and this estimated value can thenbe used as an input to
reestimate the warrant’s value until there is convergence.
Black-Scholes Model for Valuing Puts
Thevalueofaputcanbederivedfromthevalueofacallwith
the same strike price and the same expiration date.
whereCisthevalueofthecallandPisthevalueoftheput.
This relationshipbetween thecall andput valuesis called
put-callparity,andanydeviationsfromparitycanbeusedby
investorstomakerisklessprofits.Toseewhyput-callparity
holds,considersellingacallandbuyingaputwithexercise
priceKandexpirationdatet,andsimultaneouslybuyingthe
underlyingassetatthecurrentpriceS.Thepayofffromthis
positionisrisklessandalwaysyieldsKatexpirationt.Tosee
this, assume that the stock price at expiration is S*. The
payoffoneachofthepositionsintheportfoliocanbewritten
as:
SincethispositionyieldsKwithcertainty,thecostofcreating
thispositionmustbeequaltothepresentvalueofKatthe
riskless rate (Ke−rt).