Third Order Compound Option Valuation Of Flexible Commodity Based Mining Enterprises

Flexibility in managerial decision making will alter the true value of real world projects. Standard actuarial practice for evaluating real-world projects such as commodity based mining operations rely upon Net Present Value methodology and in essence ignore any flexibility available to the operator to vary the project. Real Option analysis rectifies this to allow better evaluation of economic investment decisions by incorporating managerial flexibility into an option pricing framework. In this paper we extend the results of Konstandatos and Kyng (2012) to evaluate a multi-stage compound mining investment decision where the mining operators have the flexibility to delay project commencement as well as options to abandon production and to expand production to a new mining seam if conditions improve. We allow an independent abandonment of the expansion from the underlying project. We demonstrate that the flexibilities considered give rise to a third-order exotic compound structure, which are evaluated in terms of first, second and third order generalised compound option instruments (Konstandatos (2008)). Our novel representations of the project values contain generalizations of standard compound options and are interpretable as generalised call, call-on-call and call-on-call-on-call type options on the mined commodity price. We provide readily-implementable closed-form analytical formulae which are expressed in terms of the uni-variate, bi-variate and tri-variate Normal distribution functions.