalculationreflectstheeconomicdeterminantsofear
3、lyexercisediscussedinChapter9.Second,thebinomialoptionpricingformulacanbeinterpretedastheexpectedoptionpayoffoneperiodhence,discountedattherisk-freerate.InChapter10wereferredtothiscalculationasrisk-neutralpricing.Thiscalculationappearstobeinconsisten
4、twithstandarddiscountedcashflowvaluation,inwhichexpectedcashflowsarediscountedatarisk-adjustedrate,nottherisk-freerate.Weshowthat,infact,thebinomialpricingformula(and,hence,risk-neutralvaluation)isconsistentwithoptionvaluationusingstandarddiscountedcas
5、hflowtechniques.Third,wediscusstheimplicitdistributionalassumptionsinthebinomialmodel,namelythatcontinuouslycompoundedreturnsarenormallydistributedinthelimit,whichimpliesthatpricesarelognormallydistributed.Finally,wesawhowtopriceoptionsonstockindicesw
6、herethedividendiscontinu-ous.Inthischapterweadaptthebinomialmodeltopriceoptionsonstocksthatpaydiscretedividends.11.1UNDERSTANDINGEARLYEXERCISEIndecidingwhethertoearly-exerciseanoption,theoptionholdercomparesthevalueofexercisingimmediatelywiththevalue
7、ofcontinuingtoholdtheoptionandexercisesifimmediateexerciseismorevaluable.ThisisthecomparisonweperformedateachbinomialnodewhenwevaluedAmericanoptionsinChapter10.Weobtainaneconomicperspectiveontheearly-exercisedecisionbyconsideringthecostsandbenefitsofe
8、arlyexercise.AsdiscussedinSection9.3,therearethreeeconomicconsiderationsgoverningthedecisiontoexerciseearly.Byexercising,theoptionholder:323324Chapter11.BinomialOptionPricing:SelectedTopics.Receivesthestockandthereforereceivesfuturedividends..Paysthe
