Real options : duopoly dynamics with more than one source of randomness.
The valuation of real options has been of interest for some time. Recently, the model has been revised to include more than one source of randomness, e.g. Paxson and Pinto (2005). In this dissertation, we present a model with more than one diffusion process to analyze strategic interaction in a duopolistic framework. We consider a complete market where the profit per unit and the number of units sold are assumed to evolve according to distinct, but possibly correlated, geometric Brownian motions, and aim to extend Paxson and Pinto’s research to a wider context by adjusting the model to include the effect of the covariance between the stochastic factors. In particular, we present results in both the pre-emptive and non pre-emptive equilibrium case pertaining to the follower’s and leader’s value function. We also investigate the consequences for the model in relation to traditional net present value theory, and include an analysis of the comparative static relationships that exist between the parameters. We then conclude with a chapter that extends our two-variable model to three sources of randomness - first by allowing the investment cost to be modelled as a random once-off payment, and then by considering it to be a stochastically variable ongoing cost. Keywords Real options, complete markets, more than one stochastic process, competitive games, duopoly.