Notethate−rtisthepresentvaluefactorandreflectsthefact
thattheexercisepriceonthecalloptiondoesnothavetobe
paid until expiration. N(d 1 ) and N(d 2 ) are probabilities
estimated by using a cumulative standardized normal
distribution and the values of d 1 and d 2 obtained for an
option. The cumulative distribution is shown inFigure A12.4.
FIGURE A12.4Cumulative Normal Distribution
In approximate terms, N(d 2 ) yields the likelihood that an
option will generate positive cash flows for its owner at
exercise(i.e.,whenS>Kinthecaseofacall optionand
whenK>Sinthecaseofaputoption).Theportfoliothat
replicatesthecalloptioniscreatedbybuyingN(d 1 )unitsof
theunderlyingassetandborrowingKe−rtN(d 2 ).Theportfolio
willhavethesamecashflowsasthecalloptionandthusthe
samevalueastheoption.N(d 1 ),whichisthenumberofunits