Embedding Decision Tree with Binomial Lattices to Solve Real Options Problems in Incomplete Market

Li Linli

Abstract

Decision tree analysis and option pricing techniques have complementary strengths and weaknesses to solve real options problems. Decision tree analysis is more intuitive and subject to less restrictive assumptions; however, the computation is intensive and risk-adjusted discount rate is difficult to find. On the other hand, option pricing techniques are computationally efficient. It uses risk neutral probability to account for risks; thus avoids estimating project-specific discount rates. However, traditional option pricing techniques cannot be directly applied in incomplete market, because it is impossible to construct replicating portfolio with identical payoffs as the real asset in all states of nature.

This thesis reviews real options valuation methods across various fields of study, and from which proposes a three-phase integrated approach. Phase 1 is framing & formulation, where project is divided into lattice phase and non-lattice phase. In the generic decision tree, non-lattice phase is represented by a combination of decision nodes and chance nodes; whereas the whole lattice phase is represented by a special node called “lattice node”. Phase 2 is to solve lattice node; some modifications to previous real option valuation methods are made, so that private risks can be incorporated in lattice phase. With the output of lattice node, overall decision tree can be easily solved in Phase 3.

Finally, to illustrate the proposed methodology, a case study on oil exploration and production is discussed. The results show that proposed approach can solve real options problems in incomplete market, model all types of real options appropriately, and achieve computational efficiency. In addition, the modularity of lattice node makes it possible to substitute other real option valuation methods to solve it, and reasonably decompose the project into two sub-problems. Furthermore, proposed methodology can be readily implemented using currently available decision analysis software, such as DPL.