The valuation of multidimensional American real options using the LSM simulation method

Cortázar, Gonzalo; Gravet, Miguel; Urzúa, Jorge

doi:10.1016/j.cor.2006.02.016

Cited by 106 publications

(69 citation statements)

References 42 publications

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“…More broadly, our PSR approach potentially provides a solution methodology for other real option problems. Our approach differs from least squares Monte Carlo methods (Longstaff andSchwartz 2001, Tsitsiklis and, which could be used to solve such problems (Cortazar et al 2008), because it is based on linear programming rather than regression.…”

Section: Literature Reviewmentioning

confidence: 99%

Relaxations of Approximate Linear Programs for the Real Option Management of Commodity Storage

2015

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The real option management of commodity conversion assets gives rise to intractable Markov decision processes (MDPs). This is due primarily to the high dimensionality of a commodity forward curve, which is part of the MDP state when using high dimensional models of the evolution of this curve, as commonly done in practice. Focusing on commodity storage, we develop a novel approximate dynamic programming methodology that hinges on the relaxation of approximate linear programs (ALPs) obtained using value function approximations based on reducing the number of futures prices that are part of the MDP state. We derive equivalent approximate dynamic programs (ADPs) for a class of these ALPs, also subsuming a known ADP. We obtain two new ADPs, the value functions of which induce feasible policies for the original MDP, and lower and upper bounds, estimated via Monte Carlo simulation, on the value of an optimal policy of this MDP. We investigate the performance of our ADPs on existing natural gas instances and new crude oil instances. Our approach has potential relevance for the approximate solution of MDPs that arise in the real option management of other commodity conversion assets, as well as the valuation and management of real and financial options that depend on forward curve dynamics.

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Section: Literature Reviewmentioning

confidence: 99%

Relaxations of Approximate Linear Programs for the Real Option Management of Commodity Storage

2015

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“…Real options theory allows us to determine the best sequence of decisions to make in an uncertain environment, and provides the proper way to evaluate a project when such flexibility is present. The decisions are made according to the opportunities that appear along the project life time, which means that the optimal decision-path is chosen step by step, switching paths as events and opportunities appear (Cortazar et al, 2008). To evaluate or analyze an R&D project, it is important to evaluate the sequential real options that appear along the life time of the project.…”

Section: Introductionmentioning

confidence: 99%

A Tool to Manage Tasks of R&D Projects

Fialho

Godinho

Costa

2015

Operational Research

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We propose a tool for managing tasks of Research and Development (R&D) projects. We define an R&D project as a network of tasks and we assume that different amounts of resources may be allocated to a task, leading to different costs and different average execution times. The advancement of a task is stochastic, and the management may reallocate resources while the task is being performed, according to its progress. The operational cash flows depend on the task completion time, and their expected values follow a stochastic process. We consider that a strategy for completing a task is a set of rules that define the level of resources to be allocated to the task at each moment. We discuss the evaluation of strategies for completing a task, and we address the problem of finding the optimal strategy.

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“…Brennan and Schwartz (1985), were the first to apply the RO analysis in the mineral industry. Since then, RO analysis has been extended by valuing various types of managerial flexibilities inherent in the mineral industry using different valuation methods, (Mardones, 1993, Abdel Sabour & Poulin, 2006, Samis et al, 2006, Dimitrakopoulos & Abdel Sabour, 2007Topal, 2008, Cortazar et al, 2008Akbari et al, 2009, Gligoric et al, 2011.…”

Section: Introductionmentioning

confidence: 99%

Selection of the open pit mining cut-off grade strategy under price uncertainty using a risk based multi-criteria ranking system / Wybór strategii określania warunku opłacalności wydobycia w kopalniach odkrywkowych w warunkach niepewności cen w oparciu o wielokryterialny system rankingowy z uwzględnieniem czynników ryzyka

Azimi¹,

Osanloo²,

Esfahanipour³

2012

Archives of Mining Sciences

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Cut-off Grade Strategy (COGS) is a concept that directly influences the financial, technical, economic, environmental, and legal issues in relation to exploitation of a mineral resource. A decision making system is proposed to select the best technically feasible COGS under price uncertainty. In the proposed system both the conventional discounted cash flow and modern simulation based real option valuations are used to evaluate the alternative strategies. Then the conventional expected value criterion and a multiple criteria ranking system were used to rank the strategies based on the two valuation methods. In the multiple criteria ranking system besides the expected value other stochastic orders expressing abilities of strategies in producing extra profits, minimizing losses and achieving the predefined goals of the exploitation strategy are considered. Finally, the best strategy is selected based on the overall average rank of strategies through all ranking systems. The proposed system was examined using the data of Sungun Copper Mine. To assess the merits of the alternatives better, ranking process was done at both high (prevailing economic condition) and low price conditions. Ranking results revealed that at different price conditions and valuation methods, different results would be obtained. It is concluded that these differences are due to the different behavior of the embedded option to close the mine early, which is more likely to be exercised under low price condition rather than high price condition. The proposed system would enhance the quality of decision making process by providing a more informative and certain platform for project evaluation.Keywords: Open pit mining, Cut-off grade strategy, Least-squares Monte Carlo Real options valuation, Multiple criteria ranking system, Metal price uncertainty Strategia doboru granicy opłacalności (COGS) jest koncepcją mająca bezpośredni wpływ na kwestie finansowe, techniczne, ekonomiczne, środowiskowe oraz prawne związane z eksploatacją surowców naturalnych. Zaproponowano system decyzyjny umożliwiający wybór najkorzystniejszej fizycznie wykonalnej strategii doboru opłacalności wydobycia w warunkach niepewności cen. W proponowanym systemie do

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The valuation of multidimensional American real options using the LSM simulation method

Cited by 106 publications

References 42 publications

Relaxations of Approximate Linear Programs for the Real Option Management of Commodity Storage

Relaxations of Approximate Linear Programs for the Real Option Management of Commodity Storage

A Tool to Manage Tasks of R&D Projects

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