Black-Scholes and Modifications
The conventional Black-Scholes option pricing model is
designedtovalueEuropeanoptionsontradedassetsanddoes
not explicitly factor in the dilution inherent in employee
options or the illiquidity/vesting issues specific to these
options. However, adaptations of the model provide
reasonable estimates of value:
- Buildexpecteddilutionintothestockprice.Oneof
theinputsintotheBlack-Scholesmodelisthecurrent
stockprice.Totheextentthattheexerciseofoptions
increasesthenumberofsharesoutstanding(ataprice
lessthanthecurrentstockprice),thestockpricewill
droponexercise. Asimpleadjustmenttothestock
price can incorporate this effect:
The resulting lower adjusted stock price will also
reduce the option value.- Reducethelifeoftheoptiontoreflectilliquidityand
earlyexercise.Earlierinthischapter,wenotedthat
employees often exercise options well before
maturitybecausetheseoptionsareilliquid.Typically,
options are exercised about halfway through their
statedlives.Usingareducedlifefortheoptionswill
reduce their value. - Adjustoption valueforprobabilityof vesting.The
vesting adjustmentcan be made in the process of
calculating the option value. If we can assess the