Binomial Models
The possibilityof early exercise and nonvesting,which is
substantialinemployeeoptions,leadsmanypractitionersto
argue for the use of binomial lattice models to value
employee options. Unlikethe Black-Scholes, these models
not only can model for early exercise, but can also be
modified to allow for other special features specific to
employee options, including vesting.In addition, binomial
modelsallowfor moreflexibilityon inputs,with volatility
changingfromperiodtoperiodratherthanremainingconstant
(whichistheassumptionintheBlack-Scholesmodel).The
limitation of the binomial models is that they are more
informationintensive, requiringthe user to inputprices at
eachbranchofthebinomialmodel.Inanyrealisticversionof
the model, where the time intervals are short, this could
translate into hundreds of potential prices.
It is truethat we canderive binomialtrees from standard
deviationsandthusavoidtheestimationproblemsassociated
withdevelopingthesetrees,buttheresultingvaluestendtobe
closetoBlack-Scholesmodelvalues.Inotherwords,toget
thefullbenefitsofthebinomialmodel,wehavetogothrough
theexerciseofdevelopingthepricingtree.Theinitialversion
ofFAS 123Rdid require firms touse binomialmodelsto
value employee options. The final version wisely left the
model choice decision to the firm.
The primary benefit of binomial models comes from the
flexibility that they offer users to model the interaction
betweenthestockpriceandearlyexercise.Oneexampleis
theHull-Whitemodel,whichproposesreducingthelifeused
to value employee options to a more realistic level.