capacityoutputrate,aswellasestimatesofthenumberof
years itwouldtake toexhaust theinventory.Thus,a gold
minewithareserveof 3 millionouncesandacapacityoutput
rateof150,000ouncesayearwillbeexhaustedin 20 years,
which is defined as the life of the natural resource option.
4.Varianceinvalueoftheunderlyingasset.Thevariancein
the value of the underlying asset is determined by the
variabilityinthepriceoftheresourceandthevariabilityin
theestimateofavailablereserves.Inthespecialcasewhere
the quantity of the reserve is known with certainty, the
varianceintheunderlyingasset’svaluewilldependentirely
upon the variance in the price of the natural resource.
5.Costofdelay. Thenetproductionrevenue istheannual
cashflowthatwillbegenerated,oncearesourcereservehas
beendeveloped,asapercentageoftheestimatedvalueofthe
reserve.Thisis theequivalent ofthedividendyieldand is
treated the same way in calculating option values. An
alternativewayofthinkingaboutthiscostisintermsofacost
ofdelay.Onceanaturalresourceoptionisin-the-money(the
valueofthereservesisgreaterthanthecostofdeveloping
these reserves), by not developing the reserve the firm is
givinguptheproductionrevenueitcouldhavegeneratedby
doing so.
Animportantissueinusingoptionpricingmodelsto value
naturalresourceoptionsistheeffectofdevelopmentlagson
thevalue of theseoptions. Since oilor gold or any other
naturalresourcereservecannotbedevelopedinstantaneously,
atimelaghastobeallowedbetweenthedecisiontoextract
theresourcesandtheactualextraction.Asimpleadjustment
forthislagistoreducethevalueofthedevelopedreservefor