This thesis presents several real option models to address investment-timing decision problems in various scenarios. The traditional NPV method only considers the difference between the future cash flow and the cost of a project, but ignores the future risk of the project. The concept of an American call option is used to improve the NPV method, and it is re-named as a real option. Classical real option problems are considered in a framework where the instantaneous volatility of the project value is given by a constant. Ting et al. carried out an asymptotic approach in a single firm model by letting the volatility parameter be a stochastic process. In particular, they assumed that the project value is given by the Heston model. In this thesis, the project value is determined by Heston model, and a similar asymptotic approach is applied to classical real option models with two firms as well as another real option model in which suspending the project is allowed. Several numerical examples and comparisons are provided to show how the additional uncertainty in the volatility affects the investment thresholds and the payoffs of firms in different scenarios.
In addition, real option models with two firms can also be considered in competitive situations. Such models are also regarded as strategic real option games. This thesis presents several types of strategic real option games. In a standard framework of strategic real option games, 2-player non-cooperative games under complete information are considered, and both pure strategy equilibria and mixed strategy equilibria are obtained. If both firms agree to cooperate with each other in a game, then the game is called a 2-player cooperative game and the bargaining solution can be obtained. Lastly, we study mixed strategy equilibria of a strategic real option game with asymmetric information. Our result shows that the firm with complete information will always take the advantage.
