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1、CHAPTER64advanceddividendmodelingInthisChapter...•theimportanceofdividendmodeling•thestochasticdividendmodel•uncertaintyindividendamountandtiming64.1INTRODUCTIONWe’vealreadyseeninChapter8howtoincorporatedividendsintooptionmodels.Butthatsupposesthatwehaveadecentknow
2、ledgeofthetimingandtheamountofthedividend.IrelaxedtherequirementforperfectknowledgeoftheamountofthedividendinChapter52whenwelookedatbestandworstcases.HereIpresentsomemoresophisticatedmodels.64.2WHYDOWENEEDDIVIDENDMODELS?Theprimaryreasonwhythefinancialliteratureexten
3、sivelyanalyzesdividendsonequityistheperfectmarkethypothesis,i.e.thatstocksarevaluedastheirdiscounteddividendstreaminperpetuity.Toalargeextent,equityanalystsusethismodelanditsvariationstoestimateastock’sfairvalueandforecastitsfutureperformance.Derivativesanalysts,ho
4、wever,inordertovalueandhedgeaportfolioofoptionsonastockoranindex,normallyrequireasstandardparametersthecurrentspotprice,exerciseprice,risk-freerate,expirytime,volatilityand,often,thestock’sdividendyieldoverthelifeoftheoption.Formanypractitionersthedividendyieldisco
5、nsideredtoberelativelyunimportantcomparedwiththeotherparameters.Theamountofliteratureavailableondividendmodelsappliedtoderivativesistiny.Butifwecomparethesensi-tivityratiosfordifferenttypesofoptions,itbecomesapparentthatthismightnotdescribetherealworldaccurately.Co
6、mpare,forexample,optionpricesensitivitytothedividendyieldwiththesensitivitytothevolatility,thevega.Figure64.1showstheratioofthesetwosensitivitiesagainstvolatilityanddividendyield.TheoptionisaEuropeancallwithoneyeartoexpiry,struckat98,therisk-freerateis5%.Theunderly
7、ingassetis1036PartFiveadvancedtopics0−0.5−1−1.5−2−2.50.10.16−30.22Volatility0.280.340.40.460.10.120.140.520.580Dividendyield0.640.70.020.040.060.08Figure64.1Ratioofdividendsensitivitytovega,calloption.6040200−20−40−60−80−1000.1Volatility0.160.220.10.120.140.280.340
8、.400.060.08Dividendyield0.040.02Figure64.2Ratioofdividendsensitivitytovega,binaryoption.advanceddividendmodelingChapter641037100.Wecanseethatform
