eThesis - Kauppakorkeakoulun sähköiset gradut

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In this study we examine different numerical solution methods that can be used to solve differential equations arising from real options analysis and present two case studies that are solved numerically. First we examine commonly used methods in valuating investments with uncertainty. The most suitable method for long-term investments with high uncertainty is the real options analysis, which uses an underlying stochastic variable in valuation.

We introduce the framework for real options and examine the differences between infinite and finite time horizon real options. Short literature review reveals that there are several problems within real options theory for which a closed-form solution does not exist and hence numerical methods should be applied. We introduce three numerical methods commonly used in real options analysis: the Monte Carlo (MC) method, binomial lattice (BL) method, and finite difference method (FDM) with explicit and implicit solution scheme. Then we present two case studies, investment option that is used to benchmark numerical solutions, and abandonment option which cannot be solved analytically.

Comparison of numerical methods reveals that even though the MC method is stable, it is inaccurate and slow in comparison to other methods. The implicit FDM is superior to the explicit method as the latter is very unstable to grid parameters. Even though the BL method outperforms other methods with respect to simulation time and accuracy, the implicit FDM is the most advantageous method as it provides always convergent solution in the whole time domain at once. Finally, we apply BL method and FDM to solve the abandonment option case the option to abandon can be exercised at any point of time during the project.

On the grounds of the study, we suggest using the implicit FDM in further real option applications due to the output, convergence and stability properties, and the flexibility over the boundary conditions. We recommend investigating additional case studies with the presented numerical methods along with their extensions, as well as completely new approaches such as the finite element method.