date.Withoptionsonstocks,thisbasicallyrequiresthatwe
value options to each ex-dividend day and choose the
maximumoftheestimatedcallvalues.Thesecondapproach
istouseamodifiedversionofthebinomialmodeltoconsider
thepossibilityofearlyexercise.Inthis version,theupand
down movements for asset prices in each period can be
estimated from the variance and the length of each period.
20
Approach 1: Pseudo-American Valuation
Step1:Definewhendividendswillbepaidandhowmuchthe
dividends will be.
Step2:Valuethecalloptiontoeachex-dividenddateusing
thedividend-adjustedapproachdescribedearlier,where the
stock price is reduced by the present value of expected
dividends.
Step3:Choosethemaximumofthecallvaluesestimatedfor
each ex-dividend day.
Approach2:UsingtheBinomialThebinomialmodelismuch
morecapableofhandlingearlyexercisebecauseitconsiders
the cash flows at each time period rather than just at
expiration. The biggest limitation of the binomial is
determining what stock prices will be at the end of each
period, but this can be overcome by using a variant that
allows us to estimate theup and the downmovements in
stock prices from the estimated variance. Four steps are
involved: