A numerical study for a mining project using real options valuation under commodity price uncertainty

Md Aminul Haque, Erkan Topal, Eric Lilford

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

Commodity price is an important factor for mining companies, as price volatility is a key parameter for mining project evaluation and investment decision making. The conventional discounted cash flow (DCF) methods are broadly used for mining project valuations, however, based on commodity price uncertainty and operational flexibilities, it is difficult and often inappropriate to determine mining project values through traditional DCF methods alone. In order to more accurately evaluate the economic viability of a mining project, the commodity price and its inherent volatility should be modelled appropriately and incorporated into the evaluation process. As a consequence, researchers and practitioners continue to develop and introduce real options valuation (ROV) methods for mining project evaluations under commodity price uncertainty, incorporating continuous time stochastic models. Although the concept of ROV arose a few decades ago, most of the models that have been developed to-date are generally limited to theoretical research and academia and consequently, the application of ROV methods remains poorly understood and often not used in mining project valuations. Analytical and numerical solutions derived through the application of ROV methods are rarely found in practice due to the complexity associated with solving the partial differential equations (PDE), which are dependent on several conditions and parameters. As a consequence, it may not generally be applicable to evaluate mining projects under all project-specific circumstances. Therefore, the greatest challenge to ROV modelling is in finding numerically explicit project values. This paper contributes towards the further development of known theoretical work and enhances an approach to approximating explicit numerical project values. Based on this work, it is possible to formulate more complex PDEs under additional uncertainties attached to the project and to approximate its numerical value or value ranges. To ensure the project is profitable and to reduce commodity price uncertainty, delta hedging and futures contracts have been used as options for deriving the PDE. Moreover, a new parameter for taxes has been incorporated within the PDE. This new PDE has been utilised to approximate the numerical values of a mining project considering a hypothetical gold mine as a case study. The explicit finite difference method (FDM) and MatLab software have been used and implemented to solve this PDE and to determine the numerical project values considering the available options associated with a mining project. In addition, commodity price volatility has been determined from historical data, and has again revealed price volatility as having a significant impact on mining project values.

Original languageEnglish
Pages (from-to)115-123
Number of pages9
JournalResources Policy
Volume39
Issue number1
DOIs
Publication statusPublished - Mar 2014
Externally publishedYes

Fingerprint

commodity price
valuation
commodity
uncertainty
Values
project
Price uncertainty
Commodity prices
Option valuation
Real options
evaluation
gold mine
Partial differential equations
finite difference method

Keywords

  • Discounted cash flow
  • Finite difference method
  • Historical volatility
  • Partial differential equation
  • Real options valuation
  • Stochastic differential equation

ASJC Scopus subject areas

  • Economics and Econometrics
  • Management, Monitoring, Policy and Law
  • Law
  • Sociology and Political Science

Cite this

A numerical study for a mining project using real options valuation under commodity price uncertainty. / Haque, Md Aminul; Topal, Erkan; Lilford, Eric.

In: Resources Policy, Vol. 39, No. 1, 03.2014, p. 115-123.

Research output: Contribution to journalArticle

Haque, Md Aminul ; Topal, Erkan ; Lilford, Eric. / A numerical study for a mining project using real options valuation under commodity price uncertainty. In: Resources Policy. 2014 ; Vol. 39, No. 1. pp. 115-123.
@article{552195f294684ca1a02f65ba3d0b7621,
title = "A numerical study for a mining project using real options valuation under commodity price uncertainty",
abstract = "Commodity price is an important factor for mining companies, as price volatility is a key parameter for mining project evaluation and investment decision making. The conventional discounted cash flow (DCF) methods are broadly used for mining project valuations, however, based on commodity price uncertainty and operational flexibilities, it is difficult and often inappropriate to determine mining project values through traditional DCF methods alone. In order to more accurately evaluate the economic viability of a mining project, the commodity price and its inherent volatility should be modelled appropriately and incorporated into the evaluation process. As a consequence, researchers and practitioners continue to develop and introduce real options valuation (ROV) methods for mining project evaluations under commodity price uncertainty, incorporating continuous time stochastic models. Although the concept of ROV arose a few decades ago, most of the models that have been developed to-date are generally limited to theoretical research and academia and consequently, the application of ROV methods remains poorly understood and often not used in mining project valuations. Analytical and numerical solutions derived through the application of ROV methods are rarely found in practice due to the complexity associated with solving the partial differential equations (PDE), which are dependent on several conditions and parameters. As a consequence, it may not generally be applicable to evaluate mining projects under all project-specific circumstances. Therefore, the greatest challenge to ROV modelling is in finding numerically explicit project values. This paper contributes towards the further development of known theoretical work and enhances an approach to approximating explicit numerical project values. Based on this work, it is possible to formulate more complex PDEs under additional uncertainties attached to the project and to approximate its numerical value or value ranges. To ensure the project is profitable and to reduce commodity price uncertainty, delta hedging and futures contracts have been used as options for deriving the PDE. Moreover, a new parameter for taxes has been incorporated within the PDE. This new PDE has been utilised to approximate the numerical values of a mining project considering a hypothetical gold mine as a case study. The explicit finite difference method (FDM) and MatLab software have been used and implemented to solve this PDE and to determine the numerical project values considering the available options associated with a mining project. In addition, commodity price volatility has been determined from historical data, and has again revealed price volatility as having a significant impact on mining project values.",
keywords = "Discounted cash flow, Finite difference method, Historical volatility, Partial differential equation, Real options valuation, Stochastic differential equation",
author = "Haque, {Md Aminul} and Erkan Topal and Eric Lilford",
year = "2014",
month = "3",
doi = "10.1016/j.resourpol.2013.12.004",
language = "English",
volume = "39",
pages = "115--123",
journal = "Resources Policy",
issn = "0301-4207",
publisher = "Elsevier",
number = "1",

