- Long-term options. Since it becomes impractical to
estimate the present value of dividendsas the option life
becomeslonger,wewouldsuggestanalternateapproach.If
thedividendyield(y=Dividends/Currentvalueoftheasset)
on the underlying asset is expected to remain unchanged
duringthelifeoftheoption,theBlack-Scholesmodelcanbe
modified to take dividends into account.
From an intuitive standpoint, the adjustments have two
effects.First,thevalueoftheassetisdiscountedbacktothe
presentatthedividendyieldtotakeintoaccounttheexpected
dropinassetvalueresultingfromdividendpayments.Second,
theinterestrateisoffsetbythedividendyieldtoreflectthe
lowercarryingcostfromholdingtheasset(inthereplicating
portfolio).Theneteffectwillbeareductioninthevalueof
calls estimated using this model.
Early Exercise
Therearetwobasicwaysofdealingwiththepossibilityof
early exercise. One is to continue to use the unadjusted
Black-Scholesmodelandregardtheresultingvalueasafloor
orconservativeestimateofthetruevalue.Theotheristotry
toadjustthevalueoftheoptionforthepossibilityofearly
exercise.Therearetwoapproachesfordoingso.Oneusesthe
Black-Scholestovaluetheoptiontoeachpotentialexercise