of the underlying asset that are needed to create the
replicating portfolio, is called theoption delta.
Model Limitations and Fixes
TheBlack-Scholesmodelwasdesignedtovalueoptionsthat
canbeexercised onlyatmaturityandonunderlying assets
that do not pay dividends. In addition, options are valued
basedontheassumptionthatoptionexercisedoesnotaffect
thevalueoftheunderlyingasset.Inpractice,assetsdopay
dividends, options sometimes get exercised early, and
exercising anoptioncanaffectthevalueof theunderlying
asset.Adjustmentsexistthatprovidepartialcorrectionstothe
Black-Scholes model.
Dividends
Thepaymentofadividendreducesthestockprice;notethat
on theex-dividend day,the stock pricegenerallydeclines.
Consequently,calloptionswillbecomelessvaluableandput
options more valuable as expected dividend payments
increase.Therearetwowaysofdealingwithdividendsinthe
Black-Scholes model:
- Short-term options. One approach to dealing with
dividends is to estimate the present value of expected
dividendsthatwillbepaidbytheunderlyingassetduringthe
optionlifeandsubtractitfromthecurrentvalueoftheasset
to use asSin the model.