• Otto Konstandatos University of Technology, Sydney



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.

Author Biography

Otto Konstandatos, University of Technology, Sydney

Senior Lecturer, Discipline of Finance


Amram., M and Kulatilaka, N. (1991). Real Options: managing strategic investment in an uncertain world. Harvard Business School Press, Boston, MA.

Arnold, T. and Shockley, R.L. (2002). Real options analysis and the assumptions of the NPV rule.

Bhappu, R.R. and Guzman, J.. (2008). Mineral investment decision making. Engineering and Mining Journal, 58(2) pp135-157.

Black, F. and Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of political economy, 81(3), 637-654.

Boyle, P. (1977) Options: A monte-carlo approach. Journal of Financial Economics, 4(3), 323-338.

Buchen, P. (2001). Image options and the road to barriers. Risk Magazine, 14(9), 127-130.

Bradley, P.G. (1985) Has the economics of depletable resources advanced the economics of mining?. Progress in Natural Resource Economics, Clarendon Press.

Brennan, M.J. and Schwartz, E.S. (1985). Evaluating natural resource investments. Journal of Business, 58(2), 135-157.

Buchen, P. (2004). The pricing of dual-expiry exotics. Quantitative Finance, 4(1), 101-108.

Buchen, P., Konstandatos, O., and Kyng, T. (2009). Images and barriers on the road to real options valuation. Proceedings of the 18th IMACS World Congress MODSIM2009 , 1486-1492.

Colwell, D, Hencker, T, Ho, J and Fong, K.. (2003). Real options valuation of Australian gold mines and mining companies. The Journal of Alternative Investments, 6, 23-28.

Copeland, T. and Antikarov, V. (2001). Real Options: A practitioner’s guide. TEXERE New York, NY.

Cox, J., S. Ross, and M. Rubinstein, (1979). Option pricing: a simplified approach, Journal of Financial Economics, 7, 44-50.

Dixit, A., Pindyck, R. (1994). Investment under uncertainty. Princeton University Press Princeton, NJ.

Dresner, Z. and Wesolowsky, G.O. (1989) On the computation of the bivariate normal integral, Journal of Statist. Comput. Simul. 35, 101-107

Gentz, A (1992) Numerical computation of multivariate normal probabilities. Journal of Computational and Graphical Statistics, 141-149.

Geske, R. (1979). The valuation of compound options, Journal of Financial Economics, 63-81

Guj, P. (2011). A practical real option methodology for the evaluation of farm-in/out joint venture agreements in mineral exploration. Resources Policy 36(2011)80–90.

Harrison, J. and Pliska, S. (1981) Martingales and stochastic integrals in the theory of continuous trading. Stochastic Processes and their Applications, 11(3), 215-260

Hemantha S.B. Herath & Chan S. Park (2002). Multi-Stage Capital Investment Opportunities as Compound Real Options, The Engineering Economist: A Journal Devoted to the Problems of Capital Investment, 47:1, 1-27

Hull, J. (2009). Options, futures, and other derivatives. Pearson Education India

Hull, J. and White A., (1990), Valuing Derivative Securities Using the Explicit Finite Difference Method, Journal of Financial and Quantitative Analysis, 25(1), 87-100.

Kac, M. (1949). On distributions of certain Wiener functionals . Transactions of the American Mathematical Society, 65 (1), 1-13

Konstandatos, O (2003). A new framework for pricing barrier and lookback options. PhD Thesis, The University of Sydney, Sydney Australia.

Konstandatos, O (2008). Pricing path dependent options: a comprehensive mathematical framework. VDM Verlag, Saarbrucken, Germany

Konstandatos, O and Kyng, T. (2012). Real option analysis for commodity based mining enterprises with compound and barrier features. Accounting and Finance Research, 65 (1), 216-225

Lee, M., Yeh, F. and Chen, P. (2008). The generalised sequential compound options pricing and sensitivity analysis. Mathematical Social Sciences, 55 (2008), 38-54.

Merton, R. (1973). Theory of rational option pricing. Bell Journal of Economics and Management Science, 4(1), 141-183.

Merton, R. (1998). Applications of option pricing theory: Twenty-five years later. American Economic Review, 88(6), 323-349.

Myers, S. (1977). Determinants of capital borrowing. Journal of Financial Economics, 5.

Moel, A. and Tufano, P. (2002). When are real options exercised? An empirical study of mine closings. The Review of Financial Studies, 15, 35-64

Pendharkar, C.P. (2010). Valuing inter-dependent multi-stage IT investments: A real options approach, European Journal of Operational Research, 20(1), 847-859

Samuelson, P. (1965). Rational theory of warrant pricing. Industrial Management Rev, 6, 3-31.

Slade, M.E. (2001). Valuing managerial flexibility: an application of real-option theory to mining investments. Journal of Environmental Economics and Management, pp193-233.

Topal. E. (2008). Evaluation of a mining project using Discounted Cash Flow analysis, Decision Tree analysis, Monte Carlo Simulation and Real Options using an example. Int. J. Mining and Mineral Engineering, 1(1), 62-76

Trigeorgis, L. (1993). The nature of option interactions and the valuation of investments with multiple real options. Journal of Financial and Quantitative Analysis, 28(1), 1-20.

Trigeorgis, L. (1996). Real Options: Management Flexibility and Strategy in Resource

Allocation.. MIT Press, Cambridge, MA.

Wilmott, P., Howison, S. and Dewynne, J. (1995). The mathematics of financial derivatives: a student introduction. Cambridge University Press.




How to Cite