Real options : duopoly dynamics with more than one source of randomness.
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Date
2009
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Abstract
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.
Description
Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2009.
Keywords
Real options (Finance), Theses--Mathematics.