binomial algorithms for the evaluation of options on stocks with fixed per share dividends

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1、BinomialalgorithmsfortheevaluationofoptionsonstockswithfixedpersharedividendsMartinaNardonandPaoloPiancaAbstract.Weconsideroptionswrittenonassetswhichpaycashdividends.Dividendpaymentshaveaneffectonthevalueofoptions:highdividendsimplylowercallpremiaandhigherputpremia.Recently,Haugetal.[1

2、3]derivedanintegralrepresentationformulathatcanbeconsideredtheexactsolutiontoproblemsofevaluatingbothEuropeanandAmericancalloptionsandEuropeanputoptions.ForAmerican-styleputoptions,earlyexercisemaybeoptimalatanytimepriortoexpiration,evenintheabsenceofdividends.Inthiscase,numericaltechn

3、iques,suchaslatticeapproaches,arerequired.Discretedividendsproducediscreteshiftinthetree;asaresult,thetreeisnolongerreconnectingbeyondanydividenddate.Whilemethodsbasedonnon-recombiningtreesgiveconsistentresults,theyarecomputationallyexpensive.Inthiscontribution,weanalysebinomialalgorit

4、hmsfortheevaluationofoptionswrittenonstockswhichpaydiscretedividendsandperformsomeempiricalexperiments,comparingtheresultsintermsofaccuracyandspeed.Keywords:optionsonstocks,discretedividends,binomiallattices1IntroductionWeconsideroptionswrittenonassetswhichpaydividends.Dividendsareanno

5、uncedasapurecashamountDtobepaidataspecifiedex-dividenddatetD.Empirically,oneobservesthatattheex-dividenddatethestockpricedrops.Hencedividendsimplylowercallpremiaandhigherputpremia.Inordertoexcludearbitrageopportunities,thejumpinthestockpriceshouldbeequaltothesizeofthenetdividend.Sincewe

6、cannotusetheproportionalityargument,thepricedynamicsdependonthetimingofthedividendpayment.Usually,derivativepricingtheoryassumesthatstockspayknowndividends,bothinsizeandtiming.Moreover,newdividendsareoftensupposedtobeequaltotheformerones.Eveniftheseassumptionsmightbetoostrong,inwhatfol

7、lowsweassumethatweknowboththeamountofdividendsandtimesinwhichtheyarepaid.Valuationofoptionsonstockswhichpaydiscretedividendsisaratherhardproblemwhichhasreceivedalotofattentioninthefinancialliterature,butthereismuchconfusionconcerningtheevaluationapproaches.DifferentmethodshavebeenM.Co