bevaluedasafunctionofthefollowingvariables:thecurrent
valueandthevarianceinvalueoftheunderlyingasset,the
strikepriceandthetimetoexpirationoftheoption,andthe
risklessinterestrate.ThiswasfirstestablishedbyBlackand
Scholes (1972)
4 and has been extended and refined subsequently in
numerous variants.While theBlack-Scholes option pricing
modelignoreddividendsandassumedthatoptionswouldnot
beexercised early,itcanbemodified toallowforboth.A
discrete-timevariant,thebinomialoptionpricingmodel,has
also been developed to price options.
FIGURE 1.4 Payoffs on Options as a Function of the
Underlying Asset’s Value
Anassetcanbevaluedasacalloptionifthepayoffsonitare
afunctionofthevalueofan underlyinginvestment;if that
value exceeds a prespecified level, the asset is worth the
difference;ifnot,itisworthnothing.Itcanbevaluedasaput
option if it gains value as the value of the underlying
investmentdropsbelowaprespecifiedlevel,anditisworth
nothingwhentheunderlyinginvestment’svalueexceedsthat