}

TY - JOUR

T1 - A numerical study for a mining project using real options valuation under commodity price uncertainty

AU - Haque, Md Aminul

AU - Topal, Erkan

AU - Lilford, Eric

PY - 2014/3

Y1 - 2014/3

N2 - Commodity price is an important factor for mining companies, as price volatility is a key parameter for mining project evaluation and investment decision making. The conventional discounted cash flow (DCF) methods are broadly used for mining project valuations, however, based on commodity price uncertainty and operational flexibilities, it is difficult and often inappropriate to determine mining project values through traditional DCF methods alone. In order to more accurately evaluate the economic viability of a mining project, the commodity price and its inherent volatility should be modelled appropriately and incorporated into the evaluation process. As a consequence, researchers and practitioners continue to develop and introduce real options valuation (ROV) methods for mining project evaluations under commodity price uncertainty, incorporating continuous time stochastic models. Although the concept of ROV arose a few decades ago, most of the models that have been developed to-date are generally limited to theoretical research and academia and consequently, the application of ROV methods remains poorly understood and often not used in mining project valuations. Analytical and numerical solutions derived through the application of ROV methods are rarely found in practice due to the complexity associated with solving the partial differential equations (PDE), which are dependent on several conditions and parameters. As a consequence, it may not generally be applicable to evaluate mining projects under all project-specific circumstances. Therefore, the greatest challenge to ROV modelling is in finding numerically explicit project values. This paper contributes towards the further development of known theoretical work and enhances an approach to approximating explicit numerical project values. Based on this work, it is possible to formulate more complex PDEs under additional uncertainties attached to the project and to approximate its numerical value or value ranges. To ensure the project is profitable and to reduce commodity price uncertainty, delta hedging and futures contracts have been used as options for deriving the PDE. Moreover, a new parameter for taxes has been incorporated within the PDE. This new PDE has been utilised to approximate the numerical values of a mining project considering a hypothetical gold mine as a case study. The explicit finite difference method (FDM) and MatLab software have been used and implemented to solve this PDE and to determine the numerical project values considering the available options associated with a mining project. In addition, commodity price volatility has been determined from historical data, and has again revealed price volatility as having a significant impact on mining project values.

AB - Commodity price is an important factor for mining companies, as price volatility is a key parameter for mining project evaluation and investment decision making. The conventional discounted cash flow (DCF) methods are broadly used for mining project valuations, however, based on commodity price uncertainty and operational flexibilities, it is difficult and often inappropriate to determine mining project values through traditional DCF methods alone. In order to more accurately evaluate the economic viability of a mining project, the commodity price and its inherent volatility should be modelled appropriately and incorporated into the evaluation process. As a consequence, researchers and practitioners continue to develop and introduce real options valuation (ROV) methods for mining project evaluations under commodity price uncertainty, incorporating continuous time stochastic models. Although the concept of ROV arose a few decades ago, most of the models that have been developed to-date are generally limited to theoretical research and academia and consequently, the application of ROV methods remains poorly understood and often not used in mining project valuations. Analytical and numerical solutions derived through the application of ROV methods are rarely found in practice due to the complexity associated with solving the partial differential equations (PDE), which are dependent on several conditions and parameters. As a consequence, it may not generally be applicable to evaluate mining projects under all project-specific circumstances. Therefore, the greatest challenge to ROV modelling is in finding numerically explicit project values. This paper contributes towards the further development of known theoretical work and enhances an approach to approximating explicit numerical project values. Based on this work, it is possible to formulate more complex PDEs under additional uncertainties attached to the project and to approximate its numerical value or value ranges. To ensure the project is profitable and to reduce commodity price uncertainty, delta hedging and futures contracts have been used as options for deriving the PDE. Moreover, a new parameter for taxes has been incorporated within the PDE. This new PDE has been utilised to approximate the numerical values of a mining project considering a hypothetical gold mine as a case study. The explicit finite difference method (FDM) and MatLab software have been used and implemented to solve this PDE and to determine the numerical project values considering the available options associated with a mining project. In addition, commodity price volatility has been determined from historical data, and has again revealed price volatility as having a significant impact on mining project values.

KW - Discounted cash flow

KW - Finite difference method

KW - Historical volatility

KW - Partial differential equation

KW - Real options valuation

KW - Stochastic differential equation

UR - http://www.scopus.com/inward/record.url?scp=84893517021&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893517021&partnerID=8YFLogxK

U2 - 10.1016/j.resourpol.2013.12.004

DO - 10.1016/j.resourpol.2013.12.004

M3 - Article

VL - 39

SP - 115

EP - 123

JO - Resources Policy

JF - Resources Policy

SN - 0301-4207

IS - 1

ER -