12 Withabinomialmodel,wearriveatanestimateofvalueof
$99.15 million.
13 Ifweownsomereservesinperpetuity,weshouldcapthe
lifeofthereserveatalargevalue—say, 30 years—inmaking
this estimate.
14 With a binomial model, we estimate the value of the
reserves to be $13.73 billion.
15 See Appendix 12.1 for more information on how this
conversion is done.
16 Wecan valuethe cappedcall by valuing theexpansion
optiontwiceintheBlack-Scholesmodel,oncewithastrike
price of $1 billion (yielding the original expansion option
valueof$218 million)andone withthestrikepriceof $2
billion (yielding an option value of $76 million). The
difference between the two is thevalue of the expansion
optionwithacaponthepresentvalue.Wecouldalsovalueit
explicitlyin thebinomialbysettingthevalueto$2billion
whenever it exceeds that number in the binomial tree.
17 Thebinomialmodelyieldsavalueof$34.74millionfor
this option.
18 Note,though,thathighervariancecanreducethevalueof
theunderlyingasset.Asacall optionbecomesmoreinthe
money,themoreitresemblestheunderlyingasset.Forvery
deepin-the-moneycalloptions, highervariancecanreduce
the value of the option.